# Minimum operation to make all elements equal in array

Given an array with n positive integers. We need to find the minimum number of operation to make all elements equal. We can perform addition, multiplication, subtraction or division with any element on an array element.

**Examples:**

Input : arr[] = {1, 2, 3, 4} Output : 3 Since all elements are different, we need to perform at least three operations to make them same. For example, we can make them all 1 by doing three subtractions. Or make them all 3 by doing three additions. Input : arr[] = {1, 1, 1, 1} Output : 0

For making all elements equal you can select a target value and then you can make all elements equal to that. Now, for converting a single element to target value you can perform a single operation only once. In this manner you can achieve your task in maximum of n operations but you have to minimize this number of operation and for this your selection of target is very important because if you select a target whose frequency in array is x then you have to perform only n-x more operations as you have already x elements equal to your target value. So finally, our task is reduced to finding the element with maximum frequency. This can be achieved by different means such as iterative method in O(n^2), sorting in O(nlogn) and hashing in O(n) time complexity.

**Implementation:**

## C++

`// CPP program to find the minimum number of ` `// operations required to make all elements ` `// of array equal` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// function for min operation ` `int` `minOperation (` `int` `arr[], ` `int` `n) ` `{` ` ` `// Insert all elements in hash. ` ` ` `unordered_map<` `int` `, ` `int` `> hash; ` ` ` `for` `(` `int` `i=0; i<n; i++)` ` ` `hash[arr[i]]++;` ` ` `// find the max frequency` ` ` `int` `max_count = 0;` ` ` `for` `(` `auto` `i : hash)` ` ` `if` `(max_count < i.second)` ` ` `max_count = i.second;` ` ` `// return result` ` ` `return` `(n - max_count); ` `}` `// driver program` `int` `main()` `{` ` ` `int` `arr[] = {1, 5, 2, 1, 3, 2, 1};` ` ` `int` `n = ` `sizeof` `(arr) / ` `sizeof` `(arr[0]);` ` ` `cout << minOperation(arr, n);` ` ` `return` `0;` `} ` |

## Java

`// JAVA Code For Minimum operation to make` `// all elements equal in array` `import` `java.util.*;` `class` `GFG {` ` ` ` ` `// function for min operation ` ` ` `public` `static` `int` `minOperation (` `int` `arr[], ` `int` `n) ` ` ` `{` ` ` `// Insert all elements in hash. ` ` ` `HashMap<Integer, Integer> hash = ` `new` `HashMap<Integer, ` ` ` `Integer>(); ` ` ` ` ` `for` `(` `int` `i=` `0` `; i<n; i++)` ` ` `if` `(hash.containsKey(arr[i]))` ` ` `hash.put(arr[i], hash.get(arr[i])+` `1` `);` ` ` `else` `hash.put(arr[i], ` `1` `);` ` ` ` ` `// find the max frequency` ` ` `int` `max_count = ` `0` `;` ` ` `Set<Integer> s = hash.keySet(); ` ` ` ` ` `for` `(` `int` `i : s)` ` ` `if` `(max_count < hash.get(i))` ` ` `max_count = hash.get(i);` ` ` ` ` `// return result` ` ` `return` `(n - max_count); ` ` ` `}` ` ` ` ` `/* Driver program to test above function */` ` ` `public` `static` `void` `main(String[] args) ` ` ` `{` ` ` `int` `arr[] = {` `1` `, ` `5` `, ` `2` `, ` `1` `, ` `3` `, ` `2` `, ` `1` `};` ` ` `int` `n = arr.length;` ` ` `System.out.print(minOperation(arr, n));` ` ` ` ` `}` `}` ` ` `// This code is contributed by Arnav Kr. Mandal.` |

## Python3

`# Python3 program to find the minimum ` `# number of operations required to ` `# make all elements of array equal ` `from` `collections ` `import` `defaultdict` `# Function for min operation ` `def` `minOperation(arr, n): ` ` ` `# Insert all elements in hash. ` ` ` `Hash` `=` `defaultdict(` `lambda` `:` `0` `) ` ` ` `for` `i ` `in` `range` `(` `0` `, n): ` ` ` `Hash` `[arr[i]] ` `+` `=` `1` ` ` `# find the max frequency ` ` ` `max_count ` `=` `0` ` ` `for` `i ` `in` `Hash` `: ` ` ` `if` `max_count < ` `Hash` `[i]: ` ` ` `max_count ` `=` `Hash` `[i] ` ` ` `# return result ` ` ` `return` `n ` `-` `max_count ` `# Driver Code` `if` `__name__ ` `=` `=` `"__main__"` `: ` ` ` `arr ` `=` `[` `1` `, ` `5` `, ` `2` `, ` `1` `, ` `3` `, ` `2` `, ` `1` `] ` ` ` `n ` `=` `len` `(arr) ` ` ` `print` `(minOperation(arr, n))` ` ` `# This code is contributed ` `# by Rituraj Jain` |

## C#

`// C# Code For Minimum operation to make` `// all elements equal in array` `using` `System;` `using` `System.Collections.Generic;` ` ` `class` `GFG ` `{` ` ` ` ` `// function for min operation ` ` ` `public` `static` `int` `minOperation (` `int` `[]arr, ` `int` `n) ` ` ` `{` ` ` `// Insert all elements in hash. ` ` ` `Dictionary<` `int` `,` `int` `> m = ` `new` `Dictionary<` `int` `,` `int` `>();` ` ` `for` `(` `int` `i = 0 ; i < n; i++)` ` ` `{` ` ` `if` `(m.ContainsKey(arr[i]))` ` ` `{` ` ` `var` `val = m[arr[i]];` ` ` `m.Remove(arr[i]);` ` ` `m.Add(arr[i], val + 1); ` ` ` `}` ` ` `else` ` ` `{` ` ` `m.Add(arr[i], 1);` ` ` `}` ` ` `}` ` ` ` ` `// find the max frequency` ` ` `int` `max_count = 0;` ` ` `HashSet<` `int` `> s = ` `new` `HashSet<` `int` `>(m.Keys); ` ` ` ` ` `foreach` `(` `int` `i ` `in` `s)` ` ` `if` `(max_count < m[i])` ` ` `max_count = m[i];` ` ` ` ` `// return result` ` ` `return` `(n - max_count); ` ` ` `}` ` ` ` ` `/* Driver code */` ` ` `public` `static` `void` `Main(String[] args) ` ` ` `{` ` ` `int` `[]arr = {1, 5, 2, 1, 3, 2, 1};` ` ` `int` `n = arr.Length;` ` ` `Console.Write(minOperation(arr, n));` ` ` ` ` `}` `}` `// This code is contributed by 29AjayKumar` |

## Javascript

`<script>` `// JavaScript Code For Minimum operation to make` `// all elements equal in array` `// function for min operation` `function` `minOperation(arr, n) {` ` ` `// Insert all elements in hash.` ` ` `let hash = ` `new` `Map();` ` ` `for` `(let i = 0; i < n; i++)` ` ` `if` `(hash.has(arr[i]))` ` ` `hash.set(arr[i], hash.get(arr[i]) + 1);` ` ` `else` `hash.set(arr[i], 1);` ` ` `// find the max frequency` ` ` `let max_count = 0;` ` ` `let s = hash.keys();` ` ` `for` `(let i of s)` ` ` `if` `(max_count < hash.get(i))` ` ` `max_count = hash.get(i);` ` ` `// return result` ` ` `return` `(n - max_count);` `}` `/* Driver program to test above function */` `let arr = [1, 5, 2, 1, 3, 2, 1];` `let n = arr.length;` `document.write(minOperation(arr, n));` `// This code is contributed by _saurabh_jaiswal` `</script>` |

**Output**

4

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

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