# Find maximum height to cut all chocolates horizontally such that at least K amount remains

Given an array **arr[] **consisting of heights of **N** chocolate bars, the task is to find the maximum height at which the horizontal cut is made to all the chocolates such that the sum remaining amount of chocolate is **at least K**.

**Examples:**

Input:K = 7, arr[] = [15, 20, 8, 17]Output:15Explanation:If a cut is made at height 8 the total chocolate removed is 24 and chocolate wasted is 24 – 7 = 17 units. If a cut is made at height 15 then chocolate removed is 7 and no chocolate is wasted.

Therefore 15 is the answer.

Input:K = 12 arr[] = [30, 25, 22, 17, 20]Output:21Explanation:After a cut at height 18, the chocolate removed is 25 and chocolate wastage is (25 – 12) = 13 units. But if the cut is made at height 21 is made then 14 units of chocolate is removed and the wastage is (14 – 12) = 2 which is the least, hence 21 is the answer

**Approach:** The given problem can be solved based on Binary Search. The idea is to perform the Binary Search over then range **[0, ****max element of the array****]** and find that value in the range that, say **M** such that the sum of remaining chocolate after making the horizontal cut at **M** give minimum difference with **K**. Follow the steps below to solve the given problem:

- Initialize two variables, say
**low**and**high**as**0**and the maximum array element respectively. - Iterate until
**low <= high**and perform the following steps:- Find the value of
**mid**as**(low + high)/2**. - Find the sum of remaining chocolates after making the horizontal cut at height
**mid**as**M**. - If the value of
**M**is less than**K**, then update the value of**high**as**(mid – 1)**. Otherwise, update the value of**low**as**(mid + 1)**.

- Find the value of
- After performing the above steps, print the value as
**high**as the resultant maximum height that must be cut.

Below is the implementation of the above approach:

## C++

`// C++ program for the above approach` `#include<bits/stdc++.h>` `using` `namespace` `std;` `// Function to find the sum of remaining` `// chocolate after making the horizontal` `// cut at height mid` `int` `cal(vector<` `int` `> arr, ` `int` `mid)` `{` ` ` ` ` `// Stores the sum of chocolates` ` ` `int` `chocolate = 0; ` ` ` ` ` `// Traverse the array arr[]` ` ` `for` `(` `auto` `i : arr){` ` ` ` ` `// If the height is at least mid` ` ` `if` `(i >= mid)` ` ` `chocolate += i - mid;` ` ` `}` ` ` ` ` ` ` `// Return the possible sum` ` ` `return` `chocolate;` `}` ` ` `// Function to find the maximum horizontal` `// cut made to all the chocolates such that` `// the sum of the remaining element is` `// at least K` `int` `maximumCut(vector<` `int` `> arr, ` `int` `K){` ` ` ` ` `// Ranges of Binary Search` ` ` `int` `low = 0;` ` ` `int` `high = *max_element(arr.begin(),arr.end());` ` ` ` ` `// Perform the Binary Search` ` ` `while` `(low <= high){` ` ` `int` `mid = (low + high) / 2;` ` ` `// Find the sum of removed after` ` ` `// making cut at height mid` ` ` `int` `chocolate = cal(arr,mid);` ` ` `// If the chocolate removed is` ` ` `// same as the chocolate needed` ` ` `// then return the height` ` ` `if` `(chocolate == K)` ` ` `return` `mid;` ` ` `// If the chocolate removed is` ` ` `// less than chocolate needed` ` ` `// then shift to the left range` ` ` `else` `if` `(chocolate < K)` ` ` `high = mid - 1;` ` ` `// Otherwise, shift to the right` ` ` `// range` ` ` `else` `{` ` ` `low = mid + 1;` ` ` `if` `(mid > high)` ` ` `high = mid;` ` ` `}` ` ` `} ` ` ` ` ` `// Return the possible cut` ` ` `return` `high;` `}` `// Driver Code` `int` `main(){` ` ` `int` `N = 4;` ` ` `int` `K = 7;` ` ` `vector<` `int` `> arr{15, 20, 8, 17};` ` ` `cout<<(maximumCut(arr, K));` `}` `// This code is contributed by ipg2016107.` |

## Java

`// Java program for the above approach` `import` `java.util.*;` `import` `java.util.Arrays;` `class` `GFG {` ` ` `// Function to find the sum of remaining` ` ` `// chocolate after making the horizontal` ` ` `// cut at height mid` ` ` `static` `int` `cal(` `int` `arr[], ` `int` `mid)` ` ` `{` ` ` `// Stores the sum of chocolates` ` ` `int` `chocolate = ` `0` `;` ` ` `// Traverse the array arr[]` ` ` `for` `(` `int` `i = ` `0` `; i < arr.length; i++) {` ` ` `// If the height is at least mid` ` ` `if` `(arr[i] >= mid)` ` ` `chocolate += arr[i] - mid;` ` ` `}` ` ` `// Return the possible sum` ` ` `return` `chocolate;` ` ` `}` ` ` `// Function to find the maximum horizontal` ` ` `// cut made to all the chocolates such that` ` ` `// the sum of the remaining element is` ` ` `// at least K` ` ` `static` `int` `maximumCut(` `int` `arr[], ` `int` `K)` ` ` `{` ` ` `// Ranges of Binary Search` ` ` `int` `low = ` `0` `;` ` ` `int` `high = Arrays.stream(arr).max().getAsInt();` ` ` `// Perform the Binary Search` ` ` `while` `(low <= high) {` ` ` `int` `mid = (low + high) / ` `2` `;` ` ` `// Find the sum of removed after` ` ` `// making cut at height mid` ` ` `int` `chocolate = cal(arr, mid);` ` ` `// If the chocolate removed is` ` ` `// same as the chocolate needed` ` ` `// then return the height` ` ` `if` `(chocolate == K)` ` ` `return` `mid;` ` ` `// If the chocolate removed is` ` ` `// less than chocolate needed` ` ` `// then shift to the left range` ` ` `else` `if` `(chocolate < K)` ` ` `high = mid - ` `1` `;` ` ` `// Otherwise, shift to the right` ` ` `// range` ` ` `else` `{` ` ` `low = mid + ` `1` `;` ` ` `if` `(mid > high)` ` ` `high = mid;` ` ` `}` ` ` `}` ` ` `// Return the possible cut` ` ` `return` `high;` ` ` `}` ` ` `// Driver Code` ` ` `public` `static` `void` `main(String[] args)` ` ` `{` ` ` `int` `K = ` `7` `;` ` ` `int` `arr[] = { ` `15` `, ` `20` `, ` `8` `, ` `17` `};` ` ` `System.out.println(maximumCut(arr, K));` ` ` `}` `}` `// This code is contributed by ukasp.` |

## Python3

`# Python program for the above approach` `# Function to find the sum of remaining` `# chocolate after making the horizontal` `# cut at height mid` `def` `cal(arr, mid):` ` ` ` ` `# Stores the sum of chocolates` ` ` `chocolate ` `=` `0` ` ` ` ` `# Traverse the array arr[]` ` ` `for` `i ` `in` `arr:` ` ` ` ` `# If the height is at least mid` ` ` `if` `i >` `=` `mid:` ` ` `chocolate ` `+` `=` `i ` `-` `mid` ` ` ` ` `# Return the possible sum` ` ` `return` `chocolate` `# Function to find the maximum horizontal` `# cut made to all the chocolates such that` `# the sum of the remaining element is` `# at least K` `def` `maximumCut(arr, K):` ` ` ` ` `# Ranges of Binary Search` ` ` `low ` `=` `0` ` ` `high ` `=` `max` `(arr)` ` ` ` ` `# Perform the Binary Search` ` ` `while` `low <` `=` `high:` ` ` `mid ` `=` `(low ` `+` `high) ` `/` `/` `2` ` ` `# Find the sum of removed after` ` ` `# making cut at height mid` ` ` `chocolate ` `=` `cal(arr, mid)` ` ` `# If the chocolate removed is` ` ` `# same as the chocolate needed` ` ` `# then return the height` ` ` `if` `chocolate ` `=` `=` `K:` ` ` `return` `mid` ` ` `# If the chocolate removed is` ` ` `# less than chocolate needed` ` ` `# then shift to the left range` ` ` `elif` `chocolate < K:` ` ` `high ` `=` `mid ` `-` `1` ` ` `# Otherwise, shift to the right` ` ` `# range` ` ` `else` `:` ` ` `low ` `=` `mid ` `+` `1` ` ` `if` `mid > high:` ` ` `high ` `=` `mid` ` ` ` ` `# Return the possible cut` ` ` `return` `high` `# Driver Code` `N, K ` `=` `4` `, ` `7` `arr ` `=` `[` `15` `, ` `20` `, ` `8` `, ` `17` `]` `print` `(maximumCut(arr, K))` |

## C#

`// C# program for the above approach` `using` `System;` `using` `System.Collections.Generic;` `using` `System.Linq;` `class` `GFG{` `// Function to find the sum of remaining` `// chocolate after making the horizontal` `// cut at height mid` `static` `int` `cal(List<` `int` `> arr, ` `int` `mid)` `{` ` ` ` ` `// Stores the sum of chocolates` ` ` `int` `chocolate = 0; ` ` ` ` ` `// Traverse the array arr[]` ` ` `foreach` `(` `int` `i ` `in` `arr){` ` ` ` ` `// If the height is at least mid` ` ` `if` `(i >= mid)` ` ` `chocolate += i - mid;` ` ` `}` ` ` ` ` ` ` `// Return the possible sum` ` ` `return` `chocolate;` `}` ` ` `// Function to find the maximum horizontal` `// cut made to all the chocolates such that` `// the sum of the remaining element is` `// at least K` `static` `int` `maximumCut(List<` `int` `> arr, ` `int` `K){` ` ` ` ` `// Ranges of Binary Search` ` ` `int` `low = 0;` ` ` `int` `high = arr.Max();` ` ` ` ` `// Perform the Binary Search` ` ` `while` `(low <= high){` ` ` `int` `mid = (low + high) / 2;` ` ` `// Find the sum of removed after` ` ` `// making cut at height mid` ` ` `int` `chocolate = cal(arr,mid);` ` ` `// If the chocolate removed is` ` ` `// same as the chocolate needed` ` ` `// then return the height` ` ` `if` `(chocolate == K)` ` ` `return` `mid;` ` ` `// If the chocolate removed is` ` ` `// less than chocolate needed` ` ` `// then shift to the left range` ` ` `else` `if` `(chocolate < K)` ` ` `high = mid - 1;` ` ` `// Otherwise, shift to the right` ` ` `// range` ` ` `else` `{` ` ` `low = mid + 1;` ` ` `if` `(mid > high)` ` ` `high = mid;` ` ` `}` ` ` `} ` ` ` ` ` `// Return the possible cut` ` ` `return` `high;` `}` `// Driver Code` `public` `static` `void` `Main(){` ` ` `int` `K = 7;` ` ` `List<` `int` `> arr = ` `new` `List<` `int` `>(){15, 20, 8, 17};` ` ` `Console.Write(maximumCut(arr, K));` `}` `}` `// This code is contributed by SURENDRA_GANGWAR.` |

## Javascript

`<script>` ` ` `// JavaScript Program to implement` ` ` `// the above approach` ` ` `// Function to find the sum of remaining` ` ` `// chocolate after making the horizontal` ` ` `// cut at height mid` ` ` `function` `cal(arr, mid) {` ` ` `// Stores the sum of chocolates` ` ` `let chocolate = 0` ` ` `// Traverse the array arr[]` ` ` `for` `(let i = 0; i < arr.length; i++) {` ` ` `// If the height is at least mid` ` ` `if` `(arr[i] >= mid)` ` ` `chocolate += arr[i] - mid` ` ` `}` ` ` `// Return the possible sum` ` ` `return` `chocolate` ` ` `}` ` ` `// Function to find the maximum horizontal` ` ` `// cut made to all the chocolates such that` ` ` `// the sum of the remaining element is` ` ` `// at least K` ` ` `function` `maximumCut(arr, K) {` ` ` `// Ranges of Binary Search` ` ` `let low = 0` ` ` `let high = arr[0];` ` ` `for` `(let i = 1; i < arr.length; i++) {` ` ` `high = Math.max(high, arr[i]);` ` ` `}` ` ` `// Perform the Binary Search` ` ` `while` `(low <= high) {` ` ` `mid = Math.floor((low + high) / 2);` ` ` `// Find the sum of removed after` ` ` `// making cut at height mid` ` ` `chocolate = cal(arr, mid)` ` ` `// If the chocolate removed is` ` ` `// same as the chocolate needed` ` ` `// then return the height` ` ` `if` `(chocolate == K) {` ` ` `return` `mid` ` ` `}` ` ` `// If the chocolate removed is` ` ` `// less than chocolate needed` ` ` `// then shift to the left range` ` ` `else` `if` `(chocolate < K) {` ` ` `high = mid - 1` ` ` `}` ` ` `// Otherwise, shift to the right` ` ` `// range` ` ` `else` `{` ` ` `low = mid + 1` ` ` `if` `(mid > high)` ` ` `high = mid` ` ` `}` ` ` `}` ` ` ` ` `// Return the possible cut` ` ` `return` `high` ` ` `}` ` ` ` ` `// Driver Code` ` ` `let N = 4;` ` ` `let K = 7;` ` ` `let arr = [15, 20, 8, 17];` ` ` `document.write(maximumCut(arr, K))` ` ` `// This code is contributed by Potta Lokesh` ` ` `</script>` |

**Output:**

15

**Time Complexity:** O(N*log N)**Auxiliary Space:** O(1)

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