Improving performance of addition with very big numbers - java

I wrote this program to calculate very big numbers without using any BigInteger method. I finished it and it's working properly. I used StringBuilder and lots of parseInt call to get it done. Is there a more efficient way to do this?
By the way, this is just worksheet, ignore bad programming style, after finishing my job, I will reorganize that.
private String add (String x, String y)
{
String g = "";
StringBuilder str = new StringBuilder();
int sum;
double atHand = 0;
int dif = (int)(Math.abs(x.length()-y.length()));
if(x.length() >= y.length()) //adding zero for equalise number of digits.
{
for(int i = 0; i<dif; i++)
g += "0";
y = g+y;
}
else
{
for(int i = 0; i<dif; i++)
g += "0";
x = g + x;
}
for (int i = y.length()-1; i >=0 ; i--)
{
sum = Integer.parseInt(x.substring(i, i+1)) +Integer.parseInt(y.substring(i,i+1)) + (int)atHand;
if(sum<10)
{
str.insert(0, Integer.toString(sum));
atHand = 0;
}else
{
if(i==0)
str.insert(0, Integer.toString(sum));
else
{
atHand = sum *0.1;
sum = sum %10;
str.insert(0, Integer.toString(sum));
}
}
}
return str.toString();
}

Instead of doing it character by character, you should take k chars at a time, such that it can fit into a Java int or long. use some predetermined threshold that can hold both the "block", and depending on implementation, any overflow (i.e. such that (threshold * 2) < positive_type_limit). To make things easier, use a threshold that is a power of ten, so you can directly map it to characters in a string-representation of a base 10 number (e.g. if your overflow threshold is one million, then you can take 6 characters at a time) - this also have the added benefit that you can efficiently convert it back to a string.
Then your "blocks" are much bigger. you would then add and do overflow using these blocks and your limit/threshold (which is based on what integer primitive type you use). So basically you are operating on an array of ints.
You will still have time complexity of O(n), but it will be a smaller n (more specifically, it will be O(n/k) where k is the number of decimal digits one block represents.)
I believe that all solutions involve splitting the big number into smaller blocks and operating on them. You have already done this, just your current solution is the special case of blocksize=k=1.
To get the most of the block, you might use a power of 2 as the limit e.g. for a 32 bit unsigned integer type, you would set your threshold to 2^31 (or you could set it to 2^32, but it depends on where and how you are storing the overflow to pass over to the next element).
I would not be surprised if BigInteger uses a similar technique.

Related

Java - Trying to avoid duplicates when using random to get lines in a text file [duplicate]

In this case, the MAX is only 5, so I could check the duplicates one by one, but how could I do this in a simpler way? For example, what if the MAX has a value of 20?
Thanks.
int MAX = 5;
for (i = 1 , i <= MAX; i++)
{
drawNum[1] = (int)(Math.random()*MAX)+1;
while (drawNum[2] == drawNum[1])
{
drawNum[2] = (int)(Math.random()*MAX)+1;
}
while ((drawNum[3] == drawNum[1]) || (drawNum[3] == drawNum[2]) )
{
drawNum[3] = (int)(Math.random()*MAX)+1;
}
while ((drawNum[4] == drawNum[1]) || (drawNum[4] == drawNum[2]) || (drawNum[4] == drawNum[3]) )
{
drawNum[4] = (int)(Math.random()*MAX)+1;
}
while ((drawNum[5] == drawNum[1]) ||
(drawNum[5] == drawNum[2]) ||
(drawNum[5] == drawNum[3]) ||
(drawNum[5] == drawNum[4]) )
{
drawNum[5] = (int)(Math.random()*MAX)+1;
}
}
The simplest way would be to create a list of the possible numbers (1..20 or whatever) and then shuffle them with Collections.shuffle. Then just take however many elements you want. This is great if your range is equal to the number of elements you need in the end (e.g. for shuffling a deck of cards).
That doesn't work so well if you want (say) 10 random elements in the range 1..10,000 - you'd end up doing a lot of work unnecessarily. At that point, it's probably better to keep a set of values you've generated so far, and just keep generating numbers in a loop until the next one isn't already present:
if (max < numbersNeeded)
{
throw new IllegalArgumentException("Can't ask for more numbers than are available");
}
Random rng = new Random(); // Ideally just create one instance globally
// Note: use LinkedHashSet to maintain insertion order
Set<Integer> generated = new LinkedHashSet<Integer>();
while (generated.size() < numbersNeeded)
{
Integer next = rng.nextInt(max) + 1;
// As we're adding to a set, this will automatically do a containment check
generated.add(next);
}
Be careful with the set choice though - I've very deliberately used LinkedHashSet as it maintains insertion order, which we care about here.
Yet another option is to always make progress, by reducing the range each time and compensating for existing values. So for example, suppose you wanted 3 values in the range 0..9. On the first iteration you'd generate any number in the range 0..9 - let's say you generate a 4.
On the second iteration you'd then generate a number in the range 0..8. If the generated number is less than 4, you'd keep it as is... otherwise you add one to it. That gets you a result range of 0..9 without 4. Suppose we get 7 that way.
On the third iteration you'd generate a number in the range 0..7. If the generated number is less than 4, you'd keep it as is. If it's 4 or 5, you'd add one. If it's 6 or 7, you'd add two. That way the result range is 0..9 without 4 or 6.
Here's how I'd do it
import java.util.ArrayList;
import java.util.Random;
public class Test {
public static void main(String[] args) {
int size = 20;
ArrayList<Integer> list = new ArrayList<Integer>(size);
for(int i = 1; i <= size; i++) {
list.add(i);
}
Random rand = new Random();
while(list.size() > 0) {
int index = rand.nextInt(list.size());
System.out.println("Selected: "+list.remove(index));
}
}
}
As the esteemed Mr Skeet has pointed out:
If n is the number of randomly selected numbers you wish to choose and N is the total sample space of numbers available for selection:
If n << N, you should just store the numbers that you have picked and check a list to see if the number selected is in it.
If n ~= N, you should probably use my method, by populating a list containing the entire sample space and then removing numbers from it as you select them.
//random numbers are 0,1,2,3
ArrayList<Integer> numbers = new ArrayList<Integer>();
Random randomGenerator = new Random();
while (numbers.size() < 4) {
int random = randomGenerator .nextInt(4);
if (!numbers.contains(random)) {
numbers.add(random);
}
}
This would be a lot simpler in java-8:
Stream.generate(new Random()::ints)
.flatMap(IntStream::boxed)
.distinct()
.limit(16) // whatever limit you might need
.toArray(Integer[]::new);
There is another way of doing "random" ordered numbers with LFSR, take a look at:
http://en.wikipedia.org/wiki/Linear_feedback_shift_register
with this technique you can achieve the ordered random number by index and making sure the values are not duplicated.
But these are not TRUE random numbers because the random generation is deterministic.
But depending your case you can use this technique reducing the amount of processing on random number generation when using shuffling.
Here a LFSR algorithm in java, (I took it somewhere I don't remeber):
public final class LFSR {
private static final int M = 15;
// hard-coded for 15-bits
private static final int[] TAPS = {14, 15};
private final boolean[] bits = new boolean[M + 1];
public LFSR() {
this((int)System.currentTimeMillis());
}
public LFSR(int seed) {
for(int i = 0; i < M; i++) {
bits[i] = (((1 << i) & seed) >>> i) == 1;
}
}
/* generate a random int uniformly on the interval [-2^31 + 1, 2^31 - 1] */
public short nextShort() {
//printBits();
// calculate the integer value from the registers
short next = 0;
for(int i = 0; i < M; i++) {
next |= (bits[i] ? 1 : 0) << i;
}
// allow for zero without allowing for -2^31
if (next < 0) next++;
// calculate the last register from all the preceding
bits[M] = false;
for(int i = 0; i < TAPS.length; i++) {
bits[M] ^= bits[M - TAPS[i]];
}
// shift all the registers
for(int i = 0; i < M; i++) {
bits[i] = bits[i + 1];
}
return next;
}
/** returns random double uniformly over [0, 1) */
public double nextDouble() {
return ((nextShort() / (Integer.MAX_VALUE + 1.0)) + 1.0) / 2.0;
}
/** returns random boolean */
public boolean nextBoolean() {
return nextShort() >= 0;
}
public void printBits() {
System.out.print(bits[M] ? 1 : 0);
System.out.print(" -> ");
for(int i = M - 1; i >= 0; i--) {
System.out.print(bits[i] ? 1 : 0);
}
System.out.println();
}
public static void main(String[] args) {
LFSR rng = new LFSR();
Vector<Short> vec = new Vector<Short>();
for(int i = 0; i <= 32766; i++) {
short next = rng.nextShort();
// just testing/asserting to make
// sure the number doesn't repeat on a given list
if (vec.contains(next))
throw new RuntimeException("Index repeat: " + i);
vec.add(next);
System.out.println(next);
}
}
}
Another approach which allows you to specify how many numbers you want with size and the min and max values of the returned numbers
public static int getRandomInt(int min, int max) {
Random random = new Random();
return random.nextInt((max - min) + 1) + min;
}
public static ArrayList<Integer> getRandomNonRepeatingIntegers(int size, int min,
int max) {
ArrayList<Integer> numbers = new ArrayList<Integer>();
while (numbers.size() < size) {
int random = getRandomInt(min, max);
if (!numbers.contains(random)) {
numbers.add(random);
}
}
return numbers;
}
To use it returning 7 numbers between 0 and 25.
ArrayList<Integer> list = getRandomNonRepeatingIntegers(7, 0, 25);
for (int i = 0; i < list.size(); i++) {
System.out.println("" + list.get(i));
}
The most efficient, basic way to have non-repeating random numbers is explained by this pseudo-code. There is no need to have nested loops or hashed lookups:
// get 5 unique random numbers, possible values 0 - 19
// (assume desired number of selections < number of choices)
const int POOL_SIZE = 20;
const int VAL_COUNT = 5;
declare Array mapping[POOL_SIZE];
declare Array results[VAL_COUNT];
declare i int;
declare r int;
declare max_rand int;
// create mapping array
for (i=0; i<POOL_SIZE; i++) {
mapping[i] = i;
}
max_rand = POOL_SIZE-1; // start loop searching for maximum value (19)
for (i=0; i<VAL_COUNT; i++) {
r = Random(0, max_rand); // get random number
results[i] = mapping[r]; // grab number from map array
mapping[r] = max_rand; // place item past range at selected location
max_rand = max_rand - 1; // reduce random scope by 1
}
Suppose first iteration generated random number 3 to start (from 0 - 19). This would make results[0] = mapping[3], i.e., the value 3. We'd then assign mapping[3] to 19.
In the next iteration, the random number was 5 (from 0 - 18). This would make results[1] = mapping[5], i.e., the value 5. We'd then assign mapping[5] to 18.
Now suppose the next iteration chose 3 again (from 0 - 17). results[2] would be assigned the value of mapping[3], but now, this value is not 3, but 19.
This same protection persists for all numbers, even if you got the same number 5 times in a row. E.g., if the random number generator gave you 0 five times in a row, the results would be: [ 0, 19, 18, 17, 16 ].
You would never get the same number twice.
Generating all the indices of a sequence is generally a bad idea, as it might take a lot of time, especially if the ratio of the numbers to be chosen to MAX is low (the complexity becomes dominated by O(MAX)). This gets worse if the ratio of the numbers to be chosen to MAX approaches one, as then removing the chosen indices from the sequence of all also becomes expensive (we approach O(MAX^2/2)). But for small numbers, this generally works well and is not particularly error-prone.
Filtering the generated indices by using a collection is also a bad idea, as some time is spent in inserting the indices into the sequence, and progress is not guaranteed as the same random number can be drawn several times (but for large enough MAX it is unlikely). This could be close to complexity O(k n log^2(n)/2), ignoring the duplicates and assuming the collection uses a tree for efficient lookup (but with a significant constant cost k of allocating the tree nodes and possibly having to rebalance).
Another option is to generate the random values uniquely from the beginning, guaranteeing progress is being made. That means in the first round, a random index in [0, MAX] is generated:
items i0 i1 i2 i3 i4 i5 i6 (total 7 items)
idx 0 ^^ (index 2)
In the second round, only [0, MAX - 1] is generated (as one item was already selected):
items i0 i1 i3 i4 i5 i6 (total 6 items)
idx 1 ^^ (index 2 out of these 6, but 3 out of the original 7)
The values of the indices then need to be adjusted: if the second index falls in the second half of the sequence (after the first index), it needs to be incremented to account for the gap. We can implement this as a loop, allowing us to select arbitrary number of unique items.
For short sequences, this is quite fast O(n^2/2) algorithm:
void RandomUniqueSequence(std::vector<int> &rand_num,
const size_t n_select_num, const size_t n_item_num)
{
assert(n_select_num <= n_item_num);
rand_num.clear(); // !!
// b1: 3187.000 msec (the fastest)
// b2: 3734.000 msec
for(size_t i = 0; i < n_select_num; ++ i) {
int n = n_Rand(n_item_num - i - 1);
// get a random number
size_t n_where = i;
for(size_t j = 0; j < i; ++ j) {
if(n + j < rand_num[j]) {
n_where = j;
break;
}
}
// see where it should be inserted
rand_num.insert(rand_num.begin() + n_where, 1, n + n_where);
// insert it in the list, maintain a sorted sequence
}
// tier 1 - use comparison with offset instead of increment
}
Where n_select_num is your 5 and n_number_num is your MAX. The n_Rand(x) returns random integers in [0, x] (inclusive). This can be made a bit faster if selecting a lot of items (e.g. not 5 but 500) by using binary search to find the insertion point. To do that, we need to make sure that we meet the requirements.
We will do binary search with the comparison n + j < rand_num[j] which is the same as n < rand_num[j] - j. We need to show that rand_num[j] - j is still a sorted sequence for a sorted sequence rand_num[j]. This is fortunately easily shown, as the lowest distance between two elements of the original rand_num is one (the generated numbers are unique, so there is always difference of at least 1). At the same time, if we subtract the indices j from all the elements rand_num[j], the differences in index are exactly 1. So in the "worst" case, we get a constant sequence - but never decreasing. The binary search can therefore be used, yielding O(n log(n)) algorithm:
struct TNeedle { // in the comparison operator we need to make clear which argument is the needle and which is already in the list; we do that using the type system.
int n;
TNeedle(int _n)
:n(_n)
{}
};
class CCompareWithOffset { // custom comparison "n < rand_num[j] - j"
protected:
std::vector<int>::iterator m_p_begin_it;
public:
CCompareWithOffset(std::vector<int>::iterator p_begin_it)
:m_p_begin_it(p_begin_it)
{}
bool operator ()(const int &r_value, TNeedle n) const
{
size_t n_index = &r_value - &*m_p_begin_it;
// calculate index in the array
return r_value < n.n + n_index; // or r_value - n_index < n.n
}
bool operator ()(TNeedle n, const int &r_value) const
{
size_t n_index = &r_value - &*m_p_begin_it;
// calculate index in the array
return n.n + n_index < r_value; // or n.n < r_value - n_index
}
};
And finally:
void RandomUniqueSequence(std::vector<int> &rand_num,
const size_t n_select_num, const size_t n_item_num)
{
assert(n_select_num <= n_item_num);
rand_num.clear(); // !!
// b1: 3578.000 msec
// b2: 1703.000 msec (the fastest)
for(size_t i = 0; i < n_select_num; ++ i) {
int n = n_Rand(n_item_num - i - 1);
// get a random number
std::vector<int>::iterator p_where_it = std::upper_bound(rand_num.begin(), rand_num.end(),
TNeedle(n), CCompareWithOffset(rand_num.begin()));
// see where it should be inserted
rand_num.insert(p_where_it, 1, n + p_where_it - rand_num.begin());
// insert it in the list, maintain a sorted sequence
}
// tier 4 - use binary search
}
I have tested this on three benchmarks. First, 3 numbers were chosen out of 7 items, and a histogram of the items chosen was accumulated over 10,000 runs:
4265 4229 4351 4267 4267 4364 4257
This shows that each of the 7 items was chosen approximately the same number of times, and there is no apparent bias caused by the algorithm. All the sequences were also checked for correctness (uniqueness of contents).
The second benchmark involved choosing 7 numbers out of 5000 items. The time of several versions of the algorithm was accumulated over 10,000,000 runs. The results are denoted in comments in the code as b1. The simple version of the algorithm is slightly faster.
The third benchmark involved choosing 700 numbers out of 5000 items. The time of several versions of the algorithm was again accumulated, this time over 10,000 runs. The results are denoted in comments in the code as b2. The binary search version of the algorithm is now more than two times faster than the simple one.
The second method starts being faster for choosing more than cca 75 items on my machine (note that the complexity of either algorithm does not depend on the number of items, MAX).
It is worth mentioning that the above algorithms generate the random numbers in ascending order. But it would be simple to add another array to which the numbers would be saved in the order in which they were generated, and returning that instead (at negligible additional cost O(n)). It is not necessary to shuffle the output: that would be much slower.
Note that the sources are in C++, I don't have Java on my machine, but the concept should be clear.
EDIT:
For amusement, I have also implemented the approach that generates a list with all the indices 0 .. MAX, chooses them randomly and removes them from the list to guarantee uniqueness. Since I've chosen quite high MAX (5000), the performance is catastrophic:
// b1: 519515.000 msec
// b2: 20312.000 msec
std::vector<int> all_numbers(n_item_num);
std::iota(all_numbers.begin(), all_numbers.end(), 0);
// generate all the numbers
for(size_t i = 0; i < n_number_num; ++ i) {
assert(all_numbers.size() == n_item_num - i);
int n = n_Rand(n_item_num - i - 1);
// get a random number
rand_num.push_back(all_numbers[n]); // put it in the output list
all_numbers.erase(all_numbers.begin() + n); // erase it from the input
}
// generate random numbers
I have also implemented the approach with a set (a C++ collection), which actually comes second on benchmark b2, being only about 50% slower than the approach with the binary search. That is understandable, as the set uses a binary tree, where the insertion cost is similar to binary search. The only difference is the chance of getting duplicate items, which slows down the progress.
// b1: 20250.000 msec
// b2: 2296.000 msec
std::set<int> numbers;
while(numbers.size() < n_number_num)
numbers.insert(n_Rand(n_item_num - 1)); // might have duplicates here
// generate unique random numbers
rand_num.resize(numbers.size());
std::copy(numbers.begin(), numbers.end(), rand_num.begin());
// copy the numbers from a set to a vector
Full source code is here.
Your problem seems to reduce to choose k elements at random from a collection of n elements. The Collections.shuffle answer is thus correct, but as pointed out inefficient: its O(n).
Wikipedia: Fisher–Yates shuffle has a O(k) version when the array already exists. In your case, there is no array of elements and creating the array of elements could be very expensive, say if max were 10000000 instead of 20.
The shuffle algorithm involves initializing an array of size n where every element is equal to its index, picking k random numbers each number in a range with the max one less than the previous range, then swapping elements towards the end of the array.
You can do the same operation in O(k) time with a hashmap although I admit its kind of a pain. Note that this is only worthwhile if k is much less than n. (ie k ~ lg(n) or so), otherwise you should use the shuffle directly.
You will use your hashmap as an efficient representation of the backing array in the shuffle algorithm. Any element of the array that is equal to its index need not appear in the map. This allows you to represent an array of size n in constant time, there is no time spent initializing it.
Pick k random numbers: the first is in the range 0 to n-1, the second 0 to n-2, the third 0 to n-3 and so on, thru n-k.
Treat your random numbers as a set of swaps. The first random index swaps to the final position. The second random index swaps to the second to last position. However, instead of working against a backing array, work against your hashmap. Your hashmap will store every item that is out of position.
int getValue(i)
{
if (map.contains(i))
return map[i];
return i;
}
void setValue(i, val)
{
if (i == val)
map.remove(i);
else
map[i] = val;
}
int[] chooseK(int n, int k)
{
for (int i = 0; i < k; i++)
{
int randomIndex = nextRandom(0, n - i); //(n - i is exclusive)
int desiredIndex = n-i-1;
int valAtRandom = getValue(randomIndex);
int valAtDesired = getValue(desiredIndex);
setValue(desiredIndex, valAtRandom);
setValue(randomIndex, valAtDesired);
}
int[] output = new int[k];
for (int i = 0; i < k; i++)
{
output[i] = (getValue(n-i-1));
}
return output;
}
You could use one of the classes implementing the Set interface (API), and then each number you generate, use Set.add() to insert it.
If the return value is false, you know the number has already been generated before.
Instead of doing all this create a LinkedHashSet object and random numbers to it by Math.random() function .... if any duplicated entry occurs the LinkedHashSet object won't add that number to its List ... Since in this Collection Class no duplicate values are allowed .. in the end u get a list of random numbers having no duplicated values .... :D
With Java 8 upwards you can use the ints method from the IntStream interface:
Returns an effectively unlimited stream of pseudorandom int values.
Random r = new Random();
int randomNumberOrigin = 0;
int randomNumberBound = 10;
int size = 5;
int[] unique = r.ints(randomNumberOrigin, randomNumberBound)
.distinct()
.limit(size)
.toArray();
Following code create a sequence random number between [1,m] that was not generated before.
public class NewClass {
public List<Integer> keys = new ArrayList<Integer>();
public int rand(int m) {
int n = (int) (Math.random() * m + 1);
if (!keys.contains(n)) {
keys.add(n);
return n;
} else {
return rand(m);
}
}
public static void main(String[] args) {
int m = 4;
NewClass ne = new NewClass();
for (int i = 0; i < 4; i++) {
System.out.println(ne.rand(m));
}
System.out.println("list: " + ne.keys);
}
}
The most easy way is use nano DateTime as long format.
System.nanoTime();
There is algorithm of card batch: you create ordered array of numbers (the "card batch") and in every iteration you select a number at random position from it (removing the selected number from the "card batch" of course).
Here is an efficient solution for fast creation of a randomized array. After randomization you can simply pick the n-th element e of the array, increment n and return e. This solution has O(1) for getting a random number and O(n) for initialization, but as a tradeoff requires a good amount of memory if n gets large enough.
There is a more efficient and less cumbersome solution for integers than a Collections.shuffle.
The problem is the same as successively picking items from only the un-picked items in a set and setting them in order somewhere else. This is exactly like randomly dealing cards or drawing winning raffle tickets from a hat or bin.
This algorithm works for loading any array and achieving a random order at the end of the load. It also works for adding into a List collection (or any other indexed collection) and achieving a random sequence in the collection at the end of the adds.
It can be done with a single array, created once, or a numerically ordered collectio, such as a List, in place. For an array, the initial array size needs to be the exact size to contain all the intended values. If you don't know how many values might occur in advance, using a numerically orderred collection, such as an ArrayList or List, where the size is not immutable, will also work. It will work universally for an array of any size up to Integer.MAX_VALUE which is just over 2,000,000,000. List objects will have the same index limits. Your machine may run out of memory before you get to an array of that size. It may be more efficient to load an array typed to the object types and convert it to some collection, after loading the array. This is especially true if the target collection is not numerically indexed.
This algorithm, exactly as written, will create a very even distribution where there are no duplicates. One aspect that is VERY IMPORTANT is that it has to be possible for the insertion of the next item to occur up to the current size + 1. Thus, for the second item, it could be possible to store it in location 0 or location 1. For the 20th item, it could be possible to store it in any location, 0 through 19. It is just as possible the first item to stay in location 0 as it is for it to end up in any other location. It is just as possible for the next new item to go anywhere, including the next new location.
The randomness of the sequence will be as random as the randomness of the random number generator.
This algorithm can also be used to load reference types into random locations in an array. Since this works with an array, it can also work with collections. That means you don't have to create the collection and then shuffle it or have it ordered on whatever orders the objects being inserted. The collection need only have the ability to insert an item anywhere in the collection or append it.
// RandomSequence.java
import java.util.Random;
public class RandomSequence {
public static void main(String[] args) {
// create an array of the size and type for which
// you want a random sequence
int[] randomSequence = new int[20];
Random randomNumbers = new Random();
for (int i = 0; i < randomSequence.length; i++ ) {
if (i == 0) { // seed first entry in array with item 0
randomSequence[i] = 0;
} else { // for all other items...
// choose a random pointer to the segment of the
// array already containing items
int pointer = randomNumbers.nextInt(i + 1);
randomSequence[i] = randomSequence[pointer];
randomSequence[pointer] = i;
// note that if pointer & i are equal
// the new value will just go into location i and possibly stay there
// this is VERY IMPORTANT to ensure the sequence is really random
// and not biased
} // end if...else
} // end for
for (int number: randomSequence) {
System.out.printf("%2d ", number);
} // end for
} // end main
} // end class RandomSequence
It really all depends on exactly WHAT you need the random generation for, but here's my take.
First, create a standalone method for generating the random number.
Be sure to allow for limits.
public static int newRandom(int limit){
return generatedRandom.nextInt(limit); }
Next, you will want to create a very simple decision structure that compares values. This can be done in one of two ways. If you have a very limited amount of numbers to verify, a simple IF statement will suffice:
public static int testDuplicates(int int1, int int2, int int3, int int4, int int5){
boolean loopFlag = true;
while(loopFlag == true){
if(int1 == int2 || int1 == int3 || int1 == int4 || int1 == int5 || int1 == 0){
int1 = newRandom(75);
loopFlag = true; }
else{
loopFlag = false; }}
return int1; }
The above compares int1 to int2 through int5, as well as making sure that there are no zeroes in the randoms.
With these two methods in place, we can do the following:
num1 = newRandom(limit1);
num2 = newRandom(limit1);
num3 = newRandom(limit1);
num4 = newRandom(limit1);
num5 = newRandom(limit1);
Followed By:
num1 = testDuplicates(num1, num2, num3, num4, num5);
num2 = testDuplicates(num2, num1, num3, num4, num5);
num3 = testDuplicates(num3, num1, num2, num4, num5);
num4 = testDuplicates(num4, num1, num2, num3, num5);
num5 = testDuplicates(num5, num1, num2, num3, num5);
If you have a longer list to verify, then a more complex method will yield better results both in clarity of code and in processing resources.
Hope this helps. This site has helped me so much, I felt obliged to at least TRY to help as well.
I created a snippet that generates no duplicate random integer. the advantage of this snippet is that you can assign the list of an array to it and generate the random item, too.
No duplication random generator class
With Java 8 using the below code, you can create 10 distinct random Integer Numbers within a range of 1000.
Random random = new Random();
Integer[] input9 = IntStream.range(1, 10).map(i -> random.nextInt(1000)).boxed().distinct()
.toArray(Integer[]::new);
System.out.println(Arrays.toString(input9));
Modify the range to generate more numbers example : range(1,X). It will generate X distinct random numbers.
Modify the nextInt value to select the random number range : random.nextInt(Y)::random number will be generated within the range Y

Reducing the time of execution of the following code [closed]

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I am working on a problem. Out of 17 test cases 10 works fine and gives the result in less than a second but in 7 cases it is taking 2 seconds which are beyond the time limit. Following is the code
import java.util.*;
import java.io.*;
class TestClass
{
static PrintWriter wr = new PrintWriter(System.out);
public static void func1(int arr[], int n)
{
int temp = arr[0];
for (int jj = 0; jj < n; jj++)
{
if (jj == (n - 1))
arr[jj] = temp;
else
arr[jj] = arr[jj + 1];
}
}
public static void func2(int arr[], int n, int rt)
{
int count = 0;
for (int a = 0; a < n; a++)
{
for (int b = a; b < n; b++)
{
if (arr[a] > arr[b])
count++;
}
}
if (rt == (n - 1))
wr.print(count);
else
wr.print(count + " ");
}
public static void main(String args[]) throws Exception
{
BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
String str = br.readLine().trim();
StringTokenizer st = new StringTokenizer(str);
int t = Integer.parseInt(st.nextToken());
for (int i = 0; i < t; i++) //for test cases
{
str = br.readLine().trim();
st = new StringTokenizer(str);
int n = Integer.parseInt(st.nextToken());
int arr[] = new int[n];
str = br.readLine().trim();
st = new StringTokenizer(str);
for (int j = 0; j < n; j++) //to take input of array for each test case
{
arr[j] = Integer.parseInt(st.nextToken());
}
for (int rt = 0; rt < n; rt++) //for number of times circular shifting of array is done
{
func1(arr, n); //circularly shifts the array by one position
func2(arr, n, rt); //prints the number of inversion counts
}
if (i != (t - 1))
wr.println();
}
wr.close();
br.close();
}
}
Can someone suggest how to optimize the code so that it takes less time in execution.
I know BufferReader and PrintWriter takes less time as compared to Scanner and System.out.print. I was using scanner and System.out.print earlier but changed it later in hope of getting less time but it didn't help. Also I did it earlier without the use of func1 and func2 and did all the operations in main only. The time in both the cases remains the same.
I am getting the currect output in all the cases so code is correct, I just need help in optimizing it.
The website you are using acquires questions from past programming competitions. I recognize this as a familiar problem
Like most optimization questions, the preferred steps are:
Do less.
Do the same in fewer instructions.
Don't use functions.
Use faster instructions.
In your case, you have an array, and you wish to rotate it a number of times, and then to process it from the rotated position.
Rotating an array is an incredibly expensive operation, because you typically need to copy every element in the array into a new location. What is worse for you is that you are doing it the simplest way, you are rotating the array one step for every step needing rotation.
So, if you have a 100 element array that needs rotated 45 steps, you would then have (3 copies per element swap) 100 * 45 * 3 copies to perform your rotation.
In the above example, a better approach would be to figure out a routine that rotates an array 45 elements at a time. There are a number of ways to do this. The easiest is to double the RAM requirements and just have two arrays
b[x] = a[(mod(x+45), a.length)]
An even faster "do less" would be to never rotate the array, but to perform the calculation in reverse. This is conceptually the function of the desired index in the rotated array to the actual index in the pre-rotated array. This avoids all copying, and the index numbers (by virtue of being heavily manipulated in the math processing unit) will already be stored in the CPU registers, which is the fastest RAM a computer has.
Note that once you have the starting index in the original array, you can then calculate the next index without going through the calculation again.
I might have read this problem a bit wrong; because, it is not written to highlight the problem being solved. However, the core principles above apply, and it will be up to you to apply them to the exact specifics of your programming challenge.
An example of a faster rotate that does less
public static void func1(int arr[], int shift) {
int offset = shift % arr.length;
int [] rotated = new int[arr.length];
// (arr.length - 1) is the last index, walk up till we need to copy from the head of arr
for (int index = 0; index < (arr.length - 1) - offset; index++) {
rotated[index] = arr[index+offset];
}
// copy the end of the array back into the beginning
for ( int index = (arr.length - 1) - offset; index < arr.length; index++ ) {
rotated[index] = (offset - ((arr.length - 1) - index) - 1);
}
System.arraycopy(rotated, 0, arr, 0, arr.length);
}
This copies the array into its rotated position in one pass, instead of doing a pass per index to be rotated.
The first rule of optimisation (having decided it is necessary) is to use a profiler. This counts how many times methods are invoked, and measures the accumulated time within each method, and gives you a report.
It doesn't matter if a method is slow if you only run it a few times. If you run it hundreds of thousands of times, you need to either make it faster, or run it fewer times.
If you're using a mainstream IDE, you already have a profiler. Read its documentation and use it.
The other first rule of optimisation is, if there's already literature about the problem you're trying to solve, read it. Most of us might have invented bubble-sort independently. Fewer of us would have come up with QuickSort, but it's a better solution.
It looks as if you're counting inversions in the array. Your implementation is about as efficient as you can get, given that naive approach.
for(int i=0; i< array.length; i++) {
int n1 = array[i];
for(int j=i+1; j< array.length; j++) {
n2 = array[j];
if(n1 > n2) {
count++;
}
}
}
For an array of length l this will take ( l - 1) + ( l - 2 ) ... 1 -- that's a triangular number, and grows proportionally to the square of l.
So for l=1000 you're doing ~500,000 comparisons. Then since you're repeating the count for all 1000 rotations of the array, that would be 500,000,000 comparisons, which is definitely the sort of number where things start taking a noticeable amount of time.
Googling for inversion count reveals a more sophisticated approach, which is to perform a merge sort, counting inversions as they are encountered.
Otherwise, we need to look for opportunities for huge numbers of loop iterations. A loop inside a loop makes for big numbers. A loop inside a loop inside another loop makes for even bigger numbers.
You have:
for (int i = 0; i < t; i++) {
// stuff removed
for (int rt = 0; rt < n; rt++) {
// snip
func2(arr, n, rt); //prints the number of inversion counts
}
// snip
}
public static void func2(int arr[], int n, int rt) {
// snip
for (int a = 0; a < n; a++) {
for (int b = a; b < n; b++) {
// stuff
}
}
// snip
}
That's four levels of looping. Look at the input values for your slow tests, and work out what n * n * n * t is -- that an indicator of how many times it'll do the work in the inner block.
We don't know what your algorithm is supposed to achieve. But think about whether you're doing the same thing twice in any of these loops.
It looks as if func1() is supposed to rotate an array. Have a look at System.arrayCopy() for moving whole chunks of array at a time. Most CPUs will do this in a single operation.

Time complexity on iterative and recursive solution

I'm trying to solve the following problem:
I feel like I've given it a lot of thoughts and tried a lot of stuff. I manage to solve it, and produce correct values but the problem is that it isn't time efficient enough. It completes 2 out of the Kattis tests and fails on the 3 because of the time limit 1 second was exceeded. There is noway for me to see what the input was that they tested with I'm afraid.
I started out with a recursive solution and finished that. But then I realised that it wasn't time efficient enough so I instead tried to switch to an iterative solution.
I start with reading input and add those to an ArrayList. And then I call the following method with target as 1000.
public static int getCorrectWeight(List<Integer> platesArr, int target) {
/* Creates two lists, one for storing completed values after each iteration,
one for storing new values during iteration. */
List<Integer> vals = new ArrayList<>();
List<Integer> newVals = new ArrayList<>();
// Inserts 0 as a first value so that we can start the first iteration.
int best = 0;
vals.add(best);
for(int i=0; i < platesArr.size(); i++) {
for(int j=0; j < vals.size(); j++) {
int newVal = vals.get(j) + platesArr.get(i);
if (newVal <= target) {
newVals.add(newVal);
if (newVal > best) {
best = newVal;
}
} else if ((Math.abs(target-newVal) < Math.abs(target-best)) || (Math.abs(target-newVal) == Math.abs(target-best) && newVal > best)) {
best = newVal;
}
}
vals.addAll(newVals);
}
return best;
}
My question is, is there some way that I can reduce the time complexity on this one for large number of data?
The main problem is that the size of vals and newVals can grow very quickly, as each iteration can double their size. You only need to store 1000 or so values which should be manageable. You're limiting the values but because they're stored in an ArrayList, it ends up with a lot of duplicate values.
If instead, you used a HashSet, then it should help the efficiency a lot.
You only need to store a DP table of size 2001 (0 to 2000)
Let dp[i] represent if it is possible to form ikg of weights. If the weight goes over the array bounds, ignore it.
For example:
dp[0] = 1;
for (int i = 0; i < values.size(); i++){
for (int j = 2000; j >= values[i]; j--){
dp[j] = max(dp[j],dp[j-values[i]);
}
}
Here, values is where all the original weights are stored. All values of dp are to be set to 0 except for dp[0].
Then, check 1000 if it is possible to make it. If not, check 999 and 1001 and so on.
This should run in O(1000n + 2000) time, since n is at most 1000 this should run in time.
By the way, this is a modified knapsack algorithm, you might want to look up some other variants.
If you think too generally about this type of problem, you may think you have to check all possible combinations of input (each weight can be included or excluded), giving you 2n combinations to test if you have n inputs. This is, however, rather beside the point. Rather, the key here is that all weights are integers, and that the goal is 1000.
Let's examine corner cases first, because that limits the search space.
If all weights are >= 1000, pick the smallest.
If there is at least one weight < 1000, that is always better than any weight >= 2000, so you can ignore any weight >= 1000 for combination purposes.
Then, apply dynamic programming. Keep a set (you got HashSet as suggestion from other poster, but BitSet is even better since the maximum value in it is so small) of all combinations of the first k inputs, and increase k by combining all previous solutions with the k+1'th input.
When you have considered all possibilities, just search the bit vector for the best response.
static int count() {
int[] weights = new int[]{900, 500, 498, 4};
// Check for corner case to limit search later
int min = Integer.MAX_VALUE;
for (int weight : weights) min = Math.min(min, weight);
if (min >= 1000) {
return min;
}
// Get all interesting combinations
BitSet combos = new BitSet();
for (int weight : weights) {
if (weight < 1000) {
for (int t = combos.previousSetBit(2000 - weight) ; t >= 0; t = combos.previousSetBit(t-1)) {
combos.set(weight + t);
}
combos.set(weight);
}
}
// Pick best combo
for (int distance = 0; distance <= 1000; distance++) {
if (combos.get(1000 + distance)) {
return 1000 + distance;
}
if (combos.get(1000 - distance)) {
return 1000 - distance;
}
}
return 0;
}

Java random with low percentage on boolean array (quantile function)

I have a boolean array of aproximattely 10 000 elements. I would like to with rather low,set probability (cca 0,1-0,01) change the value of the elements, while knowing the indexes of changed elements. The code that comes to mind is something like:
int count = 10000;
Random r = new Random();
for (int i = 0; i < count; i++) {
double x = r.nextDouble();
if (x < rate) {
field[i]=!field[i];
do something with the index...
}
}
However, as I do this in a greater loop (inevitably), this is slow. The only other possibility that I can come up with is using quantile function (gaussian math), however I have yet to find any free to use code or library to use. Do you have any good idea how to work around this problem, or any library (standard would be best) that could be used?
Basically, you have set up a binomial model, with n == count and p == rate. The relevant number of values you should get, x, can be modeled as a normal model with center n*p == count*rate and standard deviation sigma == Math.sqrt(p*(1-p)/n) == Math.sqrt(rate * (1-rate) / count).
You can easily calculate
int x = (int) Math.round(Math.sqrt(rate * (1-rate) / count)
* r.nextGaussian() + count * rate)
Then you can generate x random numbers in the range using the following code.
Set<Integer> indices = new HashSet<Integer>();
while(indices.size() < x){
indices.add(r.nextInt(count));
}
indices will now contain the correct indices, which you can use as you wish.
You'll only have to call nextInt a little more than x times, which should be much less than the count times you had to call it before.

Creating random numbers with no duplicates

In this case, the MAX is only 5, so I could check the duplicates one by one, but how could I do this in a simpler way? For example, what if the MAX has a value of 20?
Thanks.
int MAX = 5;
for (i = 1 , i <= MAX; i++)
{
drawNum[1] = (int)(Math.random()*MAX)+1;
while (drawNum[2] == drawNum[1])
{
drawNum[2] = (int)(Math.random()*MAX)+1;
}
while ((drawNum[3] == drawNum[1]) || (drawNum[3] == drawNum[2]) )
{
drawNum[3] = (int)(Math.random()*MAX)+1;
}
while ((drawNum[4] == drawNum[1]) || (drawNum[4] == drawNum[2]) || (drawNum[4] == drawNum[3]) )
{
drawNum[4] = (int)(Math.random()*MAX)+1;
}
while ((drawNum[5] == drawNum[1]) ||
(drawNum[5] == drawNum[2]) ||
(drawNum[5] == drawNum[3]) ||
(drawNum[5] == drawNum[4]) )
{
drawNum[5] = (int)(Math.random()*MAX)+1;
}
}
The simplest way would be to create a list of the possible numbers (1..20 or whatever) and then shuffle them with Collections.shuffle. Then just take however many elements you want. This is great if your range is equal to the number of elements you need in the end (e.g. for shuffling a deck of cards).
That doesn't work so well if you want (say) 10 random elements in the range 1..10,000 - you'd end up doing a lot of work unnecessarily. At that point, it's probably better to keep a set of values you've generated so far, and just keep generating numbers in a loop until the next one isn't already present:
if (max < numbersNeeded)
{
throw new IllegalArgumentException("Can't ask for more numbers than are available");
}
Random rng = new Random(); // Ideally just create one instance globally
// Note: use LinkedHashSet to maintain insertion order
Set<Integer> generated = new LinkedHashSet<Integer>();
while (generated.size() < numbersNeeded)
{
Integer next = rng.nextInt(max) + 1;
// As we're adding to a set, this will automatically do a containment check
generated.add(next);
}
Be careful with the set choice though - I've very deliberately used LinkedHashSet as it maintains insertion order, which we care about here.
Yet another option is to always make progress, by reducing the range each time and compensating for existing values. So for example, suppose you wanted 3 values in the range 0..9. On the first iteration you'd generate any number in the range 0..9 - let's say you generate a 4.
On the second iteration you'd then generate a number in the range 0..8. If the generated number is less than 4, you'd keep it as is... otherwise you add one to it. That gets you a result range of 0..9 without 4. Suppose we get 7 that way.
On the third iteration you'd generate a number in the range 0..7. If the generated number is less than 4, you'd keep it as is. If it's 4 or 5, you'd add one. If it's 6 or 7, you'd add two. That way the result range is 0..9 without 4 or 6.
Here's how I'd do it
import java.util.ArrayList;
import java.util.Random;
public class Test {
public static void main(String[] args) {
int size = 20;
ArrayList<Integer> list = new ArrayList<Integer>(size);
for(int i = 1; i <= size; i++) {
list.add(i);
}
Random rand = new Random();
while(list.size() > 0) {
int index = rand.nextInt(list.size());
System.out.println("Selected: "+list.remove(index));
}
}
}
As the esteemed Mr Skeet has pointed out:
If n is the number of randomly selected numbers you wish to choose and N is the total sample space of numbers available for selection:
If n << N, you should just store the numbers that you have picked and check a list to see if the number selected is in it.
If n ~= N, you should probably use my method, by populating a list containing the entire sample space and then removing numbers from it as you select them.
//random numbers are 0,1,2,3
ArrayList<Integer> numbers = new ArrayList<Integer>();
Random randomGenerator = new Random();
while (numbers.size() < 4) {
int random = randomGenerator .nextInt(4);
if (!numbers.contains(random)) {
numbers.add(random);
}
}
This would be a lot simpler in java-8:
Stream.generate(new Random()::ints)
.flatMap(IntStream::boxed)
.distinct()
.limit(16) // whatever limit you might need
.toArray(Integer[]::new);
There is another way of doing "random" ordered numbers with LFSR, take a look at:
http://en.wikipedia.org/wiki/Linear_feedback_shift_register
with this technique you can achieve the ordered random number by index and making sure the values are not duplicated.
But these are not TRUE random numbers because the random generation is deterministic.
But depending your case you can use this technique reducing the amount of processing on random number generation when using shuffling.
Here a LFSR algorithm in java, (I took it somewhere I don't remeber):
public final class LFSR {
private static final int M = 15;
// hard-coded for 15-bits
private static final int[] TAPS = {14, 15};
private final boolean[] bits = new boolean[M + 1];
public LFSR() {
this((int)System.currentTimeMillis());
}
public LFSR(int seed) {
for(int i = 0; i < M; i++) {
bits[i] = (((1 << i) & seed) >>> i) == 1;
}
}
/* generate a random int uniformly on the interval [-2^31 + 1, 2^31 - 1] */
public short nextShort() {
//printBits();
// calculate the integer value from the registers
short next = 0;
for(int i = 0; i < M; i++) {
next |= (bits[i] ? 1 : 0) << i;
}
// allow for zero without allowing for -2^31
if (next < 0) next++;
// calculate the last register from all the preceding
bits[M] = false;
for(int i = 0; i < TAPS.length; i++) {
bits[M] ^= bits[M - TAPS[i]];
}
// shift all the registers
for(int i = 0; i < M; i++) {
bits[i] = bits[i + 1];
}
return next;
}
/** returns random double uniformly over [0, 1) */
public double nextDouble() {
return ((nextShort() / (Integer.MAX_VALUE + 1.0)) + 1.0) / 2.0;
}
/** returns random boolean */
public boolean nextBoolean() {
return nextShort() >= 0;
}
public void printBits() {
System.out.print(bits[M] ? 1 : 0);
System.out.print(" -> ");
for(int i = M - 1; i >= 0; i--) {
System.out.print(bits[i] ? 1 : 0);
}
System.out.println();
}
public static void main(String[] args) {
LFSR rng = new LFSR();
Vector<Short> vec = new Vector<Short>();
for(int i = 0; i <= 32766; i++) {
short next = rng.nextShort();
// just testing/asserting to make
// sure the number doesn't repeat on a given list
if (vec.contains(next))
throw new RuntimeException("Index repeat: " + i);
vec.add(next);
System.out.println(next);
}
}
}
Another approach which allows you to specify how many numbers you want with size and the min and max values of the returned numbers
public static int getRandomInt(int min, int max) {
Random random = new Random();
return random.nextInt((max - min) + 1) + min;
}
public static ArrayList<Integer> getRandomNonRepeatingIntegers(int size, int min,
int max) {
ArrayList<Integer> numbers = new ArrayList<Integer>();
while (numbers.size() < size) {
int random = getRandomInt(min, max);
if (!numbers.contains(random)) {
numbers.add(random);
}
}
return numbers;
}
To use it returning 7 numbers between 0 and 25.
ArrayList<Integer> list = getRandomNonRepeatingIntegers(7, 0, 25);
for (int i = 0; i < list.size(); i++) {
System.out.println("" + list.get(i));
}
The most efficient, basic way to have non-repeating random numbers is explained by this pseudo-code. There is no need to have nested loops or hashed lookups:
// get 5 unique random numbers, possible values 0 - 19
// (assume desired number of selections < number of choices)
const int POOL_SIZE = 20;
const int VAL_COUNT = 5;
declare Array mapping[POOL_SIZE];
declare Array results[VAL_COUNT];
declare i int;
declare r int;
declare max_rand int;
// create mapping array
for (i=0; i<POOL_SIZE; i++) {
mapping[i] = i;
}
max_rand = POOL_SIZE-1; // start loop searching for maximum value (19)
for (i=0; i<VAL_COUNT; i++) {
r = Random(0, max_rand); // get random number
results[i] = mapping[r]; // grab number from map array
mapping[r] = max_rand; // place item past range at selected location
max_rand = max_rand - 1; // reduce random scope by 1
}
Suppose first iteration generated random number 3 to start (from 0 - 19). This would make results[0] = mapping[3], i.e., the value 3. We'd then assign mapping[3] to 19.
In the next iteration, the random number was 5 (from 0 - 18). This would make results[1] = mapping[5], i.e., the value 5. We'd then assign mapping[5] to 18.
Now suppose the next iteration chose 3 again (from 0 - 17). results[2] would be assigned the value of mapping[3], but now, this value is not 3, but 19.
This same protection persists for all numbers, even if you got the same number 5 times in a row. E.g., if the random number generator gave you 0 five times in a row, the results would be: [ 0, 19, 18, 17, 16 ].
You would never get the same number twice.
Generating all the indices of a sequence is generally a bad idea, as it might take a lot of time, especially if the ratio of the numbers to be chosen to MAX is low (the complexity becomes dominated by O(MAX)). This gets worse if the ratio of the numbers to be chosen to MAX approaches one, as then removing the chosen indices from the sequence of all also becomes expensive (we approach O(MAX^2/2)). But for small numbers, this generally works well and is not particularly error-prone.
Filtering the generated indices by using a collection is also a bad idea, as some time is spent in inserting the indices into the sequence, and progress is not guaranteed as the same random number can be drawn several times (but for large enough MAX it is unlikely). This could be close to complexity O(k n log^2(n)/2), ignoring the duplicates and assuming the collection uses a tree for efficient lookup (but with a significant constant cost k of allocating the tree nodes and possibly having to rebalance).
Another option is to generate the random values uniquely from the beginning, guaranteeing progress is being made. That means in the first round, a random index in [0, MAX] is generated:
items i0 i1 i2 i3 i4 i5 i6 (total 7 items)
idx 0 ^^ (index 2)
In the second round, only [0, MAX - 1] is generated (as one item was already selected):
items i0 i1 i3 i4 i5 i6 (total 6 items)
idx 1 ^^ (index 2 out of these 6, but 3 out of the original 7)
The values of the indices then need to be adjusted: if the second index falls in the second half of the sequence (after the first index), it needs to be incremented to account for the gap. We can implement this as a loop, allowing us to select arbitrary number of unique items.
For short sequences, this is quite fast O(n^2/2) algorithm:
void RandomUniqueSequence(std::vector<int> &rand_num,
const size_t n_select_num, const size_t n_item_num)
{
assert(n_select_num <= n_item_num);
rand_num.clear(); // !!
// b1: 3187.000 msec (the fastest)
// b2: 3734.000 msec
for(size_t i = 0; i < n_select_num; ++ i) {
int n = n_Rand(n_item_num - i - 1);
// get a random number
size_t n_where = i;
for(size_t j = 0; j < i; ++ j) {
if(n + j < rand_num[j]) {
n_where = j;
break;
}
}
// see where it should be inserted
rand_num.insert(rand_num.begin() + n_where, 1, n + n_where);
// insert it in the list, maintain a sorted sequence
}
// tier 1 - use comparison with offset instead of increment
}
Where n_select_num is your 5 and n_number_num is your MAX. The n_Rand(x) returns random integers in [0, x] (inclusive). This can be made a bit faster if selecting a lot of items (e.g. not 5 but 500) by using binary search to find the insertion point. To do that, we need to make sure that we meet the requirements.
We will do binary search with the comparison n + j < rand_num[j] which is the same as n < rand_num[j] - j. We need to show that rand_num[j] - j is still a sorted sequence for a sorted sequence rand_num[j]. This is fortunately easily shown, as the lowest distance between two elements of the original rand_num is one (the generated numbers are unique, so there is always difference of at least 1). At the same time, if we subtract the indices j from all the elements rand_num[j], the differences in index are exactly 1. So in the "worst" case, we get a constant sequence - but never decreasing. The binary search can therefore be used, yielding O(n log(n)) algorithm:
struct TNeedle { // in the comparison operator we need to make clear which argument is the needle and which is already in the list; we do that using the type system.
int n;
TNeedle(int _n)
:n(_n)
{}
};
class CCompareWithOffset { // custom comparison "n < rand_num[j] - j"
protected:
std::vector<int>::iterator m_p_begin_it;
public:
CCompareWithOffset(std::vector<int>::iterator p_begin_it)
:m_p_begin_it(p_begin_it)
{}
bool operator ()(const int &r_value, TNeedle n) const
{
size_t n_index = &r_value - &*m_p_begin_it;
// calculate index in the array
return r_value < n.n + n_index; // or r_value - n_index < n.n
}
bool operator ()(TNeedle n, const int &r_value) const
{
size_t n_index = &r_value - &*m_p_begin_it;
// calculate index in the array
return n.n + n_index < r_value; // or n.n < r_value - n_index
}
};
And finally:
void RandomUniqueSequence(std::vector<int> &rand_num,
const size_t n_select_num, const size_t n_item_num)
{
assert(n_select_num <= n_item_num);
rand_num.clear(); // !!
// b1: 3578.000 msec
// b2: 1703.000 msec (the fastest)
for(size_t i = 0; i < n_select_num; ++ i) {
int n = n_Rand(n_item_num - i - 1);
// get a random number
std::vector<int>::iterator p_where_it = std::upper_bound(rand_num.begin(), rand_num.end(),
TNeedle(n), CCompareWithOffset(rand_num.begin()));
// see where it should be inserted
rand_num.insert(p_where_it, 1, n + p_where_it - rand_num.begin());
// insert it in the list, maintain a sorted sequence
}
// tier 4 - use binary search
}
I have tested this on three benchmarks. First, 3 numbers were chosen out of 7 items, and a histogram of the items chosen was accumulated over 10,000 runs:
4265 4229 4351 4267 4267 4364 4257
This shows that each of the 7 items was chosen approximately the same number of times, and there is no apparent bias caused by the algorithm. All the sequences were also checked for correctness (uniqueness of contents).
The second benchmark involved choosing 7 numbers out of 5000 items. The time of several versions of the algorithm was accumulated over 10,000,000 runs. The results are denoted in comments in the code as b1. The simple version of the algorithm is slightly faster.
The third benchmark involved choosing 700 numbers out of 5000 items. The time of several versions of the algorithm was again accumulated, this time over 10,000 runs. The results are denoted in comments in the code as b2. The binary search version of the algorithm is now more than two times faster than the simple one.
The second method starts being faster for choosing more than cca 75 items on my machine (note that the complexity of either algorithm does not depend on the number of items, MAX).
It is worth mentioning that the above algorithms generate the random numbers in ascending order. But it would be simple to add another array to which the numbers would be saved in the order in which they were generated, and returning that instead (at negligible additional cost O(n)). It is not necessary to shuffle the output: that would be much slower.
Note that the sources are in C++, I don't have Java on my machine, but the concept should be clear.
EDIT:
For amusement, I have also implemented the approach that generates a list with all the indices 0 .. MAX, chooses them randomly and removes them from the list to guarantee uniqueness. Since I've chosen quite high MAX (5000), the performance is catastrophic:
// b1: 519515.000 msec
// b2: 20312.000 msec
std::vector<int> all_numbers(n_item_num);
std::iota(all_numbers.begin(), all_numbers.end(), 0);
// generate all the numbers
for(size_t i = 0; i < n_number_num; ++ i) {
assert(all_numbers.size() == n_item_num - i);
int n = n_Rand(n_item_num - i - 1);
// get a random number
rand_num.push_back(all_numbers[n]); // put it in the output list
all_numbers.erase(all_numbers.begin() + n); // erase it from the input
}
// generate random numbers
I have also implemented the approach with a set (a C++ collection), which actually comes second on benchmark b2, being only about 50% slower than the approach with the binary search. That is understandable, as the set uses a binary tree, where the insertion cost is similar to binary search. The only difference is the chance of getting duplicate items, which slows down the progress.
// b1: 20250.000 msec
// b2: 2296.000 msec
std::set<int> numbers;
while(numbers.size() < n_number_num)
numbers.insert(n_Rand(n_item_num - 1)); // might have duplicates here
// generate unique random numbers
rand_num.resize(numbers.size());
std::copy(numbers.begin(), numbers.end(), rand_num.begin());
// copy the numbers from a set to a vector
Full source code is here.
Your problem seems to reduce to choose k elements at random from a collection of n elements. The Collections.shuffle answer is thus correct, but as pointed out inefficient: its O(n).
Wikipedia: Fisher–Yates shuffle has a O(k) version when the array already exists. In your case, there is no array of elements and creating the array of elements could be very expensive, say if max were 10000000 instead of 20.
The shuffle algorithm involves initializing an array of size n where every element is equal to its index, picking k random numbers each number in a range with the max one less than the previous range, then swapping elements towards the end of the array.
You can do the same operation in O(k) time with a hashmap although I admit its kind of a pain. Note that this is only worthwhile if k is much less than n. (ie k ~ lg(n) or so), otherwise you should use the shuffle directly.
You will use your hashmap as an efficient representation of the backing array in the shuffle algorithm. Any element of the array that is equal to its index need not appear in the map. This allows you to represent an array of size n in constant time, there is no time spent initializing it.
Pick k random numbers: the first is in the range 0 to n-1, the second 0 to n-2, the third 0 to n-3 and so on, thru n-k.
Treat your random numbers as a set of swaps. The first random index swaps to the final position. The second random index swaps to the second to last position. However, instead of working against a backing array, work against your hashmap. Your hashmap will store every item that is out of position.
int getValue(i)
{
if (map.contains(i))
return map[i];
return i;
}
void setValue(i, val)
{
if (i == val)
map.remove(i);
else
map[i] = val;
}
int[] chooseK(int n, int k)
{
for (int i = 0; i < k; i++)
{
int randomIndex = nextRandom(0, n - i); //(n - i is exclusive)
int desiredIndex = n-i-1;
int valAtRandom = getValue(randomIndex);
int valAtDesired = getValue(desiredIndex);
setValue(desiredIndex, valAtRandom);
setValue(randomIndex, valAtDesired);
}
int[] output = new int[k];
for (int i = 0; i < k; i++)
{
output[i] = (getValue(n-i-1));
}
return output;
}
You could use one of the classes implementing the Set interface (API), and then each number you generate, use Set.add() to insert it.
If the return value is false, you know the number has already been generated before.
Instead of doing all this create a LinkedHashSet object and random numbers to it by Math.random() function .... if any duplicated entry occurs the LinkedHashSet object won't add that number to its List ... Since in this Collection Class no duplicate values are allowed .. in the end u get a list of random numbers having no duplicated values .... :D
With Java 8 upwards you can use the ints method from the IntStream interface:
Returns an effectively unlimited stream of pseudorandom int values.
Random r = new Random();
int randomNumberOrigin = 0;
int randomNumberBound = 10;
int size = 5;
int[] unique = r.ints(randomNumberOrigin, randomNumberBound)
.distinct()
.limit(size)
.toArray();
Following code create a sequence random number between [1,m] that was not generated before.
public class NewClass {
public List<Integer> keys = new ArrayList<Integer>();
public int rand(int m) {
int n = (int) (Math.random() * m + 1);
if (!keys.contains(n)) {
keys.add(n);
return n;
} else {
return rand(m);
}
}
public static void main(String[] args) {
int m = 4;
NewClass ne = new NewClass();
for (int i = 0; i < 4; i++) {
System.out.println(ne.rand(m));
}
System.out.println("list: " + ne.keys);
}
}
The most easy way is use nano DateTime as long format.
System.nanoTime();
There is algorithm of card batch: you create ordered array of numbers (the "card batch") and in every iteration you select a number at random position from it (removing the selected number from the "card batch" of course).
Here is an efficient solution for fast creation of a randomized array. After randomization you can simply pick the n-th element e of the array, increment n and return e. This solution has O(1) for getting a random number and O(n) for initialization, but as a tradeoff requires a good amount of memory if n gets large enough.
There is a more efficient and less cumbersome solution for integers than a Collections.shuffle.
The problem is the same as successively picking items from only the un-picked items in a set and setting them in order somewhere else. This is exactly like randomly dealing cards or drawing winning raffle tickets from a hat or bin.
This algorithm works for loading any array and achieving a random order at the end of the load. It also works for adding into a List collection (or any other indexed collection) and achieving a random sequence in the collection at the end of the adds.
It can be done with a single array, created once, or a numerically ordered collectio, such as a List, in place. For an array, the initial array size needs to be the exact size to contain all the intended values. If you don't know how many values might occur in advance, using a numerically orderred collection, such as an ArrayList or List, where the size is not immutable, will also work. It will work universally for an array of any size up to Integer.MAX_VALUE which is just over 2,000,000,000. List objects will have the same index limits. Your machine may run out of memory before you get to an array of that size. It may be more efficient to load an array typed to the object types and convert it to some collection, after loading the array. This is especially true if the target collection is not numerically indexed.
This algorithm, exactly as written, will create a very even distribution where there are no duplicates. One aspect that is VERY IMPORTANT is that it has to be possible for the insertion of the next item to occur up to the current size + 1. Thus, for the second item, it could be possible to store it in location 0 or location 1. For the 20th item, it could be possible to store it in any location, 0 through 19. It is just as possible the first item to stay in location 0 as it is for it to end up in any other location. It is just as possible for the next new item to go anywhere, including the next new location.
The randomness of the sequence will be as random as the randomness of the random number generator.
This algorithm can also be used to load reference types into random locations in an array. Since this works with an array, it can also work with collections. That means you don't have to create the collection and then shuffle it or have it ordered on whatever orders the objects being inserted. The collection need only have the ability to insert an item anywhere in the collection or append it.
// RandomSequence.java
import java.util.Random;
public class RandomSequence {
public static void main(String[] args) {
// create an array of the size and type for which
// you want a random sequence
int[] randomSequence = new int[20];
Random randomNumbers = new Random();
for (int i = 0; i < randomSequence.length; i++ ) {
if (i == 0) { // seed first entry in array with item 0
randomSequence[i] = 0;
} else { // for all other items...
// choose a random pointer to the segment of the
// array already containing items
int pointer = randomNumbers.nextInt(i + 1);
randomSequence[i] = randomSequence[pointer];
randomSequence[pointer] = i;
// note that if pointer & i are equal
// the new value will just go into location i and possibly stay there
// this is VERY IMPORTANT to ensure the sequence is really random
// and not biased
} // end if...else
} // end for
for (int number: randomSequence) {
System.out.printf("%2d ", number);
} // end for
} // end main
} // end class RandomSequence
It really all depends on exactly WHAT you need the random generation for, but here's my take.
First, create a standalone method for generating the random number.
Be sure to allow for limits.
public static int newRandom(int limit){
return generatedRandom.nextInt(limit); }
Next, you will want to create a very simple decision structure that compares values. This can be done in one of two ways. If you have a very limited amount of numbers to verify, a simple IF statement will suffice:
public static int testDuplicates(int int1, int int2, int int3, int int4, int int5){
boolean loopFlag = true;
while(loopFlag == true){
if(int1 == int2 || int1 == int3 || int1 == int4 || int1 == int5 || int1 == 0){
int1 = newRandom(75);
loopFlag = true; }
else{
loopFlag = false; }}
return int1; }
The above compares int1 to int2 through int5, as well as making sure that there are no zeroes in the randoms.
With these two methods in place, we can do the following:
num1 = newRandom(limit1);
num2 = newRandom(limit1);
num3 = newRandom(limit1);
num4 = newRandom(limit1);
num5 = newRandom(limit1);
Followed By:
num1 = testDuplicates(num1, num2, num3, num4, num5);
num2 = testDuplicates(num2, num1, num3, num4, num5);
num3 = testDuplicates(num3, num1, num2, num4, num5);
num4 = testDuplicates(num4, num1, num2, num3, num5);
num5 = testDuplicates(num5, num1, num2, num3, num5);
If you have a longer list to verify, then a more complex method will yield better results both in clarity of code and in processing resources.
Hope this helps. This site has helped me so much, I felt obliged to at least TRY to help as well.
I created a snippet that generates no duplicate random integer. the advantage of this snippet is that you can assign the list of an array to it and generate the random item, too.
No duplication random generator class
With Java 8 using the below code, you can create 10 distinct random Integer Numbers within a range of 1000.
Random random = new Random();
Integer[] input9 = IntStream.range(1, 10).map(i -> random.nextInt(1000)).boxed().distinct()
.toArray(Integer[]::new);
System.out.println(Arrays.toString(input9));
Modify the range to generate more numbers example : range(1,X). It will generate X distinct random numbers.
Modify the nextInt value to select the random number range : random.nextInt(Y)::random number will be generated within the range Y

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