# Minimize Array elements to be reduced to make subsequences sum 1 to Array max possible

Given an array **a[]** of positive integers. Subtract any positive integer from any number of elements of the array such that there exists every possible subsequence with sum **1** to **s**, where **s** denotes the sum of all the elements of the array. Find the minimum possible number of the array element to be subtracted.

Input:a[] = {4, 3, 2, 2, 1, 6}Output:2Explanation:By subtracting 5 from 6 and 2 from 4 we get array {2, 3, 2, 2, 1, 1} which fulfills required condition.

Input:a[] = { 1, 2, 2, 2, 1, 2 }Output:0

**Approach: **The required array will be found if **s<2*(size of the** **array)** where **s** denotes the sum of all the elements of the array. If this condition is not satisfied by the array we have to subtract **s-((2*size of array )-1)** from elements of the given array. Since we have to find the minimum possible number of the array element to be subtracted. We will perform the maximum possible subtraction from the greatest element of the array and repeat the process until we get the required result. Follow the steps below to solve the problem:

- Initialize the variable
**sum**as the sum of all elements of the array**arr[]**. - Initialize the variable
**diff**as**sum – (2*size) +1.** - Initialize the variable
**ans**as**0, i**as**size-1.** - Sort the array
**arr[].** - Traverse over a while loop till
**diff**is greater than**0**and perform the following tasks:- Subtract the value of
**arr[i]-1**from the variable**diff**and increase the value of**ans**by**1**. - Decrease the value of
**i**by**1.**

- Subtract the value of
- After performing the above steps, print the value of
**ans**as the answer.

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 total number` `// of operations required` `int` `find(` `int` `arr[], ` `int` `size)` `{` ` ` `int` `sum = 0;` ` ` `// Find sum of all element of array arr.` ` ` `for` `(` `int` `i = 0; i < size; i++) {` ` ` `sum += arr[i];` ` ` `}` ` ` `// Variable to store integer which needs` ` ` `// to be subtracted from arr in total.` ` ` `int` `diff = sum - ((2 * size) - 1);` ` ` `int` `ans = 0;` ` ` `int` `i = size - 1;` ` ` `sort(arr, arr + size);` ` ` `// Iteration to calcute total number of` ` ` `// subtraction required to get desired array.` ` ` `while` `(diff > 0) {` ` ` `diff -= (arr[i] - 1);` ` ` `i--;` ` ` `ans++;` ` ` `}` ` ` `return` `ans;` `}` `// Driver Code` `int` `main()` `{` ` ` `int` `arr[] = { 4, 3, 2, 2, 1, 6 };` ` ` `cout << find(arr, 6) << ` `"\n"` `;` ` ` `return` `0;` `}` |

## Java

`// Java program for the above approach` `import` `java.io.*;` `import` `java.lang.*;` `import` `java.util.*;` `class` `GFG` `{` ` ` `// Function to find the total number` ` ` `// of operations required` ` ` `static` `int` `find(` `int` `arr[], ` `int` `size)` ` ` `{` ` ` `int` `sum = ` `0` `;` ` ` `// Find sum of all element of array arr.` ` ` `for` `(` `int` `i = ` `0` `; i < size; i++) {` ` ` `sum += arr[i];` ` ` `}` ` ` `// Variable to store integer which needs` ` ` `// to be subtracted from arr in total.` ` ` `int` `diff = sum - ((` `2` `* size) - ` `1` `);` ` ` `int` `ans = ` `0` `;` ` ` `int` `i = size - ` `1` `;` ` ` `Arrays.sort(arr);` ` ` `// Iteration to calcute total number of` ` ` `// subtraction required to get desired array.` ` ` `while` `(diff > ` `0` `) {` ` ` `diff -= (arr[i] - ` `1` `);` ` ` `i--;` ` ` `ans++;` ` ` `}` ` ` `return` `ans;` ` ` `}` ` ` `// Driver code` ` ` `public` `static` `void` `main (String[] args) {` ` ` `int` `arr[] = { ` `4` `, ` `3` `, ` `2` `, ` `2` `, ` `1` `, ` `6` `};` ` ` `int` `N = arr.length;` ` ` `System.out.println( find(arr, N));` ` ` `}` `}` `// This code is contributed by hrithikgarg03188` |

## Python

`# Python program for the above approach` `# Function to find the total number` `# of operations required` `def` `find(arr, size):` ` ` `sum` `=` `0` ` ` `# Find sum of all element of array arr.` ` ` `for` `i ` `in` `range` `(` `0` `, size):` ` ` `sum` `=` `sum` `+` `arr[i]` ` ` `# Variable to store integer which needs` ` ` `# to be subtracted from arr in total.` ` ` `diff ` `=` `sum` `-` `((` `2` `*` `size) ` `-` `1` `)` ` ` `ans ` `=` `0` ` ` `i ` `=` `size ` `-` `1` ` ` `arr.sort()` ` ` `# Iteration to calcute total number of` ` ` `# subtraction required to get desired array.` ` ` `while` `(diff > ` `0` `):` ` ` `diff ` `=` `diff ` `-` `(arr[i] ` `-` `1` `)` ` ` `i ` `=` `i ` `-` `1` ` ` `ans ` `=` `ans ` `+` `1` ` ` `return` `ans` `# Driver Code` `arr ` `=` `[` `4` `, ` `3` `, ` `2` `, ` `2` `, ` `1` `, ` `6` `]` `print` `(find(arr, ` `6` `))` `# This code is contributed by Taranpreet` |

## C#

`// C# program for the above approach` `using` `System;` `class` `GFG {` ` ` `// Function to find the total number` ` ` `// of operations required` ` ` `static` `int` `find(` `int` `[] arr, ` `int` `size)` ` ` `{` ` ` `int` `sum = 0;` ` ` `// Find sum of all element of array arr.` ` ` `for` `(` `int` `i = 0; i < size; i++) {` ` ` `sum += arr[i];` ` ` `}` ` ` `// Variable to store integer which needs` ` ` `// to be subtracted from arr in total.` ` ` `int` `diff = sum - ((2 * size) - 1);` ` ` `int` `ans = 0;` ` ` `int` `j = size - 1;` ` ` `Array.Sort(arr);` ` ` `// Iteration to calcute total number of` ` ` `// subtraction required to get desired array.` ` ` `while` `(diff > 0) {` ` ` `diff -= (arr[j] - 1);` ` ` `j--;` ` ` `ans++;` ` ` `}` ` ` `return` `ans;` ` ` `}` ` ` `// Driver Code` ` ` `public` `static` `void` `Main()` ` ` `{` ` ` `int` `[] arr = { 4, 3, 2, 2, 1, 6 };` ` ` `Console.WriteLine(find(arr, 6));` ` ` `}` `}` `// This code is contributed by ukasp.` |

## Javascript

`<script>` ` ` `// JavaScript code for the above approach` ` ` `// Function to find the total number` ` ` `// of operations required` ` ` `function` `find(arr, size) {` ` ` `let sum = 0;` ` ` `// Find sum of all element of array arr.` ` ` `for` `(let i = 0; i < size; i++) {` ` ` `sum += arr[i];` ` ` `}` ` ` `// Variable to store integer which needs` ` ` `// to be subtracted from arr in total.` ` ` `let diff = sum - ((2 * size) - 1);` ` ` `let ans = 0;` ` ` `let i = size - 1;` ` ` `arr.sort(` `function` `(a, b) { ` `return` `a - b })` ` ` `// Iteration to calcute total number of` ` ` `// subtraction required to get desired array.` ` ` `while` `(diff > 0) {` ` ` `diff -= (arr[i] - 1);` ` ` `i--;` ` ` `ans++;` ` ` `}` ` ` `return` `ans;` ` ` `}` ` ` `// Driver Code` ` ` `let arr = [4, 3, 2, 2, 1, 6];` ` ` `document.write(find(arr, 6) + ` `'<br>'` `);` ` ` `// This code is contributed by Potta Lokesh` ` ` `</script>` |

**Output:**

2

**Time Complexity:** O(n*log(n))**Auxiliary Space:** O(n)