Consider the following Accumulator class with a missing method
'prodA(int m)'
which is supposed to return the product of all elements of the array A
if such product is less than or equal to m and return m otherwise.
For example if A is the array {2,4,3} then
prodA(2) will return 2
prodA(0) will return 0
prodA(50) will return 24
(Hint: the length of an array A is given by A.length)
Insert the code for the body of the method prodA where
marked.
public class Accumulator {
private int[] A;
public Accumulator(int[] X) {
A= new int[X.length];
for (int i=0; i<X.length; i++)
A[i] = X[i];
}
public int prodA(int m) {
// insert your code here
}
}
You simply multiply the elements of the array A, then check if the sum is smaller than m, if so, you return it, otherwise you return m.
I won't show you a full solution, but computing the multiplication of the elements is extremely easy, you should have an int res = 1; and then multiply it by each element from the array and reassign the result to res (using a loop).
int prod=1;
for(int i:A){
prod=prod*i;
}
if(prod<m)
return prod;
else
return m;
int product=1;
for(int num:A) {
product=product*num;
}
return (product<=m)?product:m;
There are not many things to consider here, but three come to my mind:
How to treat the empty array? I assume that the result should be 1 in this case, as it lends itself by being the neutral element of multiplication
How large is the array? Might it be worth to implement an "early return"? That is, when the array contains 1000000 elements, and you notice that the result of multiplying the first 2 elements already is greater than the limit, you could already return this limit, and not waste time by performing the remaining 999998 multiplications (assuming that the array does not contains zeros!)
How to structure the methods? I think that separating the computation of the product and the computation of the actual result, like return Math.min(limit, product(A)) with an appropriate product method that only has the single responsibility of computing a product of the elements of an array. However, this makes the "early return" impossible.
The "early return" could do something like this:
public int prodA(int m)
{
int product = 1;
for (int i = 0; i < A.length; i++)
{
product *= A[i];
if (product >= m)
{
return m;
}
}
return product;
}
while from a standpoint of reusability, something like this might be nicer:
public int prodA(int m)
{
return Math.min(m, product(A));
}
private static int product(int array[] )
{
int product = 1;
for (int i = 1; i < array.length; i++)
{
product *= array[i];
}
return product;
}
public int prodA(int m) {
int p=1;
for(int i=0;i<A.lenght.i++){
p=p*A[i];
}
if(p<=m)
return p;
else
return m;
}
Related
I have the task of determining whether each value from 1, 2, 3... n is in an unordered int array. I'm not sure if this is the most efficient way to go about this, but I created an int[] called range that just has all the numbers from 1-n in order at range[i] (range[0]=1, range[1]=2, ect). Then I tried to use the containsAll method to check if my array of given numbers contains all of the numbers in the range array. However, when I test this it returns false. What's wrong with my code, and what would be a more efficient way to solve this problem?
public static boolean hasRange(int [] givenNums, int[] range) {
boolean result = true;
int n = range.length;
for (int i = 1; i <= n; i++) {
if (Arrays.asList(givenNums).containsAll(Arrays.asList(range)) == false) {
result = false;
}
}
return result;
}
(I'm pretty sure I'm supposed to do this manually rather than using the containsAll method, so if anyone knows how to solve it that way it would be especially helpful!)
Here's where this method is implicated for anyone who is curious:
public static void checkMatrix(int[][] intMatrix) {
File numberFile = new File("valid3x3") ;
intMatrix= readMatrix(numberFile);
int nSquared = sideLength * sideLength;
int[] values = new int[nSquared];
int[] range = new int[nSquared];
int valCount = 0;
for (int i = 0; i<sideLength; i++) {
for (int j=0; j<sideLength; j++) {
values[valCount] = intMatrix[i][j];
valCount++;
}
}
for (int i=0; i<range.length; i++) {
range[i] = i+1;
}
Boolean valuesThere = hasRange(values, range);
valuesThere is false when printed.
First style:
if (condition == false) // Works, but at the end you have if (true == false) or such
if (!condition) // Better: not condition
// Do proper usage, if you have a parameter, do not read it in the method.
File numberFile = new File("valid3x3") ;
intMatrix = readMatrix(numberFile);
checkMatrix(intMatrix);
public static void checkMatrix(int[][] intMatrix) {
int nSquared = sideLength * sideLength;
int[] values = new int[nSquared];
Then the problem. It is laudable to see that a List or even better a Set approach is the exact abstraction level: going into detail not sensible. Here however just that is wanted.
To know whether every element in a range [1, ..., n] is present.
You could walk through the given numbers,
and for every number look whether it new in the range, mark it as no longer new,
and if n new numbers are reached: return true.
int newRangeNumbers = 0;
boolean[] foundRangeNumbers = new boolean[n]; // Automatically false
Think of better names.
You say you have a one dimensional array right?
Good. Then I think you are thinking to complicated.
I try to explain you another way to check if all numbers in an array are in number order.
For instance you have the array with following values:
int[] array = {9,4,6,7,8,1,2,3,5,8};
First of all you can order the Array simpel with
Arrays.sort(array);
After you've done this you can loop through the array and compare with the index like (in a method):
for(int i = array[0];i < array.length; i++){
if(array[i] != i) return false;
One way to solve this is to first sort the unsorted int array like you said then run a binary search to look for all values from 1...n. Sorry I'm not familiar with Java so I wrote in pseudocode. Instead of a linear search which takes O(N), binary search runs in O(logN) so is much quicker. But precondition is the array you are searching through must be sorted.
//pseudocode
int range[N] = {1...n};
cnt = 0;
while(i<-inputStream)
int unsortedArray[cnt]=i
cnt++;
sort(unsortedArray);
for(i from 0 to N-1)
{
bool res = binarySearch(unsortedArray, range[i]);
if(!res)
return false;
}
return true;
What I comprehended from your description is that the array is not necessarily sorted (in order). So, we can try using linear search method.
public static void main(String[] args){
boolean result = true;
int[] range <- Contains all the numbers
int[] givenNums <- Contains the numbers to check
for(int i=0; i<givenNums.length; i++){
if(!has(range, givenNums[i])){
result = false;
break;
}
}
System.out.println(result==false?"All elements do not exist":"All elements exist");
}
private static boolean has(int[] range, int n){
//we do linear search here
for(int i:range){
if(i == n)
return true;
}
return false;
}
This code displays whether all the elements in array givenNums exist in the array range.
Arrays.asList(givenNums).
This does not do what you think. It returns a List<int[]> with a single element, it does not box the values in givenNums to Integer and return a List<Integer>. This explains why your approach does not work.
Using Java 8 streams, assuming you don't want to permanently sort givens. Eliminate the copyOf() if you don't care:
int[] sorted = Arrays.copyOf(givens,givens.length);
Arrays.sort(sorted);
boolean result = Arrays.stream(range).allMatch(t -> Arrays.binarySearch(sorted, t) >= 0);
public static boolean hasRange(int [] givenNums, int[] range) {
Set result = new HashSet();
for (int givenNum : givenNums) {
result.add(givenNum);
}
for (int num : range) {
result.add(num);
}
return result.size() == givenNums.length;
}
The problem with your code is that the function hasRange takes two primitive int array and when you pass primitive int array to Arrays.asList it will return a List containing a single element of type int[]. In this containsAll will not check actual elements rather it will compare primitive array object references.
Solution is either you create an Integer[] and then use Arrays.asList or if that's not possible then convert the int[] to Integer[].
public static boolean hasRange(Integer[] givenNums, Integer[] range) {
return Arrays.asList(givenNums).containsAll(Arrays.asList(range));
}
Check here for sample code and output.
If you are using ApacheCommonsLang library you can directly convert int[] to Integer[].
Integer[] newRangeArray = ArrayUtils.toObject(range);
A mathematical approach: if you know the max value (or search the max value) check the sum. Because the sum for the numbers 1,2,3,...,n is always equal to n*(n+1)/2. So if the sum is equal to that expression all values are in your array and if not some values are missing. Example
public class NewClass12 {
static int [] arr = {1,5,2,3,4,7,9,8};
public static void main(String [] args){
System.out.println(containsAllValues(arr, highestValue(arr)));
}
public static boolean containsAllValues(int[] arr, int n){
int sum = 0;
for(int k = 0; k<arr.length;k++){
sum +=arr[k];
}
return (sum == n*(n+1)/2);
}
public static int highestValue(int[]arr){
int highest = arr[0];
for(int i = 0; i < arr.length; i++) {
if(highest<arr[i]) highest = arr[i];
}
return highest;
}
}
according to this your method could look like this
public static boolen hasRange (int [] arr){
int highest = arr[0];
int sum = 0;
for(int i = 0; i < arr.length; i++) {
if(highest<arr[i]) highest = arr[i];
}
for(int k = 0; k<arr.length;k++){
sum +=arr[k];
}
return (sum == highest *(highest +1)/2);
}
I am trying to solve a problem "Given an even number ( greater than 2 ), return two prime numbers whose sum will be equal to given number." and getting the above error.
Error is due to code complexity which is clear.
Please suggest any way to reduce complexity
My code is:
public ArrayList<Integer> primesum(int A) {
ArrayList<Integer> arr = new ArrayList<Integer>();
for(int i=0;i<=A;i++)
{
//All the numbers are prime
arr.add(1);
}
arr.set(0,0);//
arr.set(1,0);
for(int i=2; i<=Math.sqrt(A);i++)
{
if(arr.get(i)==1)
for(int j=2;i*j<=A;j++)
{
arr.set(i*j,0);
}
}
for(int i=0;i<=Math.sqrt(A);i++)
{
if(arr.get(i)==1)
{
boolean b = checkprime((A-i));
if(b)
{
arr.clear();
arr.add(i);
arr.add(A-i);
break;
}
}
}
return arr;
}
private static boolean checkprime(int p)
{
boolean k =true;
if(p==1)
return false;
for(int i=2;i<=Math.sqrt(p);i++)
{
if(p%i==0)
k=false;
}
return k;
}
The first step in your algorithm constructs a list of all Integers up to A, which could potentially be very large. The wrapper classes are quite inefficient, each Integer takes 16 bytes, not to mention the space the List takes. Since you know the size of this list, I'd suggest using an int array instead, with code something like:
public int[] primesum(int A) {
int[] arr = new int[A + 1];
for (int i = 0; i <= A; i++) {
// All the numbers are prime
arr[i] = 1;
}
arr[0] = 0;//
arr[1] = 0;
for (int i = 2; i <= Math.sqrt(A); i++) {
if (arr[i] == 1)
for (int j = 2; i * j <= A; j++) {
arr[i * j] = 0;
}
}
for (int i = 0; i <= Math.sqrt(A); i++) {
if (arr[i] == 1) {
boolean b = checkprime((A - i));
if (b) {
arr = new int[2];
arr[0] = i;
arr[1] = A - i;
break;
}
}
}
return arr;
}
private static boolean checkprime(int p) {
boolean k = true;
if (p == 1)
return false;
for (int i = 2; i <= Math.sqrt(p); i++) {
if (p % i == 0)
k = false;
}
return k;
}
(It's still possible to get heap errors with very large values of A, but with this version they at least happen as soon as the array is declared. To optimize further I'm afraid you'd need to rethink your algorithm to not need that array, although of course as olambert says, you could always resize your heap space to make it fit.)
You can increase the heap size of your java application which will allow you to process a larger set of data before running out of memory. You can specify the heap size for your application by using -Xms and -Xmx flags when you run your program. For example:
java -Xmx1G myProgram
would run "myProgram" with a maximum heap size of 1GB. You can get more information about jvm arguments you can specify by running:
java -X
Of course you may find that you need to use a more efficient algorithm which uses less memory if you need to solve the problem for large integers.
The following algorithm uses Sieve of Eratosthenes for generating all prime numbers lesser than the given number and then checks if their sum equals the given number and returns valid pairs. This approach spares the use of checkPrime() method altogether:
public static void main(String[] args) {
// TODO Auto-generated method stub
int n = 120;
int[] chk = new int[n];
chk[0]=1;
chk[1]=1;
for(int i=2;i<n;i++) {
if(chk[i]!=1){
chk[i]=-1;
}
if(chk[i]==1) {
continue;
} else {
for(int j=2;j*i<n;j++){
chk[j*i]=1;
}
}
}
for(int i=2;i<n/2;i++) {
if(chk[i]==-1) {
if(chk[n-i]==-1) {
System.out.println(i+"+"+(n-i));
}
}
}
}
o/p
7+113
11+109
13+107
17+103
19+101
23+97
31+89
37+83
41+79
47+73
53+67
59+61
Hope that helps. You can throw in a break to skip loop after one matching pair is found.(I haven't quite checked the corner cases so there might be some issues with the code but hope it gets the idea across)
Where ever I see Recursive Fibonacci Series everyone tell that
a[i] = fib(i - 1) + fib( i - 2)
But it can also be solved with
a[i] = fib(i - 1) + a[i-2] // If array 'a' is a global variable.
If array 'a' is a global Variable, then a[i-2] will be calculated when it is calculating for a[i-2];
It can be solved with below program in java..
public class Fibonacci {
public static int maxNumbers = 10;
public static double[] arr = new double[maxNumbers];
public static void main(String args[])
{
arr[0] = 0;
arr[1] = 1;
recur(maxNumbers - 1);
}
public static double recur(int i)
{
if( i > 1)
{
arr[i] = recur(i - 1) + arr[i - 2];
}
return arr[i];
}
}
Further more, complexity is also less when compared with original procedure. Is there any disadvantage of doing this way?
You have done the first step for Dynamic Programming calculation of Fibonacci, idea of DP is to avoid redundant calculations, and your algorithm achieve its goal.
A "classic" Bottom-Up DP Fibonacci implementation is filling the elements from lower to higher:
arr[0] = 0
arr[1] = 1
for (int i = 2; i <= n; i++)
arr[i] = arr[i-1] + arr[i-2]
(Optimization could be storing curr,last alone, and modifying them at each iteration.
Your approach is basically the same in principle.
As a side note, the DP approach to calculate Fibonacci is taking O(n) time, where there is even more efficient solution with exponential of the matrix:
1 1
1 0
The above holds because you use the fact that
1 1 F_{n+1} 1*F{n+1} + 1*F{n} F_{n+2}
* = =
1 0 F_{n} 1*F{n+1} + 0*F{n} F_{n+1}
Using exponent by squaring on the above matrix, this can be solved in O(logn).
If you just want the nth fibonacci number you could do this:
static double fib(double prev, double curr, int n) {
if(n == 0)
return curr;
return fib(curr, prev+curr, n-1);
}
Initial conditions would be prev = 0, curr = 1, n = maxNumbers. This function is tail recursive because you don't need to store the return value of the recursive call for any additional calculations. The initial stack frame gets reused (which saves memory) and once you hit your base case the value that's returned is the same value that would be returned from every other recursive call.
By using an array like you do you only recalculate one of the two branches (the longest one in each iteration) ending up with a O(n) complexity.
If you were to keep track on how large fibonacci number you have caclulated earlier you can use that and produce O(max(n-prevn, 1)). Here is an altered version of your code that fills the array from bottom to i if needed:
public class Fibonacci {
public static final int maxNumbers = 93; // fib(93) > Long.MAX_VALUE
public static long[] arr = new long[maxNumbers];
public static int calculatedN = 0;
public static long fib(int i) throws Exception
{
if( i >= maxNumbers )
throw new Exception("value out of bounds");
if( calculatedN == 0 ) {
arr[0] = 0L;
arr[1] = 1L;
calculatedN = 1;
}
if( i > calculatedN ) {
for( int x=calculatedN+1; x<=i; x++ ){
arr[x] = arr[x-2] + arr[x-1];
}
calculatedN = i;
}
return arr[i];
}
public static void main (String args[]) {
try {
System.out.println(fib(50)); // O(50-2)
System.out.println(fib(30)); // O(1)
System.out.println(fib(92)); // O(92-50)
System.out.println(fib(92)); // O(1)
} catch ( Exception e ) { e.printStackTrace(); }
}
}
I changed double to long. If you need larger fibonacci numbers than fib(92) I would change from long to Biginteger.
You can also code using two recursive function but as the same value is calculating over again and again so all You can do a dynamic programming approach where You can store the value and return it where need.Like this one in C++
#include <bits/stdc++.h>
using namespace std;
int dp[100];
int fib(int n){
if(n <= 1)
return n;
if(dp[n]!= -1)
return dp[n];
dp[n] = fib(n-1) + fib(n-2);
return dp[n];
}
int main(){
memset(dp,-1,sizeof(dp));
for(int i=1 ;i<10 ;i++)
cout<<fib(i)<<endl;
}
This is only step from non recursive version:
https://gist.github.com/vividvilla/4641152
General this partially recursive approach looks incredibly messy
I'm looking to make this much quicker. I've contemplated using a tree, but I'm not sure if that would actually help much.
I feel like the problem is for most cases you don't need to calculate all the possible maximums only a hand full, but I'm not sure where to draw the line
Thanks so much for the input,
Jasper
public class SpecialMax {
//initialized to the lowest possible value of j;
public static int jdex = 0;
//initialized to the highest possible value of i;
public static int idex;
//will hold possible maximums
public static Stack<Integer> possibleMaxs = new Stack<Integer> ();
public static int calculate (int[] a){
if (isPositive(a)){
int size = a.length;
int counterJ;
counterJ = size-1;
//find and return an ordered version of a
int [] ordered = orderBySize (a);
while (counterJ>0){
/* The first time this function is called, the Jvalue will be
* the largest it can be, similarly, the Ivalue that is found
* is the smallest
*/
int jVal = ordered[counterJ];
int iVal = test (a, jVal);
possibleMaxs.push(jVal-iVal);
counterJ--;
}
int answer = possibleMaxs.pop();
while (!possibleMaxs.empty()){
if (answer<possibleMaxs.peek()){
answer = possibleMaxs.pop();
} else {
possibleMaxs.pop();
}
}
System.out.println("The maximum of a[j]-a[i] with j>=i is: ");
return answer;
} else {
System.out.println ("Invalid input, array must be positive");
return 0; //error
}
}
//Check to make sure the array contains positive numbers
public static boolean isPositive(int[] a){
boolean positive = true;
int size = a.length;
for (int i=0; i<size; i++){
if (a[i]<0){
positive = false;
break;
}
}
return positive;
}
public static int[] orderBySize (int[] a){
//orders the array into ascending order
int [] answer = a.clone();
Arrays.sort(answer);
return answer;
}
/*Test returns an Ival to match the input Jval it accounts for
* the fact that jdex<idex.
*/
public static int test (int[] a, int jVal){
int size = a.length;
//initialized to highest possible value
int tempMin = jVal;
//keeps a running tally
Stack<Integer> mIndices = new Stack<Integer> ();
//finds the index of the jVal being tested
for (int i=0; i<size; i++) {
if (jVal==a[i]){
//finds the highest index for instance
if (jdex<i){
jdex = i;
}
}
}
//look for the optimal minimal below jdex;
for (int i=0; i<jdex; i++){
if (a[i]<tempMin){
tempMin = a[i];
mIndices.push(i);
}
}
//returns the index of the last min
if (!mIndices.empty()){
idex = mIndices.pop();
}
return tempMin;
}
}
It can be done in linear time and linear memory. The idea is: find the minimum over each suffix of the array and maximum over each prefix, then find the point where the difference between the two is the highest. You'll also have to store the index on which the maximum/minimum for each prefix is reached if you need the indices, rather than just the difference value.
Pre-sorting a[] makes the procedure complicated and impairs performance. It is not necessary, so we leave a[] unsorted.
Then (EDITED, because I had read j>=i in the body of your code, rather than i>=j in the problem description/title, which I now assume is what is required (I didn't go over your coding details); The two varieties can easily be derived from each other anyway.)
// initialize result(indices)
int iFound = 0;
int jFound = 0;
// initialize a candidate that MAY replace jFound
int jAlternative = -1; // -1 signals: no candidate currently available
// process the (remaining) elements of the array - skip #0: we've already handled that one at the initialization
for (int i=1; i<size; i++)
{
// if we have an alternative, see if that combines with the current element to a higher "max".
if ((jAlternative != -1) && (a[jAlternative]-a[i] > a[jFound]-a[iFound]))
{
jFound = jAlternative;
iFound = i;
jAlternative = -1;
}
else if (a[i] < a[iFound]) // then we can set a[iFound] lower, thereby increasing "max"
{
iFound = i;
}
else if (a[i] > a[jFound])
{ // we cannot directly replace jFound, because of the condition iFound>=jFound,
// but when we later may find a lower a[i], then it can jump in:
// set it as a waiting candidate (replacing an existing one if the new one is more promising).
if ((jAlternative = -1) || (a[i] > a[jAlternative]))
{
jAlternative = i;
}
}
}
double result = a[jFound] - a[iFound];
I'm trying to calculate the total, mean and median of an array thats populated by input received by a textfield. I've managed to work out the total and the mean, I just can't get the median to work. I think the array needs to be sorted before I can do this, but I'm not sure how to do this. Is this the problem, or is there another one that I didn't find? Here is my code:
import java.applet.Applet;
import java.awt.Graphics;
import java.awt.*;
import java.awt.event.*;
public class whileloopq extends Applet implements ActionListener
{
Label label;
TextField input;
int num;
int index;
int[] numArray = new int[20];
int sum;
int total;
double avg;
int median;
public void init ()
{
label = new Label("Enter numbers");
input = new TextField(5);
add(label);
add(input);
input.addActionListener(this);
index = 0;
}
public void actionPerformed (ActionEvent ev)
{
int num = Integer.parseInt(input.getText());
numArray[index] = num;
index++;
if (index == 20)
input.setEnabled(false);
input.setText("");
sum = 0;
for (int i = 0; i < numArray.length; i++)
{
sum += numArray[i];
}
total = sum;
avg = total / index;
median = numArray[numArray.length/2];
repaint();
}
public void paint (Graphics graf)
{
graf.drawString("Total = " + Integer.toString(total), 25, 85);
graf.drawString("Average = " + Double.toString(avg), 25, 100);
graf.drawString("Median = " + Integer.toString(median), 25, 115);
}
}
The Arrays class in Java has a static sort function, which you can invoke with Arrays.sort(numArray).
Arrays.sort(numArray);
double median;
if (numArray.length % 2 == 0)
median = ((double)numArray[numArray.length/2] + (double)numArray[numArray.length/2 - 1])/2;
else
median = (double) numArray[numArray.length/2];
Sorting the array is unnecessary and inefficient. There's a variation of the QuickSort (QuickSelect) algorithm which has an average run time of O(n); if you sort first, you're down to O(n log n). It actually finds the nth smallest item in a list; for a median, you just use n = half the list length. Let's call it quickNth (list, n).
The concept is that to find the nth smallest, choose a 'pivot' value. (Exactly how you choose it isn't critical; if you know the data will be thoroughly random, you can take the first item on the list.)
Split the original list into three smaller lists:
One with values smaller than the pivot.
One with values equal to the pivot.
And one with values greater than the pivot.
You then have three cases:
The "smaller" list has >= n items. In that case, you know that the nth smallest is in that list. Return quickNth(smaller, n).
The smaller list has < n items, but the sum of the lengths of the smaller and equal lists have >= n items. In this case, the nth is equal to any item in the "equal" list; you're done.
n is greater than the sum of the lengths of the smaller and equal lists. In that case, you can essentially skip over those two, and adjust n accordingly. Return quickNth(greater, n - length(smaller) - length(equal)).
Done.
If you're not sure that the data is thoroughly random, you need to be more sophisticated about choosing the pivot. Taking the median of the first value in the list, the last value in the list, and the one midway between the two works pretty well.
If you're very unlucky with your choice of pivots, and you always choose the smallest or highest value as your pivot, this takes O(n^2) time; that's bad. But, it's also very unlikely if you choose your pivot with a decent algorithm.
Sample code:
import java.util.*;
public class Utility {
/****************
* #param coll an ArrayList of Comparable objects
* #return the median of coll
*****************/
public static <T extends Number> double median(ArrayList<T> coll, Comparator<T> comp) {
double result;
int n = coll.size()/2;
if (coll.size() % 2 == 0) // even number of items; find the middle two and average them
result = (nth(coll, n-1, comp).doubleValue() + nth(coll, n, comp).doubleValue()) / 2.0;
else // odd number of items; return the one in the middle
result = nth(coll, n, comp).doubleValue();
return result;
} // median(coll)
/*****************
* #param coll a collection of Comparable objects
* #param n the position of the desired object, using the ordering defined on the list elements
* #return the nth smallest object
*******************/
public static <T> T nth(ArrayList<T> coll, int n, Comparator<T> comp) {
T result, pivot;
ArrayList<T> underPivot = new ArrayList<>(), overPivot = new ArrayList<>(), equalPivot = new ArrayList<>();
// choosing a pivot is a whole topic in itself.
// this implementation uses the simple strategy of grabbing something from the middle of the ArrayList.
pivot = coll.get(n/2);
// split coll into 3 lists based on comparison with the pivot
for (T obj : coll) {
int order = comp.compare(obj, pivot);
if (order < 0) // obj < pivot
underPivot.add(obj);
else if (order > 0) // obj > pivot
overPivot.add(obj);
else // obj = pivot
equalPivot.add(obj);
} // for each obj in coll
// recurse on the appropriate list
if (n < underPivot.size())
result = nth(underPivot, n, comp);
else if (n < underPivot.size() + equalPivot.size()) // equal to pivot; just return it
result = pivot;
else // everything in underPivot and equalPivot is too small. Adjust n accordingly in the recursion.
result = nth(overPivot, n - underPivot.size() - equalPivot.size(), comp);
return result;
} // nth(coll, n)
public static void main (String[] args) {
Comparator<Integer> comp = Comparator.naturalOrder();
Random rnd = new Random();
for (int size = 1; size <= 10; size++) {
ArrayList<Integer> coll = new ArrayList<>(size);
for (int i = 0; i < size; i++)
coll.add(rnd.nextInt(100));
System.out.println("Median of " + coll.toString() + " is " + median(coll, comp));
} // for a range of possible input sizes
} // main(args)
} // Utility
If you want to use any external library here is Apache commons math library using you can calculate the Median.
For more methods and use take look at the API documentation
import org.apache.commons.math3.*;
.....
......
........
//calculate median
public double getMedian(double[] values){
Median median = new Median();
double medianValue = median.evaluate(values);
return medianValue;
}
.......
For more on evaluate method AbstractUnivariateStatistic#evaluate
Update
Calculate in program
Generally, median is calculated using the following two formulas given here
If n is odd then Median (M) = value of ((n + 1)/2)th item term.
If n is even then Median (M) = value of [((n)/2)th item term + ((n)/2 + 1)th item term ]/2
In your program you have numArray, first you need to sort array using Arrays#sort
Arrays.sort(numArray);
int middle = numArray.length/2;
int medianValue = 0; //declare variable
if (numArray.length%2 == 1)
medianValue = numArray[middle];
else
medianValue = (numArray[middle-1] + numArray[middle]) / 2;
Arrays.sort(numArray);
return (numArray[size/2] + numArray[(size-1)/2]) / 2;
Arrays.sort(numArray);
int middle = ((numArray.length) / 2);
if(numArray.length % 2 == 0){
int medianA = numArray[middle];
int medianB = numArray[middle-1];
median = (medianA + medianB) / 2;
} else{
median = numArray[middle + 1];
}
EDIT: I initially had medianB setting to middle+1 in the even length arrays, this was wrong due to arrays starting count at 0. I have updated it to use middle-1 which is correct and should work properly for an array with an even length.
You can find good explanation at https://www.youtube.com/watch?time_continue=23&v=VmogG01IjYc
The idea it to use 2 Heaps viz one max heap and mean heap.
class Heap {
private Queue<Integer> low = new PriorityQueue<>(Comparator.reverseOrder());
private Queue<Integer> high = new PriorityQueue<>();
public void add(int number) {
Queue<Integer> target = low.size() <= high.size() ? low : high;
target.add(number);
balance();
}
private void balance() {
while(!low.isEmpty() && !high.isEmpty() && low.peek() > high.peek()) {
Integer lowHead= low.poll();
Integer highHead = high.poll();
low.add(highHead);
high.add(lowHead);
}
}
public double median() {
if(low.isEmpty() && high.isEmpty()) {
throw new IllegalStateException("Heap is empty");
} else {
return low.size() == high.size() ? (low.peek() + high.peek()) / 2.0 : low.peek();
}
}
}
Try sorting the array first. Then after it's sorted, if the array has an even amount of elements the mean of the middle two is the median, if it has a odd number, the middle element is the median.
Use Arrays.sort and then take the middle element (in case the number n of elements in the array is odd) or take the average of the two middle elements (in case n is even).
public static long median(long[] l)
{
Arrays.sort(l);
int middle = l.length / 2;
if (l.length % 2 == 0)
{
long left = l[middle - 1];
long right = l[middle];
return (left + right) / 2;
}
else
{
return l[middle];
}
}
Here are some examples:
#Test
public void evenTest()
{
long[] l = {
5, 6, 1, 3, 2
};
Assert.assertEquals((3 + 4) / 2, median(l));
}
#Test
public oddTest()
{
long[] l = {
5, 1, 3, 2, 4
};
Assert.assertEquals(3, median(l));
}
And in case your input is a Collection, you might use Google Guava to do something like this:
public static long median(Collection<Long> numbers)
{
return median(Longs.toArray(numbers)); // requires import com.google.common.primitives.Longs;
}
I was looking at the same statistics problems. The approach you are thinking it is good and it will work. (Answer to the sorting has been given)
But in case you are interested in algorithm performance, I think there are a couple of algorithms that have better performance than just sorting the array, one (QuickSelect) is indicated by #bruce-feist's answer and is very well explained.
[Java implementation: https://discuss.leetcode.com/topic/14611/java-quick-select ]
But there is a variation of this algorithm named median of medians, you can find a good explanation on this link:
http://austinrochford.com/posts/2013-10-28-median-of-medians.html
Java implementation of this:
- https://stackoverflow.com/a/27719796/957979
I faced a similar problem yesterday.
I wrote a method with Java generics in order to calculate the median value of every collection of Numbers; you can apply my method to collections of Doubles, Integers, Floats and returns a double. Please consider that my method creates another collection in order to not alter the original one.
I provide also a test, have fun. ;-)
public static <T extends Number & Comparable<T>> double median(Collection<T> numbers){
if(numbers.isEmpty()){
throw new IllegalArgumentException("Cannot compute median on empty collection of numbers");
}
List<T> numbersList = new ArrayList<>(numbers);
Collections.sort(numbersList);
int middle = numbersList.size()/2;
if(numbersList.size() % 2 == 0){
return 0.5 * (numbersList.get(middle).doubleValue() + numbersList.get(middle-1).doubleValue());
} else {
return numbersList.get(middle).doubleValue();
}
}
JUnit test code snippet:
/**
* Test of median method, of class Utils.
*/
#Test
public void testMedian() {
System.out.println("median");
Double expResult = 3.0;
Double result = Utils.median(Arrays.asList(3.0,2.0,1.0,9.0,13.0));
assertEquals(expResult, result);
expResult = 3.5;
result = Utils.median(Arrays.asList(3.0,2.0,1.0,9.0,4.0,13.0));
assertEquals(expResult, result);
}
Usage example (consider the class name is Utils):
List<Integer> intValues = ... //omitted init
Set<Float> floatValues = ... //omitted init
.....
double intListMedian = Utils.median(intValues);
double floatSetMedian = Utils.median(floatValues);
Note: my method works on collections, you can convert arrays of numbers to list of numbers as pointed here
And nobody paying attention when list contains only one element (list.size == 1). All your answers will crash with index out of bound exception, because integer division returns zero (1 / 2 = 0). Correct answer (in Kotlin):
MEDIAN("MEDIAN") {
override fun calculate(values: List<BigDecimal>): BigDecimal? {
if (values.size == 1) {
return values.first()
}
if (values.size > 1) {
val valuesSorted = values.sorted()
val mid = valuesSorted.size / 2
return if (valuesSorted.size % 2 != 0) {
valuesSorted[mid]
} else {
AVERAGE.calculate(listOf(valuesSorted[mid - 1], valuesSorted[mid]))
}
}
return null
}
},
As #Bruce-Feist mentions, for a large number of elements, I'd avoid any solution involving sort if performance is something you are concerned about. A different approach than those suggested in the other answers is Hoare's algorithm to find the k-th smallest of element of n items. This algorithm runs in O(n).
public int findKthSmallest(int[] array, int k)
{
if (array.length < 10)
{
Arrays.sort(array);
return array[k];
}
int start = 0;
int end = array.length - 1;
int x, temp;
int i, j;
while (start < end)
{
x = array[k];
i = start;
j = end;
do
{
while (array[i] < x)
i++;
while (x < array[j])
j--;
if (i <= j)
{
temp = array[i];
array[i] = array[j];
array[j] = temp;
i++;
j--;
}
} while (i <= j);
if (j < k)
start = i;
if (k < i)
end = j;
}
return array[k];
}
And to find the median:
public int median(int[] array)
{
int length = array.length;
if ((length & 1) == 0) // even
return (findKthSmallest(array, array.length / 2) + findKthSmallest(array, array.length / 2 + 1)) / 2;
else // odd
return findKthSmallest(array, array.length / 2);
}
public static int median(int[] arr) {
int median = 0;
java.util.Arrays.sort(arr);
for (int i=0;i<arr.length;i++) {
if (arr.length % 2 == 1) {
median = Math.round(arr[arr.length/2]);
} else {
median = (arr[(arr.length/2)] + arr[(arr.length/2)-1])/2;
}
}
return median;
}
Check out the Arrays.sort methods:
http://docs.oracle.com/javase/6/docs/api/java/util/Arrays.html
You should also really abstract finding the median into its own method, and just return the value to the calling method. This will make testing your code much easier.
public int[] data={31, 29, 47, 48, 23, 30, 21
, 40, 23, 39, 47, 47, 42, 44, 23, 26, 44, 32, 20, 40};
public double median()
{
Arrays.sort(this.data);
double result=0;
int size=this.data.length;
if(size%2==1)
{
result=data[((size-1)/2)+1];
System.out.println(" uneven size : "+result);
}
else
{
int middle_pair_first_index =(size-1)/2;
result=(data[middle_pair_first_index+1]+data[middle_pair_first_index])/2;
System.out.println(" Even size : "+result);
}
return result;
}
package arrays;
public class Arraymidleelement {
static public double middleArrayElement(int [] arr)
{
double mid;
if(arr.length%2==0)
{
mid=((double)arr[arr.length/2]+(double)arr[arr.length/2-1])/2;
return mid;
}
return arr[arr.length/2];
}
public static void main(String[] args) {
int arr[]= {1,2,3,4,5,6};
System.out.println( middleArrayElement(arr));
}
}