Construct Sum Array with Sum of Elements in Given Range in C++

Given an array arr[ ] containing integers only and an odd number sum. The goal is to create a sum array arr_2[ ] such each arr_2[i] is the sum of previous sum/2 elements of arr[] + arr[i] + next sum/2 elements of arr[]. If sum is 1 then arr_2[i]=arr[i]

For Example

Input

arr[] = { 4, 1, 7, 5, 2, 9} sum=3

Output

Construction of sum-array with sum of elements in given range are: 5 12 13 14
16 17 17 9 3

Explanation

The sum array is constructed as:
arr_2[0]=arr[0]+arr[1] = 4+1 = 5
arr_2[1]=arr[0]+arr[1]+arr[2] = 4+1+7 = 12
arr_2[2]=arr[1]+arr[2]+arr[3] = 1+7+5 = 13
arr_2[3]=arr[2]+arr[3]+arr[4] = 7+5+2 = 14
arr_2[4]=arr[3]+arr[4]+arr[5] = 5+2+9 = 16
arr_2[5]=arr[4]+arr[5] = 2+9 = 11s

Input

arr[] = { 1,2,3,4,5 } sum=5

Output

Construction of sum-array with sum of elements in given range are − 6 10 15 14
12

Explanation

The sum array is constructed as:
arr_2[0]=arr[0]+arr[1]+arr[2] = 1+2+3 = 6
arr_2[1]=arr[0]+arr[1]+arr[2]+arr[3] = 1+2+3+4= 10
arr_2[2]=arr[0]+arr[1]+arr[2]+arr[3]+arr[4] = 1+2+3+4+5 = 15
arr_2[3]=arr[1]+arr[2]+arr[3]+arr[4] = 2+3+4+5= 14
arr_2[4]=arr[2]+arr[3]+arr[4]= 3+4+5 = 12

Approach used in the below program is as follows −

In this approach we will use the sliding window concept. Add the next rightmost element to the previous window sum and remove the leftmost element from that.

• Take an integer array arr[] and a value sum as input.

• Function sum_array(int arr[], int size, int sum) returns the sum-array with sum of elements in the given range.

• Take the initial count as 0.

• Take the sum array as arr_2[size].

• Take temp = sum / 2 + 1.

• Add temp number of elements from 0 to temp to count. And set arr_2[0] as count.

• For next elements of sum array, traverse using for loop from i=1 to i<size.

• Take temp_1 = i − (sum / 2) − 1. If it is >=0 then subtract arr[temp_1] from count.

• Take temp_2 = i + (sum / 2). If it is < size then add arr[temp_2] to count.

• Set arr_2[i] = count.

• At the end of for loop we will have arr_2[] as a sum array.

• Print the sum array arr_2[] using for loop.

Example

 Live Demo

#include <bits/stdc++.h>
using namespace std;
void sum_array(int arr[], int size, int sum){
   int count = 0;
   int arr_2[size];
   int temp = sum / 2 + 1;
   for (int i = 0; i < temp; i++){
      count = count + arr[i];
   }
   arr_2[0] = count;
   for (int i = 1; i < size; i++){
      int temp_1 = i − (sum / 2) − 1;
      if (temp_1 >= 0){
         count = count − arr[temp_1];
      }
      int temp_2 = i + (sum / 2);
      if (temp_2 < size){
         count = count + arr[temp_2];
      }
      arr_2[i] = count;
   }
   cout<<"Construction of sum−array with sum of elements in given range are: ";
   for (int i = 0; i < size; i++){
      cout<< arr_2[i] << " ";
   }
}
int main(){
   int arr[] = { 4, 1, 7, 5, 2, 9, 6, 2, 1 };
   int sum = 3;
   int size = sizeof(arr) / sizeof(int);
   sum_array(arr, size, sum);
   return 0;
}

Output

If we run the above code it will generate the following output −

Construction of sum-array with sum of elements in given range are − 5 12 13 14 16 17 17 9 3