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Find the index of the smallest element to be removed to make sum of array divisible by K

• Difficulty Level : Expert
• Last Updated : 21 Jun, 2021

Given an array arr[] of size N and a positive integer K, the task is to find the index of the smallest array element required to be removed to make the sum of remaining array divisible by K. If multiple solutions exist, then print the smallest index. Otherwise, print -1.

Examples:

Input: arr[ ] = {6, 7, 5, 1}, K = 7
Output: 2
Explanation:
Removing arr[0] from arr[] modifies arr[] to { 7, 5, 1 }. Therefore, sum = 13
Removing arr[1] from arr[] modifies arr[] to { 6, 5, 1 }. Therefore, sum = 12
Removing arr[2] from arr[] modifies arr[] to { 6, 7, 1 }. Therefore, sum = 14
Since the sum (= 14) is divisible by K(= 7), the required output is the index 2.

Input: arr[ ] = {14, 7, 8, 2, 4}, K = 7
Output: 1

Naive Approach: The simplest approach to solve this problem is to traverse the array and calculate the sum by removing the current element from the array. If the obtained sum is divisible by K, then print the current index. Otherwise, insert the removed element into the array.

Time Complexity: O(N2)
Auxiliary Space: O(1)

Approach: The above approach can be optimized by precalculating the sum of the array. Finally, traverse the array and check if (sum – arr[i]) is divisible by K or not. If found to be true, then print the current index. Follow the steps below to solve the problem:

• Calculate the sum of the array and store it in a variable say, sum.
• Initialize two variables say, res and mini to store the index of the smallest element and the element such that removing the elements makes the sum divisible by K.
• Traverse the array, and check if (sum – arr[i]) is divisible by K or not. If found to be true, then check if arr[i] is less than mini or not. If found to be true, then update mini = arr[i] and res = i.
• Finally, print the res.

Below is the implementation of the above approach:

C++14

 `// C++ program to implement` `// the above approach` `#include ` `using` `namespace` `std;`   `// Function to find index of the smallest array element` `// required to be removed to make sum divisible by K` `int` `findIndex(``int` `arr[], ``int` `n, ``int` `K)` `{`   `    ``// Stores sum of array elements` `    ``int` `sum = 0;`   `    ``// Stores index of the smallest element` `    ``// removed from the array to make sum` `    ``// divisible by K` `    ``int` `res = -1;`   `    ``// Stores the smallest element removed` `    ``// from the array to make sum divisible by K` `    ``int` `mini = 1e9;`   `    ``// Traverse the array, arr[]` `    ``for` `(``int` `i = 0; i < n; i++) {`   `        ``// Update sum` `        ``sum += arr[i];` `    ``}`   `    ``// Traverse the array arr[]` `    ``for` `(``int` `i = 0; i < n; i++) {`   `        ``// Calculate remaining sum` `        ``int` `temp = sum - arr[i];`   `        ``// If sum is divisible by K` `        ``if` `(temp % K == 0) {`   `            ``// If res ==-1 or mini is greater` `            ``// than arr[i]` `            ``if` `(res == -1 || mini > arr[i]) {`   `                ``// Update res and mini` `                ``res = i + 1;` `                ``mini = arr[i];` `            ``}` `        ``}` `    ``}`   `    ``return` `res;` `}`   `// Driver Code` `int` `main()` `{` `    ``int` `arr[] = { 14, 7, 8, 2, 4 };` `    ``int` `K = 7;` `    ``int` `N = ``sizeof``(arr) / ``sizeof``(arr[0]);`   `    ``cout << findIndex(arr, N, K);`   `    ``return` `0;` `}`

Java

 `// Java program to implement` `// the above approach` `import` `java.util.*;` `class` `GFG` `{`   `// Function to find index of the smallest array element` `// required to be removed to make sum divisible by K` `static` `int` `findIndex(``int` `arr[], ``int` `n, ``int` `K)` `{`   `    ``// Stores sum of array elements` `    ``int` `sum = ``0``;`   `    ``// Stores index of the smallest element` `    ``// removed from the array to make sum` `    ``// divisible by K` `    ``int` `res = -``1``;`   `    ``// Stores the smallest element removed` `    ``// from the array to make sum divisible by K` `    ``int` `mini = (``int``) 1e9;`   `    ``// Traverse the array, arr[]` `    ``for` `(``int` `i = ``0``; i < n; i++)` `    ``{`   `        ``// Update sum` `        ``sum += arr[i];` `    ``}`   `    ``// Traverse the array arr[]` `    ``for` `(``int` `i = ``0``; i < n; i++)` `    ``{`   `        ``// Calculate remaining sum` `        ``int` `temp = sum - arr[i];`   `        ``// If sum is divisible by K` `        ``if` `(temp % K == ``0``)` `        ``{`   `            ``// If res ==-1 or mini is greater` `            ``// than arr[i]` `            ``if` `(res == -``1` `|| mini > arr[i])` `            ``{`   `                ``// Update res and mini` `                ``res = i + ``1``;` `                ``mini = arr[i];` `            ``}` `        ``}` `    ``}` `    ``return` `res;` `}`   `// Driver Code` `public` `static` `void` `main(String[] args)` `{` `    ``int` `arr[] = { ``14``, ``7``, ``8``, ``2``, ``4` `};` `    ``int` `K = ``7``;` `    ``int` `N = arr.length;` `    ``System.out.print(findIndex(arr, N, K));` `}` `}`   `// This code is contributed by shikhasingrajput`

Python3

 `# Python3 program to implement` `# the above approach`   `# Function to find index of the smallest array element` `# required to be removed to make sum divisible by K` `def` `findIndex(arr, n, K) :`   `    ``# Stores sum of array elements` `    ``sum` `=` `0`   `    ``# Stores index of the smallest element` `    ``# removed from the array to make sum` `    ``# divisible by K` `    ``res ``=` `-``1`   `    ``# Stores the smallest element removed` `    ``# from the array to make sum divisible by K` `    ``mini ``=` `1e9`   `    ``# Traverse the array, arr[]` `    ``for` `i ``in` `range``(n):`   `        ``# Update sum` `        ``sum` `+``=` `arr[i]`   `    ``# Traverse the array arr[]` `    ``for` `i ``in` `range``(n):`   `        ``# Calculate remaining sum` `        ``temp ``=` `sum` `-` `arr[i]`   `        ``# If sum is divisible by K` `        ``if` `(temp ``%` `K ``=``=` `0``) :`   `            ``# If res ==-1 or mini is greater` `            ``# than arr[i]` `            ``if` `(res ``=``=` `-``1` `or` `mini > arr[i]) :`   `                ``# Update res and mini` `                ``res ``=` `i ``+` `1` `                ``mini ``=` `arr[i]` `    ``return` `res;`   `# Driver Code` `arr ``=` `[ ``14``, ``7``, ``8``, ``2``, ``4` `]` `K ``=` `7` `N ``=` `len``(arr)` `print``(findIndex(arr, N, K))`   `# This code is contributed by sanjoy_62.`

C#

 `// C# program to implement ` `// the above approach ` `using` `System;`   `class` `GFG{` `    `  `// Function to find index of the smallest` `// array element required to be removed ` `// to make sum divisible by K ` `static` `int` `findIndex(``int``[] arr, ``int` `n, ``int` `K) ` `{ ` `    `  `    ``// Stores sum of array elements ` `    ``int` `sum = 0; ` `  `  `    ``// Stores index of the smallest` `    ``// element removed from the array` `    ``// to make sum divisible by K ` `    ``int` `res = -1; ` `  `  `    ``// Stores the smallest element ` `    ``// removed from the array to ` `    ``// make sum divisible by K ` `    ``int` `mini = (``int``)1e9; ` `  `  `    ``// Traverse the array, arr[] ` `    ``for``(``int` `i = 0; i < n; i++)` `    ``{ ` `        `  `        ``// Update sum ` `        ``sum += arr[i]; ` `    ``} ` `  `  `    ``// Traverse the array arr[] ` `    ``for``(``int` `i = 0; i < n; i++) ` `    ``{ ` `        `  `        ``// Calculate remaining sum ` `        ``int` `temp = sum - arr[i]; ` `  `  `        ``// If sum is divisible by K ` `        ``if` `(temp % K == 0)` `        ``{ ` `            `  `            ``// If res ==-1 or mini is greater ` `            ``// than arr[i] ` `            ``if` `(res == -1 || mini > arr[i])` `            ``{ ` `                `  `                ``// Update res and mini ` `                ``res = i + 1; ` `                ``mini = arr[i]; ` `            ``} ` `        ``} ` `    ``} ` `    ``return` `res; ` `} `   `// Driver code    ` `static` `void` `Main() ` `{` `    ``int``[] arr = { 14, 7, 8, 2, 4 }; ` `    ``int` `K = 7; ` `    ``int` `N = arr.Length; ` `    `  `    ``Console.WriteLine(findIndex(arr, N, K));  ` `}` `}`   `// This code is contributed by divyeshrabadiya07`

Javascript

 ``

Output:

`2`

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

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