Develop Reference

Program entering in a infinite loop only with a specific value

I just started with java and while was doing an exercise about permutations (the exercise asked to create a permutation of N elements using an array a[] meeting the requirement that no a[i] is equal to i.) I've created the following code. While testing it, I realized that it entered in a infinite loop sometimes when N = 6 specifically.
Any thoughts on where is the problem?
public class GoodPerm {
public static void main(String arg[]) {
int n = Integer.parseInt(arg[0]);
int[] guests = new int[n];
for (int i = 0; i < n; i++) {
guests[i] = i;
}
for (int i = 0; i < n; i++) {
int r = i + (int) (Math.random() * (n - i));
int q = guests[r];
guests[r] = guests[i];
guests[i] = q;
if(guests[i] == i){
i --;
}
}
for(int q : guests){
System.out.println(q);
}
}
}
Maybe the code enters in a inf-loop in another values, but I didn't found any others.

This code can always enter an inf-loop. As I understand the code, you try to do some random switches to achieve your needed result. But if the last element of your array has never been switched, it won't be possible to switch it to any "later/higher" position (because there are no more). In the "last" iteration of your second for-loop (so i + 1 == n holds at the beginning) r will always evaluate to i thus no real switch happens. If the last element is still in place, you gonna repeat this forever.

Divide an Array in equal size, such that value of given function is minimum

I've came across the following problem statement.
You have a list of natural numbers of size N and you must distribute the values in two lists A and B of size N/2, so that the squared sum of A elements is the nearest possible to the multiplication of the B elements.
Example:
Consider the list 7 11 1 9 10 3 5 13 9 12.
The optimized distribution is:
List A: 5 9 9 12 13
List B: 1 3 7 10 11
which leads to the difference abs( (5+9+9+12+13)^2 - (1*3*7*10*11) ) = 6
Your program should therefore output 6, which is the minimum difference that can be achieved.
What I've tried:
I've tried Greedy approach in order to solve this problem. I took two variables sum and mul. Now I started taking elements from the given set one by one and tried adding it in both the variables and calculated current
square of sum and multiplication. Now finalize the element in one of the two sets, such that the combination gives minimum possible value.
But this approach is not working in the given example itselt. I can't figure out what approach could be used here.
I'm not asking for exact code for the solution. Any possible approach and the reason why it is working, would be fine.
EDIT:
Source: CodinGame, Community puzzle

Try out this:
import java.util.Arrays;
public class Test {
public static void main(String [] args){
int [] arr = {7, 11, 1, 9, 10, 3, 5, 13, 9, 12};
int [][] res = combinations(5, arr);
int N = Arrays.stream(arr).reduce(1, (a, b) -> a * b);
int min = Integer.MAX_VALUE;
int [] opt = new int [5];
for (int [] i : res){
int k = (int) Math.abs( Math.pow(Arrays.stream(i).sum(), 2) - N/(Arrays.stream(i).reduce(1, (a, b) -> a * b)));
if(k < min){
min = k;
opt = i;
}
}
Arrays.sort(opt);
System.out.println("minimum difference is "+ min + " with the subset containing this elements " + Arrays.toString(opt));
}
// returns all k-sized subsets of a n-sized set
public static int[][] combinations(int k, int[] set) {
int c = (int) binomial(set.length, k);
int[][] res = new int[c][Math.max(0, k)];
int[] ind = k < 0 ? null : new int[k];
for (int i = 0; i < k; ++i) {
ind[i] = i;
}
for (int i = 0; i < c; ++i) {
for (int j = 0; j < k; ++j) {
res[i][j] = set[ind[j]];
}
int x = ind.length - 1;
boolean loop;
do {
loop = false;
ind[x] = ind[x] + 1;
if (ind[x] > set.length - (k - x)) {
--x;
loop = x >= 0;
} else {
for (int x1 = x + 1; x1 < ind.length; ++x1) {
ind[x1] = ind[x1 - 1] + 1;
}
}
} while (loop);
}
return res;
}
// returns n choose k;
// there are n choose k combinations without repetition and without observance of the sequence
//
private static long binomial(int n, int k) {
if (k < 0 || k > n) return 0;
if (k > n - k) {
k = n - k;
}
long c = 1;
for (int i = 1; i < k+1; ++i) {
c = c * (n - (k - i));
c = c / i;
}
return c;
}
}
Code taken from this stackoverflow answer, also take a look at this wikipedia article about Combinations.

I am not sure if there is any exact solution in polynomial time. But you could try a simulated annealing based approach.
My approach would be:
Initialize listA and listB to a random state
With probability p run greedy step, otherwise run a random step
Keep track of the state and corresponding error (with a HashMap)
Greedy step: Find one element you can move between the list that optimizes the error.
Random Step: Pick a random element from either of these two sets and calculate the error. If the error is better, keep it. Otherwise with probability of q keep it.
At either of these two steps make sure that the new state is not already explored (or at least discourage it).
Set p to a small value (<0.1) and q could depend on the error difference.

Can this solution be optmized? [duplicate]

This question already has answers here:
Linear time algorithm for 2-SUM
(13 answers)
Closed 7 years ago.
Given an array say L= [3,4,6,7,2,1] and an Integer Z = 8, find 2 integers X,Y belonging to L such that X + Y = Z
Here is one possible solution -
public static void findIntegersSum(List<Integer> list, int z) {
for(int i = 0 ;i < list.size(); i++) {
for(int j = i+1 ; j< list.size(); j++) {
if(list.get(i) + list.get(j) == z) {
System.out.println(" X = " + list.get(i) + "\t Y=" + list.get(j));
return;
}
}
}
System.out.println(" No match found !!");
}
Question is - Can we optimize the above solution?

You can do this using an implementation of the Set data type. A Set is most often implemented as either a Hash table (HashSet in Java) or a Binary Search Tree (TreeSet in Java). Hash table implementations often use more memory, but have constant time O(1) lookups and insertions in the average case, tree implementations use linear memory, but have O(log n) lookups and insertions in the average case.
Pseudocode for using this data structure is as follows:
S = set(L) // Iterate through L and put it in a set, O(n) or O(n log n)
for element in L: // O(n)
if S.has(Z - element): // O(1) or O(log n) depending on HashSet or TreeSet
X = element
Y = Z - element
break
This solution is O(n) or O(n log n) instead of O(n^2).

This method can be solved on O(n) time if we are allowed to use additional space of O(R) where R is range of numbers. Here is the implementation
#include <stdio.h>
#define MAX 100000
void printPairs(int arr[], int arr_size, int sum)
{
int i, temp;
bool binMap[MAX] = {0}; /*initialize hash map as 0*/
for(i = 0; i < arr_size; i++)
{
temp = sum - arr[i];
if(temp >= 0 && binMap[temp] == 1)
{
printf("Pair with given sum %d is (%d, %d) \n", sum, arr[i], temp);
}
binMap[arr[i]] = 1;
}
}
/* Driver program to test above function */
int main()
{
int A[] = {1, 4, 45, 6, 10, 8};
int n = 16;
int arr_size = 6;
printPairs(A, arr_size, n);
getchar();
return 0;
}

Sort it, afterwards you only have to iterate over the array once, and check whether the matching value is in the array. This will only be more efficient for big arrays.

Following solution will be more optimized, as it is reduce List size at every steps.
static void findIntegersSum(List<Integer> list, int z) {
for(int i = 0 ;i < list.size(); i++) {
int X = list.remove(i); // Reduce your list
int Y = z - X;
if (list.contains(Y)) {
System.out.println(" X = " + X + "\t Y=" + Y);
return;
}
}
System.out.println(" No match found !!");
}

in Java, design linear algorithm that finds contiguous subsequence with highest sum

this is the question, and yes it is homework, so I don't necessarily want anyone to "do it" for me; I just need suggestions: Maximum sum: Design a linear algorithm that finds a contiguous subsequence of at most M in a sequence of N long integers that has the highest sum among all such subsequences. Implement your algorithm, and confirm that the order of growth of its running time is linear.
I think that the best way to design this program would be to use nested for loops, but because the algorithm must be linear, I cannot do that. So, I decided to approach the problem by making separate for loops (instead of nested ones).
However, I'm really not sure where to start. The values will range from -99 to 99 (as per the range of my random number generating program).
This is what I have so far (not much):
public class MaxSum {
public static void main(String[] args){
int M = Integer.parseInt(args[0]);
int N = StdIn.readInt();
long[] a = new long[N];
for (int i = 0; i < N; i++) {
a[i] = StdIn.readLong();}}}
if M were a constant, this wouldn't be so difficult. For example, if M==3:
public class MaxSum2 {
public static void main(String[] args){
int N = StdIn.readInt(); //read size for array
long[] a = new long[N]; //create array of size N
for (int i = 0; i < N; i++) { //go through values of array
a[i] = StdIn.readLong();} //read in values and assign them to
//array indices
long p = a[0] + a[1] + a[2]; //start off with first 3 indices
for (int i =0; i<N-4; i++)
{if ((a[i]+a[i+1]+a[1+2])>=p) {p=(a[i]+a[i+1]+a[1+2]);}}
//if sum of values is greater than p, p becomes that sum
for (int i =0; i<N-4; i++) //prints the subsequence that equals p
{if ((a[i]+a[i+1]+a[1+2])==p) {StdOut.println((a[i]+a[i+1]+a[1+2]));}}}}
If I must, I think MaxSum2 will be acceptable for my lab report (sadly, they don't expect much). However, I'd really like to make a general program, one that takes into consideration the possibility that, say, there could be only one positive value for the array, meaning that adding the others to it would only reduce it's value; Or if M were to equal 5, but the highest sum is a subsequence of the length 3, then I would want it to print that smaller subsequence that has the actual maximum sum.
I also think as a novice programmer, this is something I Should learn to do. Oh and although it will probably be acceptable, I don't think I'm supposed to use stacks or queues because we haven't actually covered that in class yet.

Here is my version, adapted from Petar Minchev's code and with an important addition that allows this program to work for an array of numbers with all negative values.
public class MaxSum4 {
public static void main(String[] args)
{Stopwatch banana = new Stopwatch(); //stopwatch object for runtime data.
long sum = 0;
int currentStart = 0;
long bestSum = 0;
int bestStart = 0;
int bestEnd = 0;
int M = Integer.parseInt(args[0]); // read in highest possible length of
//subsequence from command line argument.
int N = StdIn.readInt(); //read in length of array
long[] a = new long[N];
for (int i = 0; i < N; i++) {//read in values from standard input
a[i] = StdIn.readLong();}//and assign those values to array
long negBuff = a[0];
for (int i = 0; i < N; i++) { //go through values of array to find
//largest sum (bestSum)
sum += a[i]; //and updates values. note bestSum, bestStart,
// and bestEnd updated
if (sum > bestSum) { //only when sum>bestSum
bestSum = sum;
bestStart = currentStart;
bestEnd = i; }
if (sum < 0) { //in case sum<0, skip to next iteration, reseting sum=0
sum = 0; //and update currentStart
currentStart = i + 1;
continue; }
if (i - currentStart + 1 == M) { //checks if sequence length becomes equal
//to M.
do { //updates sum and currentStart
sum -= a[currentStart];
currentStart++;
} while ((sum < 0 || a[currentStart] < 0) && (currentStart <= i));
//if sum or a[currentStart]
} //is less than 0 and currentStart<=i,
} //update sum and currentStart again
if(bestSum==0){ //checks to see if bestSum==0, which is the case if
//all values are negative
for (int i=0;i<N;i++){ //goes through values of array
//to find largest value
if (a[i] >= negBuff) {negBuff=a[i];
bestSum=negBuff; bestStart=i; bestEnd=i;}}}
//updates bestSum, bestStart, and bestEnd
StdOut.print("best subsequence is from
a[" + bestStart + "] to a[" + bestEnd + "]: ");
for (int i = bestStart; i<=bestEnd; i++)
{
StdOut.print(a[i]+ " "); //prints sequence
}
StdOut.println();
StdOut.println(banana.elapsedTime());}}//prints elapsed time
also, did this little trace for Petar's code:
trace for a small array
M=2
array: length 5
index value
0 -2
1 2
2 3
3 10
4 1
for the for-loop central to program:
i = 0 sum = 0 + -2 = -2
sum>bestSum? no
sum<0? yes so sum=0, currentStart = 0(i)+1 = 1,
and continue loop with next value of i
i = 1 sum = 0 + 2 = 2
sum>bestSum? yes so bestSum=2 and bestStart=currentStart=1 and bestEnd=1=1
sum<0? no
1(i)-1(currentStart)+1==M? 1-1+1=1 so no
i = 2 sum = 2+3 = 5
sum>bestSum? yes so bestSum=5, bestStart=currentStart=1, and bestEnd=2
sum<0? no
2(i)-1(currentStart)+1=M? 2-1+1=2 so yes:
sum = sum-a[1(curentstart)] =5-2=3. currentStart++=2.
(sum<0 || a[currentStart]<0)? no
i = 3 sum=3+10=13
sum>bestSum? yes so bestSum=13 and bestStart=currentStart=2 and bestEnd=3
sum<0? no
3(i)-2(currentStart)+1=M? 3-2+1=2 so yes:
sum = sum-a[1(curentstart)] =13-3=10. currentStart++=3.
(sum<0 || a[currentStart]<0)? no
i = 4 sum=10+1=11
sum>bestSum? no
sum<0? no
4(i)-3(currentStart)+1==M? yes but changes to sum and currentStart now are
irrelevent as loop terminates
Thanks again! Just wanted to post a final answer and I was slightly proud for catching the all negative thing.

Each element is looked at most twice (one time in the outer loop, and one time in the while loop).
O(2N) = O(N)
Explanation: each element is added to the current sum. When the sum goes below zero, it is reset to zero. When we hit M length sequence, we try to remove elements from the beginning, until the sum is > 0 and there are no negative elements in the beginning of it.
By the way, when all elements are < 0 inside the array, you should take only the largest negative number. This is a special edge case which I haven't written below.
Beware of bugs in the below code - it only illustrates the idea. I haven't run it.
int sum = 0;
int currentStart = 0;
int bestSum = 0;
int bestStart = 0;
int bestEnd = 0;
for (int i = 0; i < N; i++) {
sum += a[i];
if (sum > bestSum) {
bestSum = sum;
bestStart = currentStart;
bestEnd = i;
}
if (sum < 0) {
sum = 0;
currentStart = i + 1;
continue;
}
//Our sequence length has become equal to M
if (i - currentStart + 1 == M) {
do {
sum -= a[currentStart];
currentStart++;
} while ((sum < 0 || a[currentStart] < 0) && (currentStart <= i));
}
}

I think what you are looking for is discussed in detail here
Find the subsequence with largest sum of elements in an array
I have explained 2 different solutions to resolve this problem with O(N) - linear time.

Finding the longest down sequence in a Java array

Given this array
int [] myArray = {5,-11,2,3,14,5,-14,2};
I must be able to return 3 because the longest down sequence is 14,5,-14.
What's the fastest way to do this?
PS: Down sequence is a series of non-increasing numbers.

another implementation in python:
def longest_down_sequence(seq):
max = 0
current_count = 0
last = None
for x in seq:
if x <= last: current_count += 1
else: current_count = 1
if current_count > max: max = current_count
last = x
return max

Just make one pass through the list of numbers. Pseudocode:
bestIndex = 0
bestLength = 0
curIndex = 0
curLength = 1
for index = 1..length-1
if a[index] is less than or equal to a[index-1]
curLength++
else
//restart at this index since it's a new possible starting point
curLength = 1
curIndex = index
if curLength is better than bestLength
bestIndex = curIndex
bestLength = curLength
next
Note: You can ditch any line containing bestIndex or curIndex if you don't care about knowing where that subsequence occurs, as seen in Gary's implementation.

In java:
int [] myArray = {5,-11,2,3,14,5,-14,2};
int downSequence = 1;
int longestDownSequence = 1;
for(int i = 1; i < myArray.length; i++) {
if(myArray[i] <= myArray[i-1]) downSequence++;
else {
if(downSequence > longestDownSequence)
longestDownSequence = downSequence;
downSequence = 1;
}
}
if(downSequence > longestDownSequence)
longestDownSequence = downSequence;
System.out.println(longestDownSequence);
Since you're asking for fastest or better performance, only check for the longest down sequence just before you reset the counter. Never on each iteration. However, you have to check again after the loop in case the longest sequence is at the end of the array.

Another solution in Java:
static int[] longestDownSequenceList(int[] array) {
if (array.length <= 1) {
return array;
}
int maxSize = 1;
int maxEnd = 0;
int curSize = 1;
for (int i = 1; i < array.length; i++) {
if (array[i] < array[i-1]) {
curSize++;
if (curSize > maxSize) {
maxSize = curSize;
maxEnd = i;
}
}
else {
curSize = 1;
}
}
return Arrays.copyOfRange(array, maxEnd-maxSize+1, maxEnd+1);
}

As Bill above said, this is essentially longest increasing subsequence. See the wikipedia entry for the optimal solution. This is quoted from there with small changes to work for the nondecreasing case
L = 0
for i = 1, 2, ... n:
binary search for the largest positive j ≤ L such that X[M[j]] >= X[i] (or set j = 0 if no such value exists)
P[i] = M[j]
if j == L or X[i] >= X[M[j+1]]:
M[j+1] = i
L = max(L, j+1)
See counterexample to other proposed solution in my comment above.

The fastest way might depend on the environment: computer and problemsize.
For a very large List (or array) it might be useful to parallelize the job, which could be implemented:
Split and split and split the List to simple elements.
Glue together elements which are down sequences (or non increasing) to chunks, and glue together chunks, if possible.
Search for the longest chunk.