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# Split the given array into K sub-arrays such that maximum sum of all sub arrays is minimum

• Difficulty Level : Hard
• Last Updated : 14 May, 2021

Given an Array[] of N elements and a number K. ( 1 <= K <= N ) . Split the given array into K subarrays (they must cover all the elements). The maximum subarray sum achievable out of K subarrays formed, must be minimum possible. Find that possible subarray sum.
Examples:

Input : Array[] = {1, 2, 3, 4}, K = 3
Output :
Optimal Split is {1, 2}, {3}, {4} . Maximum sum of all subarrays is 4, which is minimum possible for 3 splits.
Input : Array[] = {1, 1, 2} K = 2
Output :

Approach :

• Idea is to use Binary Search to find an optimal solution.
• For binary search minimum sum can be 1 and the maximum sum can be the sum of all the elements.
• To check if mid is maximum subarray sum possible. Maintain a count of sub – arrays, include all possible elements in sub array until their sum is less than mid. After this evaluation, if the count is less than or equal to K, then mid is achievable else not. (Since if the count is less than K, we can further divide any subarray its sum will never increase mid ).
• Find the minimum possible value of mid which satisfies the condition.

Below is the implementation of the above approach:

## C++

 `// C++ implemenattion of the above approach``#include ``using` `namespace` `std;` `// Function to check if mid can``// be maximum sub - arrays sum``bool` `check(``int` `mid, ``int` `array[], ``int` `n, ``int` `K)``{``    ``int` `count = 0;``    ``int` `sum = 0;``    ``for` `(``int` `i = 0; i < n; i++) {` `        ``// If individual element is greater``        ``// maximum possible sum``        ``if` `(array[i] > mid)``            ``return` `false``;` `        ``// Increase sum of current sub - array``        ``sum += array[i];` `        ``// If the sum is greater than``        ``// mid increase count``        ``if` `(sum > mid) {``            ``count++;``            ``sum = array[i];``        ``}``    ``}``    ``count++;` `    ``// Check condition``    ``if` `(count <= K)``        ``return` `true``;``    ``return` `false``;``}` `// Function to find maximum subarray sum``// which is minimum``int` `solve(``int` `array[], ``int` `n, ``int` `K)``{``    ``int``* max = max_element(array, array + n);``    ``int` `start = *max;``    ``int` `end = 0;` `    ``for` `(``int` `i = 0; i < n; i++) {``        ``end += array[i];``    ``}` `    ``// Answer stores possible``    ``// maximum sub array sum``    ``int` `answer = 0;``    ``while` `(start <= end) {``        ``int` `mid = (start + end) / 2;` `        ``// If mid is possible solution``        ``// Put answer = mid;``        ``if` `(check(mid, array, n, K)) {``            ``answer = mid;``            ``end = mid - 1;``        ``}``        ``else` `{``            ``start = mid + 1;``        ``}``    ``}` `    ``return` `answer;``}` `// Driver Code``int` `main()``{``    ``int` `array[] = { 1, 2, 3, 4 };``    ``int` `n = ``sizeof``(array) / ``sizeof``(array);``    ``int` `K = 3;``    ``cout << solve(array, n, K);``}`

## Java

 `// Java implemenattion of the above approach``class` `GFG {` `    ``// Function to check if mid can``    ``// be maximum sub - arrays sum``    ``static` `boolean` `check(``int` `mid, ``int` `array[], ``int` `n, ``int` `K)``    ``{` `        ``int` `count = ``0``;``        ``int` `sum = ``0``;``        ``for` `(``int` `i = ``0``; i < n; i++) {` `            ``// If individual element is greater``            ``// maximum possible sum``            ``if` `(array[i] > mid)``                ``return` `false``;` `            ``// Increase sum of current sub - array``            ``sum += array[i];` `            ``// If the sum is greater than``            ``// mid increase count``            ``if` `(sum > mid) {``                ``count++;``                ``sum = array[i];``            ``}``        ``}``        ``count++;` `        ``// Check condition``        ``if` `(count <= K)``            ``return` `true``;``        ``return` `false``;``    ``}` `    ``// Function to find maximum subarray sum``    ``// which is minimum``    ``static` `int` `solve(``int` `array[], ``int` `n, ``int` `K)``    ``{``        ``int` `start = ``1``;``        ``for` `(``int` `i = ``0``; i < n; ++i) {``            ``if` `(array[i] > start)``                ``start = array[i];``        ``}``        ``int` `end = ``0``;` `        ``for` `(``int` `i = ``0``; i < n; i++) {``            ``end += array[i];``        ``}` `        ``// Answer stores possible``        ``// maximum sub array sum``        ``int` `answer = ``0``;``        ``while` `(start <= end) {``            ``int` `mid = (start + end) / ``2``;` `            ``// If mid is possible solution``            ``// Put answer = mid;``            ``if` `(check(mid, array, n, K)) {``                ``answer = mid;``                ``end = mid - ``1``;``            ``}``            ``else` `{``                ``start = mid + ``1``;``            ``}``        ``}` `        ``return` `answer;``    ``}` `    ``// Driver Code``    ``public` `static` `void` `main(String[] args)``    ``{``        ``int` `array[] = { ``1``, ``2``, ``3``, ``4` `};``        ``int` `n = array.length;``        ``int` `K = ``3``;``        ``System.out.println(solve(array, n, K));``    ``}``}` `// This code is contributed by AnkitRai01`

## Python3

 `# Python 3 implemenattion of the above approach` `# Function to check if mid can``# be maximum sub - arrays sum``def` `check(mid, array, n, K):``    ``count ``=` `0``    ``sum` `=` `0``    ``for` `i ``in` `range``(n):``        ` `        ``# If individual element is greater``        ``# maximum possible sum``        ``if` `(array[i] > mid):``            ``return` `False` `        ``# Increase sum of current sub - array``        ``sum` `+``=` `array[i]` `        ``# If the sum is greater than``        ``# mid increase count``        ``if` `(``sum` `> mid):``            ``count ``+``=` `1``            ``sum` `=` `array[i]``    ``count ``+``=` `1` `    ``# Check condition``    ``if` `(count <``=` `K):``        ``return` `True``    ``return` `False` `# Function to find maximum subarray sum``# which is minimum``def` `solve(array, n, K):``  ` `    ``start ``=` `max``(array)``    ``end ``=` `0` `    ``for` `i ``in` `range``(n):``        ``end ``+``=` `array[i]` `    ``# Answer stores possible``    ``# maximum sub array sum``    ``answer ``=` `0``    ``while` `(start <``=` `end):``        ``mid ``=` `(start ``+` `end) ``/``/` `2` `        ``# If mid is possible solution``        ``# Put answer = mid;``        ``if` `(check(mid, array, n, K)):``            ``answer ``=` `mid``            ``end ``=` `mid ``-` `1``        ``else``:``            ``start ``=` `mid ``+` `1` `    ``return` `answer` `# Driver Code``if` `__name__ ``=``=` `'__main__'``:``    ``array ``=` `[``1``, ``2``, ``3``, ``4``]``    ``n ``=` `len``(array)``    ``K ``=` `3``    ``print``(solve(array, n, K))``    ` `# This code is contributed by``# Surendra_Gangwar`

## C#

 `// C# implementation of the above approach``using` `System;``    ` `class` `GFG``{``    ` `    ``// Function to check if mid can``    ``// be maximum sub - arrays sum``    ``static` `Boolean check(``int` `mid, ``int` `[]array,``                                ``int` `n, ``int` `K)``    ``{``        ` `        ``int` `count = 0;``        ``int` `sum = 0;``        ``for` `(``int` `i = 0; i < n; i++)``        ``{``    ` `            ``// If individual element is greater``            ``// maximum possible sum``            ``if` `(array[i] > mid)``                ``return` `false``;``    ` `            ``// Increase sum of current sub - array``            ``sum += array[i];``    ` `            ``// If the sum is greater than``            ``// mid increase count``            ``if` `(sum > mid)``            ``{``                ``count++;``                ``sum = array[i];``            ``}``        ``}``        ``count++;``    ` `        ``// Check condition``        ``if` `(count <= K)``            ``return` `true``;``        ``return` `false``;``    ``}``    ` `    ``// Function to find maximum subarray sum``    ``// which is minimum``    ``static` `int` `solve(``int` `[]array, ``int` `n, ``int` `K)``    ``{``        ``int` `start = 1;``        ``for` `(``int` `i = 0; i < n; ++i) {``            ``if` `(array[i] > start)``                ``start = array[i];``        ``}``        ``int` `end = 0;``    ` `        ``for` `(``int` `i = 0; i < n; i++)``        ``{``            ``end += array[i];``        ``}``    ` `        ``// Answer stores possible``        ``// maximum sub array sum``        ``int` `answer = 0;``        ``while` `(start <= end)``        ``{``            ``int` `mid = (start + end) / 2;``    ` `            ``// If mid is possible solution``            ``// Put answer = mid;``            ``if` `(check(mid, array, n, K))``            ``{``                ``answer = mid;``                ``end = mid - 1;``            ``}``            ``else``            ``{``                ``start = mid + 1;``            ``}``        ``}``    ` `        ``return` `answer;``    ``}``    ` `    ``// Driver Code``    ``public` `static` `void` `Main (String[] args)``    ``{``        ``int` `[]array = { 1, 2, 3, 4 };``        ``int` `n = array.Length ;``        ``int` `K = 3;``        ``Console.WriteLine(solve(array, n, K));``    ``}``}` `// This code is contributed by Princi Singh`

## Javascript

 ``
Output:

`4`

Time Complexity : O(N*log(Sum))
Where N is the number of elements of the array and Sum is the sum of all the elements of the array.

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