• Difficulty Level : Hard
• Last Updated : 07 May, 2021

Given an array and a value k. We have to find the maximum number of equal elements possible for the array so that we can increase the elements of the array by incrementing a total of at-most k.
Examples:

Input : array = { 2, 4, 9 }, k = 3
Output :
We are allowed to do at most three increments. We can make two elements 4 by increasing 2 by 2. Note that we can not make two elements 9 as converting 4 to 9 requires 5 increments.
Input : array = { 5, 5, 3, 1 }, k = 5
Output :
Explanation: Here 1st and 2nd elements are equal. Then we can increase 3rd element 3 upto 5. Then k becomes (k-2) = 3. Now we can’t increase 1 to 5 because k value is 3 and we need 4 for the updation. Thus equal elements possible are 3. Here we can also increase 1 to 5. Then also we have 3 because we can’t update 3 to 5.
Input : array = { 5, 5, 3, 1 }, k = 6
Output :

Naive Approach: In the naive approach we have an algorithm in O(n^2) time in which we check for each element how many other elements can be incremented so that they will become equal to them.
Efficient Approach: In this approach, first we will sort the array. Then we maintain two arrays. First is prefix sum array which stores the prefix sum of the array and another is maxx[] array which stores the maximum element found till every point, i.e., max[i] means maximum element from 1 to i. After storing these values in prefix[] array and maxx[] array, we do the binary search from 1 to n(number of elements of the array) to calculate how many elements which can be incremented to make them equal. In the binary search, we use one function in which we determine what is the number of elements can be incremented to make them equal to a single value

## C++

 `// C++ program to find maximum elements that can ` `// be made equal with k updates` `#include ` `using` `namespace` `std;`   `// Function to calculate the maximum number of` `// equal elements possible with atmost K increment` `// of values .Here we have done sliding window` `// to determine that whether there are x number of` `// elements present which on increment will become` `// equal. The loop here will run in fashion like` `// 0...x-1, 1...x, 2...x+1, ...., n-x-1...n-1` `bool` `ElementsCalculationFunc(``int` `pre[], ``int` `maxx[],` `                               ``int` `x, ``int` `k, ``int` `n)` `{` `    ``for` `(``int` `i = 0, j = x; j <= n; j++, i++) {`   `        ``// It can be explained with the reasoning` `        ``// that if for some x number of elements` `        ``// we can update the values then the` `        ``// increment to the segment (i to j having` `        ``// length -> x) so that all will be equal is` `        ``// (x*maxx[j]) this is the total sum of` `        ``// segment and (pre[j]-pre[i]) is present sum` `        ``// So difference of them should be less than k` `        ``// if yes, then that segment length(x) can be ` `        ``// possible return true` `        ``if` `(x * maxx[j] - (pre[j] - pre[i]) <= k)` `            ``return` `true``;` `    ``}` `    ``return` `false``;` `}`   `void` `MaxNumberOfElements(``int` `a[], ``int` `n, ``int` `k)` `{` `    ``// sort the array in ascending order` `    ``sort(a, a + n);` `    ``int` `pre[n + 1]; ``// prefix sum array` `    ``int` `maxx[n + 1]; ``// maximum value array`   `    ``// Initializing the prefix array` `    ``// and maximum array` `    ``for` `(``int` `i = 0; i <= n; ++i) {` `        ``pre[i] = 0;` `        ``maxx[i] = 0;` `    ``}`   `    ``for` `(``int` `i = 1; i <= n; i++) {`   `        ``// Calculating prefix sum of the array` `        ``pre[i] = pre[i - 1] + a[i - 1];`   `        ``// Calculating max value upto that position` `        ``// in the array` `        ``maxx[i] = max(maxx[i - 1], a[i - 1]);` `    ``}`   `    ``// Binary search applied for` `    ``// computation here` `    ``int` `l = 1, r = n, ans;` `    ``while` `(l < r) {` `        ``int` `mid = (l + r) / 2;`   `        ``if` `(ElementsCalculationFunc(pre, maxx,` `                              ``mid - 1, k, n)) {` `            ``ans = mid;` `            ``l = mid + 1;` `        ``}` `        ``else` `            ``r = mid - 1;` `    ``}`   `    ``// printing result` `    ``cout << ans << ``"\n"``;` `}`   `int` `main()` `{` `    ``int` `arr[] = { 2, 4, 9 };` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr);` `    ``int` `k = 3;` `    ``MaxNumberOfElements(arr, n, k);` `    ``return` `0;` `}`

## Java

 `// java program to find maximum elements that can ` `// be made equal with k updates`   `import` `java.util.Arrays;` `public` `class` `GFG {` `    `  `    ``// Function to calculate the maximum number of` `    ``// equal elements possible with atmost K increment` `    ``// of values .Here we have done sliding window` `    ``// to determine that whether there are x number of` `    ``// elements present which on increment will become` `    ``// equal. The loop here will run in fashion like` `    ``// 0...x-1, 1...x, 2...x+1, ...., n-x-1...n-1` `    ``static` `boolean` `ElementsCalculationFunc(``int` `pre[], ` `                      ``int` `maxx[], ``int` `x, ``int` `k, ``int` `n)` `    ``{` `        ``for` `(``int` `i = ``0``, j = x; j <= n; j++, i++) {` `     `  `            ``// It can be explained with the reasoning` `            ``// that if for some x number of elements` `            ``// we can update the values then the` `            ``// increment to the segment (i to j having` `            ``// length -> x) so that all will be equal is` `            ``// (x*maxx[j]) this is the total sum of` `            ``// segment and (pre[j]-pre[i]) is present sum` `            ``// So difference of them should be less than k` `            ``// if yes, then that segment length(x) can be ` `            ``// possible return true` `            ``if` `(x * maxx[j] - (pre[j] - pre[i]) <= k)` `                ``return` `true``;` `        ``}` `        ``return` `false``;` `    ``}` `     `  `    ``static` `void` `MaxNumberOfElements(``int` `a[], ``int` `n, ``int` `k)` `    ``{` `        ``// sort the array in ascending order` `        ``Arrays.sort(a);` `        ``int` `[]pre = ``new` `int``[n + ``1``]; ``// prefix sum array` `        ``int` `[]maxx = ``new` `int``[n + ``1``]; ``// maximum value array` `     `  `        ``// Initializing the prefix array` `        ``// and maximum array` `        ``for` `(``int` `i = ``0``; i <= n; ++i) {` `            ``pre[i] = ``0``;` `            ``maxx[i] = ``0``;` `        ``}` `     `  `        ``for` `(``int` `i = ``1``; i <= n; i++) {` `     `  `            ``// Calculating prefix sum of the array` `            ``pre[i] = pre[i - ``1``] + a[i - ``1``];` `     `  `            ``// Calculating max value upto that position` `            ``// in the array` `            ``maxx[i] = Math.max(maxx[i - ``1``], a[i - ``1``]);` `        ``}` `     `  `        ``// Binary search applied for` `        ``// computation here` `        ``int` `l = ``1``, r = n, ans=``0``;` `        ``while` `(l < r) {` `             `  `            ``int` `mid = (l + r) / ``2``;` `     `  `            ``if` `(ElementsCalculationFunc(pre, maxx,` `                                   ``mid - ``1``, k, n))` `            ``{` `                ``ans = mid;` `                ``l = mid + ``1``;` `            ``}` `            ``else` `                ``r = mid - ``1``;` `        ``}` `     `  `        ``// printing result` `        ``System.out.print((``int``)ans + ``"\n"``);` `    ``} ` `     `  `    ``public` `static` `void` `main(String args[]) {` `        `  `        ``int` `arr[] = { ``2``, ``4``, ``9` `};` `        ``int` `n = arr.length;` `        ``int` `k = ``3``;` `         `  `        ``MaxNumberOfElements(arr, n, k);` `         `  `    ``}` `}`   `// This code is contributed by Sam007`

## Python3

 `# Python3 program to find maximum elements ` `# that can be made equal with k updates`   `# Function to calculate the maximum number of` `# equal elements possible with atmost K increment` `# of values .Here we have done sliding window` `# to determine that whether there are x number of` `# elements present which on increment will become` `# equal. The loop here will run in fashion like` `# 0...x-1, 1...x, 2...x+1, ...., n-x-1...n-1` `def` `ElementsCalculationFunc(pre, maxx,` `                            ``x, k, n):`   `    ``i ``=` `0` `    ``j ``=` `x` `    ``while` `j <``=` `n:`   `        ``# It can be explained with the reasoning` `        ``# that if for some x number of elements` `        ``# we can update the values then the` `        ``# increment to the segment (i to j having` `        ``# length -> x) so that all will be equal is` `        ``# (x*maxx[j]) this is the total sum of` `        ``# segment and (pre[j]-pre[i]) is present sum` `        ``# So difference of them should be less than k` `        ``# if yes, then that segment length(x) can be ` `        ``# possible return true` `        ``if` `(x ``*` `maxx[j] ``-` `(pre[j] ``-` `pre[i]) <``=` `k):` `            ``return` `True`   `        ``i ``+``=` `1` `        ``j ``+``=` `1` `    `  `    ``return` `False`   `def` `MaxNumberOfElements( a, n, k):`   `    ``# sort the array in ascending order` `    ``a.sort()` `    ``pre ``=` `[``0``] ``*` `(n ``+` `1``) ``# prefix sum array` `    ``maxx ``=` `[``0``] ``*` `(n ``+` `1``) ``# maximum value array`   `    ``# Initializing the prefix array` `    ``# and maximum array` `    ``for` `i ``in` `range` `(n ``+` `1``):` `        ``pre[i] ``=` `0` `        ``maxx[i] ``=` `0`   `    ``for` `i ``in` `range``(``1``, n``+``1``):`   `        ``# Calculating prefix sum of the array` `        ``pre[i] ``=` `pre[i ``-` `1``] ``+` `a[i ``-` `1``]`   `        ``# Calculating max value upto that` `        ``# position in the array` `        ``maxx[i] ``=` `max``(maxx[i ``-` `1``], a[i ``-` `1``])`   `    ``# Binary search applied for` `    ``# computation here` `    ``l ``=` `1` `    ``r ``=` `n` `    ``while` `(l < r) :` `        ``mid ``=` `(l ``+` `r) ``/``/` `2`   `        ``if` `(ElementsCalculationFunc(pre, maxx,` `                                    ``mid ``-` `1``, k, n)):` `            ``ans ``=` `mid` `            ``l ``=` `mid ``+` `1` `        `  `        ``else``:` `            ``r ``=` `mid ``-` `1`   `    ``# printing result` `    ``print` `(ans)`   `# Driver Code` `if` `__name__ ``=``=` `"__main__"``:`   `    ``arr ``=` `[``2``, ``4``, ``9` `]` `    ``n ``=` `len``(arr)` `    ``k ``=` `3` `    ``MaxNumberOfElements(arr, n, k)`   `# This code is contributed by Ita_c`

## C#

 `// C# program to find maximum elements that can ` `// be made equal with k updates` `using` `System;`   `class` `GFG {` `    `  `    ``// Function to calculate the maximum number of` `    ``// equal elements possible with atmost K increment` `    ``// of values .Here we have done sliding window` `    ``// to determine that whether there are x number of` `    ``// elements present which on increment will become` `    ``// equal. The loop here will run in fashion like` `    ``// 0...x-1, 1...x, 2...x+1, ...., n-x-1...n-1` `    ``static` `bool` `ElementsCalculationFunc(``int` `[]pre, ` `                      ``int` `[]maxx, ``int` `x, ``int` `k, ``int` `n)` `    ``{` `        ``for` `(``int` `i = 0, j = x; j <= n; j++, i++) {` `    `  `            ``// It can be explained with the reasoning` `            ``// that if for some x number of elements` `            ``// we can update the values then the` `            ``// increment to the segment (i to j having` `            ``// length -> x) so that all will be equal is` `            ``// (x*maxx[j]) this is the total sum of` `            ``// segment and (pre[j]-pre[i]) is present sum` `            ``// So difference of them should be less than k` `            ``// if yes, then that segment length(x) can be ` `            ``// possible return true` `            ``if` `(x * maxx[j] - (pre[j] - pre[i]) <= k)` `                ``return` `true``;` `        ``}` `        ``return` `false``;` `    ``}` `    `  `    ``static` `void` `MaxNumberOfElements(``int` `[]a, ``int` `n, ``int` `k)` `    ``{` `        ``// sort the array in ascending order` `        ``Array.Sort(a);` `        ``int` `[]pre = ``new` `int``[n + 1]; ``// prefix sum array` `        ``int` `[]maxx = ``new` `int``[n + 1]; ``// maximum value array` `    `  `        ``// Initializing the prefix array` `        ``// and maximum array` `        ``for` `(``int` `i = 0; i <= n; ++i) {` `            ``pre[i] = 0;` `            ``maxx[i] = 0;` `        ``}` `    `  `        ``for` `(``int` `i = 1; i <= n; i++) {` `    `  `            ``// Calculating prefix sum of the array` `            ``pre[i] = pre[i - 1] + a[i - 1];` `    `  `            ``// Calculating max value upto that position` `            ``// in the array` `            ``maxx[i] = Math.Max(maxx[i - 1], a[i - 1]);` `        ``}` `    `  `        ``// Binary search applied for` `        ``// computation here` `        ``int` `l = 1, r = n, ans=0;` `        ``while` `(l < r) {` `            `  `            ``int` `mid = (l + r) / 2;` `    `  `            ``if` `(ElementsCalculationFunc(pre, maxx,` `                                   ``mid - 1, k, n))` `            ``{` `                ``ans = mid;` `                ``l = mid + 1;` `            ``}` `            ``else` `                ``r = mid - 1;` `        ``}` `    `  `        ``// printing result` `        ``Console.Write ((``int``)ans + ``"\n"``);` `    ``} ` `    `  `    ``// Driver code` `    ``public` `static` `void` `Main()` `    ``{` `        ``int` `[]arr = { 2, 4, 9 };` `        ``int` `n = arr.Length;` `        ``int` `k = 3;` `        `  `        ``MaxNumberOfElements(arr, n, k);` `    ``}` `}`   `// This code is contributed by Sam007`

## PHP

 ` x) so that all will be equal is` `        ``// (x*maxx[j]) this is the total sum of` `        ``// segment and (pre[j]-pre[i]) is present sum` `        ``// So difference of them should be less than k` `        ``// if yes, then that segment length(x) can be ` `        ``// possible return true` `        ``if` `(``\$x` `* ``\$maxx``[``\$j``] - (``\$pre``[``\$j``] - ``\$pre``[``\$i``]) <= ``\$k``)` `            ``return` `true;` `    ``}` `    ``return` `false;` `}`   `function`  `MaxNumberOfElements(``\$a``, ``\$n``, ``\$k``)` `{` `    ``// sort the array in ascending order` `    ``sort(``\$a``);` `    ``\$pre``[``\$n` `+ 1]=``array``(); ``// prefix sum array` `    ``\$maxx``[``\$n` `+ 1]=``array``(); ``// maximum value array`   `    ``// Initializing the prefix array` `    ``// and maximum array` `    ``for` `(``\$i` `= 0; ``\$i` `<= ``\$n``; ++``\$i``) {` `        ``\$pre``[``\$i``] = 0;` `        ``\$maxx``[``\$i``] = 0;` `    ``}`   `    ``for` `(``\$i` `= 1; ``\$i` `<= ``\$n``; ``\$i``++) {`   `        ``// Calculating prefix sum of the array` `        ``\$pre``[``\$i``] = ``\$pre``[``\$i` `- 1] + ``\$a``[``\$i` `- 1];`   `        ``// Calculating max value upto that position` `        ``// in the array` `        ``\$maxx``[``\$i``] = max(``\$maxx``[``\$i` `- 1], ``\$a``[``\$i` `- 1]);` `    ``}`   `    ``// Binary search applied for` `    ``// computation here` `    ``\$l` `= 1;` `    ``\$r` `= ``\$n``;` `    ``\$ans``;` `    ``while` `(``\$l` `< ``\$r``) {` `        ``\$mid` `= (``\$l` `+ ``\$r``) / 2;`   `        ``if` `(ElementsCalculationFunc(``\$pre``, ``\$maxx``,` `                            ``\$mid` `- 1, ``\$k``, ``\$n``)) {` `            ``\$ans` `= ``\$mid``;` `            ``\$l` `= ``\$mid` `+ 1;` `        ``}` `        ``else` `            ``\$r` `= ``\$mid` `- 1;` `    ``}`   `    ``// printing result` `    ``echo`  `\$ans` `, ``"\n"``;` `}` `//Code driven` `    ``\$arr` `= ``array``(2, 4, 9 );` `    ``\$n` `= sizeof(``\$arr``) / sizeof(``\$arr``);` `    ``\$k` `= 3;` `    ``MaxNumberOfElements(``\$arr``, ``\$n``, ``\$k``);`     `#This code is contributed by akt_mit.` `?>`

## Javascript

 ``

Output:

`2`

Time Complexity :O(nlog(n))
Space Complexity : O(n)

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