A Sum Array Puzzle - GeeksforGeeks

03 Jun, 2021
Given an array arr[] of n integers, construct a Sum Array sum[] (of same size) such that sum[i] is equal to the sum of all the elements of arr[] except arr[i]. Solve it without subtraction operator and in O(n).
Examples:
Input : arr[] = {3, 6, 4, 8, 9} Output : sum[] = {27, 24, 26, 22, 21}
Input : arr[] = {4, 5, 7, 3, 10, 1} Output : sum[] = {26, 25, 23, 27, 20, 29} 
Algorithm: 1) Construct a temporary array leftSum[] such that leftSum[i] contains sum of all elements on left of arr[i] excluding arr[i]. 2) Construct another temporary array rightSum[] such that rightSum[i] contains sum of all elements on on right of arr[i] excluding arr[i]. 3) To get sum[], sum left[] and right[].
C++
Java
Python3
C#
PHP
Javascript
// C++ implementation of above approach#include <bits/stdc++.h>using namespace std; void sumArray(int arr[], int n){    /* Allocate memory for temporary arrays leftSum[],    rightSum[] and Sum[]*/    int leftSum[n], rightSum[n], Sum[n], i, j;     /* Left most element of left array is always 0 */    leftSum[0] = 0;     /* Rightmost most element of right    array is always 0 */    rightSum[n - 1] = 0;     /* Construct the left array*/    for (i = 1; i < n; i++)        leftSum[i] = arr[i - 1] + leftSum[i - 1];     /* Construct the right array*/    for (j = n - 2; j >= 0; j--)        rightSum[j] = arr[j + 1] + rightSum[j + 1];     /* Construct the sum array using        left[] and right[] */    for (i = 0; i < n; i++)        Sum[i] = leftSum[i] + rightSum[i];     /* print the constructed prod array */    for (i = 0; i < n; i++)        cout << Sum[i] << " ";} /* Driver program to test above functions */int main(){    int arr[] = { 3, 6, 4, 8, 9 };    int n = sizeof(arr) / sizeof(arr[0]);    sumArray(arr, n);     return 0;}
// Java implementation of above approachimport java.util.*;import java.lang.*;import java.io.*; class Geeks {    public static void sumArray(int arr[], int n)    {        /* Allocate memory for temporary arrays           leftSum[], rightSum[] and Sum[]*/        int leftSum[] = new int[n];        int rightSum[] = new int[n];        int Sum[] = new int[n];         int i = 0, j = 0;         /* Left most element of left array is           always 0 */        leftSum[0] = 0;         /* Right most element of right array           is always 0 */        rightSum[n - 1] = 0;         /* Construct the left array*/        for (i = 1; i < n; i++)            leftSum[i] = arr[i - 1] + leftSum[i - 1];         /* Construct the right array*/        for (j = n - 2; j >= 0; j--)            rightSum[j] = arr[j + 1] + rightSum[j + 1];         /* Construct the sum array using        left[] and right[] */        for (i = 0; i < n; i++)            Sum[i] = leftSum[i] + rightSum[i];         /*print the sum array*/        for (i = 0; i < n; i++)            System.out.print(Sum[i] + " ");    }     /* Driver function to test above function*/    public static void main(String[] args)    {        int arr[] = { 3, 6, 4, 8, 9 };        int n = arr.length;        sumArray(arr, n);    }}
# Python3 implementation of above approach def sumArray(arr, n):     # Allocate memory for temporary arrays    # leftSum[], rightSum[] and Sum[]    leftSum = [0 for i in range(n)]    rightSum = [0 for i in range(n)]    Sum = [0 for i in range(n)]    i, j = 0, 0     # Left most element of left    # array is always 0    leftSum[0] = 0     # Rightmost most element of right    # array is always 0    rightSum[n - 1] = 0     # Construct the left array    for i in range(1, n):        leftSum[i] = arr[i - 1] + leftSum[i - 1]     # Construct the right array    for j in range(n - 2, -1, -1):        rightSum[j] = arr[j + 1] + rightSum[j + 1]     # Construct the sum array using    # left[] and right[]    for i in range(0, n):        Sum[i] = leftSum[i] + rightSum[i]     # print the constructed prod array    for i in range(n):        print(Sum[i], end = " ")  # Driver Codearr = [3, 6, 4, 8, 9]n = len(arr)sumArray(arr, n) # This code is contributed by# mohit kumar 29
// C# implementation of above approach using System ; class Geeks {    public static void sumArray(int []arr, int n)    {        /* Allocate memory for temporary arrays        leftSum[], rightSum[] and Sum[]*/        int []leftSum = new int[n];        int []rightSum = new int[n];        int []Sum = new int[n];         int i = 0, j = 0;         /* Left most element of left array is        always 0 */        leftSum[0] = 0;         /* Right most element of right array        is always 0 */        rightSum[n - 1] = 0;         /* Construct the left array*/        for (i = 1; i < n; i++)            leftSum[i] = arr[i - 1] + leftSum[i - 1];         /* Construct the right array*/        for (j = n - 2; j >= 0; j--)            rightSum[j] = arr[j + 1] + rightSum[j + 1];         /* Construct the sum array using        left[] and right[] */        for (i = 0; i < n; i++)            Sum[i] = leftSum[i] + rightSum[i];         /*print the sum array*/        for (i = 0; i < n; i++)            Console.Write(Sum[i] + " ");    }     /* Driver function to test above function*/    public static void Main()    {        int []arr = { 3, 6, 4, 8, 9 };        int n = arr.Length;        sumArray(arr, n);    }    // This code is contributed by Ryuga}
<?php// PHP implementation of above approach function sumArray($arr, $n){    /* Allocate memory for temporary    arrays leftSum[], rightSum[] and Sum[]*/    $leftSum = array_fill(0, $n, 0);    $rightSum = array_fill(0, $n, 0);    $Sum = array_fill(0, $n, 0);     /* Left most element of left       array is always 0 */    $leftSum[0] = 0;     /* Rightmost most element of right    array is always 0 */    $rightSum[$n - 1] = 0;     /* Construct the left array*/    for ($i = 1; $i < $n; $i++)        $leftSum[$i] = $arr[$i - 1] +                       $leftSum[$i - 1];     /* Construct the right array*/    for ($j = $n - 2; $j >= 0; $j--)        $rightSum[$j] = $arr[$j + 1] +                        $rightSum[$j + 1];     /* Construct the sum array using        left[] and right[] */    for ($i = 0; $i < $n; $i++)        $Sum[$i] = $leftSum[$i] + $rightSum[$i];     /* print the constructed prod array */    for ($i = 0; $i < $n; $i++)        echo $Sum[$i]." ";} // Driver Code$arr = array( 3, 6, 4, 8, 9 );$n = count($arr);sumArray($arr, $n); // This code is contributed// by chandan_jnu?>
<script>     // JavaScript implementation of above approach         function sumArray(arr, n)    {        /* Allocate memory for temporary arrays           leftSum[], rightSum[] and Sum[]*/        let leftSum = new Array(n);        let rightSum = new Array(n);        let Sum = new Array(n);          let i = 0, j = 0;          /* Left most element of left array is           always 0 */        leftSum[0] = 0;          /* Right most element of right array           is always 0 */        rightSum[n - 1] = 0;          /* Construct the left array*/        for (i = 1; i < n; i++)            leftSum[i] = arr[i - 1] + leftSum[i - 1];          /* Construct the right array*/        for (j = n - 2; j >= 0; j--)            rightSum[j] = arr[j + 1] + rightSum[j + 1];          /* Construct the sum array using        left[] and right[] */        for (i = 0; i < n; i++)            Sum[i] = leftSum[i] + rightSum[i];          /*print the sum array*/        for (i = 0; i < n; i++)            document.write(Sum[i] + " ");    }         let arr = [ 3, 6, 4, 8, 9 ];    let n = arr.length;    sumArray(arr, n); </script>
27 24 26 22 21
 
Time Complexity: O(n) Space Complexity: O(n) Auxiliary Space: O(n)
The above method can be optimized to work in O(1) auxiliary space.
C++
Java
Python3
C#
PHP
Javascript
// C++ implementation of above approach#include <bits/stdc++.h>using namespace std; void sumArray(int arr[], int n){    int i, temp = 0;     /* Allocate memory for the sum array */    int Sum[n];     /* Initialize the sum array as 0 */    memset(Sum, 0, n);     /* In this loop, temp variable contains    sum of elements on left side excluding    arr[i] */    for (i = 0; i < n; i++) {        Sum[i] = temp;        temp += arr[i];    }     /* Initialize temp to 0 for sum on right    side */    temp = 0;     /* In this loop, temp variable contains    sum of elements on right side excluding        arr[i] */    for (i = n - 1; i >= 0; i--) {        Sum[i] += temp;        temp += arr[i];    }     for (i = 0; i < n; i++)        cout << Sum[i] << " ";} /* Driver program to test above function */int main(){    int arr[] = { 3, 6, 4, 8, 9 };    int n = sizeof(arr) / sizeof(arr[0]);    sumArray(arr, n);     return 0;}
// Java implementation of above approachimport java.util.*;import java.lang.*;import java.io.*; class Geeks {    public static void sumArray(int arr[], int n)    {        int i = 0, temp = 0;        int Sum[] = new int[n];         Arrays.fill(Sum, 0);         /* In this loop, temp variable contains           sum of elements on left side excluding           arr[i] */        for (i = 0; i < n; i++) {            Sum[i] = temp;            temp += arr[i];        }         /* Initialize temp to 0 for sum on right side */        temp = 0;         /* In this loop, temp variable contains           sum of elements on right side excluding           arr[i] */        for (i = n - 1; i >= 0; i--) {            Sum[i] += temp;            temp += arr[i];        }         for (i = 0; i < n; i++)            System.out.print(Sum[i] + " ");    }     /* Driver function to test above function*/    public static void main(String[] args)    {        int arr[] = { 3, 6, 4, 8, 9 };        int n = arr.length;        sumArray(arr, n);    }}
# Python3 implementation of above approachdef sumArray(arr, n):     i, temp = 0, 0     # Allocate memory for the sum array */    Sum = [0 for i in range(n)]     '''In this loop, temp variable contains    sum of elements on left side excluding    arr[i] '''    for i in range(n):        Sum[i] = temp        temp += arr[i]         # Initialize temp to 0 for sum    # on right side */    temp = 0     ''' In this loop, temp variable contains        sum of elements on right side excluding        arr[i] */'''    for i in range(n - 1, -1, -1):        Sum[i] += temp        temp += arr[i]         for i in range(n):        print(Sum[i], end = " ") # Driver Codearr = [ 3, 6, 4, 8, 9 ]n = len(arr)sumArray(arr, n) # This code is contributed by# Mohit Kumar 29
// C# implementation of above approachusing System;class Geeks {    public static void sumArray(int []arr, int n)    {        int i = 0, temp = 0;        int []Sum = new int[n];        for( i=0;i<n;i++)        Sum[i] = 0;         /* In this loop, temp variable contains        sum of elements on left side excluding        arr[i] */        for (i = 0; i < n; i++) {            Sum[i] = temp;            temp += arr[i];        }         /* Initialize temp to 0 for sum on right side */        temp = 0;         /* In this loop, temp variable contains        sum of elements on right side excluding        arr[i] */        for (i = n - 1; i >= 0; i--) {            Sum[i] += temp;            temp += arr[i];        }         for (i = 0; i < n; i++)            Console.Write(Sum[i] + " ");    }     /* Driver function to test above function*/    public static void Main()    {        int []arr = { 3, 6, 4, 8, 9 };        int n = arr.Length;        sumArray(arr, n);    }}// This code is contributed by inder_verma..
<?php// PHP implementation of above approachfunction sumArray($arr, $n){    $temp = 0;     /* Allocate memory for the sum array */    /* Initialize the sum array as 0 */    $Sum = array_fill(0, $n, 0);     /* In this loop, temp variable contains    sum of elements on left side excluding    arr[i] */    for ($i = 0; $i < $n; $i++)    {        $Sum[$i] = $temp;        $temp += $arr[$i];    }     /* Initialize temp to 0 for sum    on right side */    $temp = 0;     /* In this loop, temp variable contains    sum of elements on right side excluding    arr[i] */    for ($i = $n - 1; $i >= 0; $i--)    {        $Sum[$i] += $temp;        $temp += $arr[$i];    }     for ($i = 0; $i < $n; $i++)        echo $Sum[$i] . " ";} // Driver Code$arr = array( 3, 6, 4, 8, 9 );$n = count($arr);sumArray($arr, $n); // This code is contributed by// chandan_jnu?>
<script>    // Javascript implementation of above approach         function sumArray(arr, n)    {        let i = 0, temp = 0;        let Sum = new Array(n);        for( i=0;i<n;i++)            Sum[i] = 0;          /* In this loop, temp variable contains        sum of elements on left side excluding        arr[i] */        for (i = 0; i < n; i++) {            Sum[i] = temp;            temp += arr[i];        }          /* Initialize temp to 0 for sum on right side */        temp = 0;          /* In this loop, temp variable contains        sum of elements on right side excluding        arr[i] */        for (i = n - 1; i >= 0; i--) {            Sum[i] += temp;            temp += arr[i];        }          for (i = 0; i < n; i++)            document.write(Sum[i] + " ");    }         let arr = [ 3, 6, 4, 8, 9 ];    let n = arr.length;    sumArray(arr, n); // This code is contributed by decode2207.</script>
27 24 26 22 21
 
Time Complexity: O(n) Auxiliary Space: O(1) 
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mohit kumar 29
Chandan_Kumar
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