Construct sum-array with sum of elements in given range

You are given an array of n-elements and an odd-integer m. You have to construct a new sum_array from given array such that sum_array[i] = Σarr[j] for (i-(m/2)) < j (i+(m/2)).
note : for 0 > j or j >= n take arr[j] = 0.

Examples:

Input : arr[] = {1, 2, 3, 4, 5}, 
            m = 3
Output : sum_array = {3, 6, 9, 12, 9}
Explanation : sum_array[0] = arr[0] + arr[1]
     sum_array[1] = arr[0] + arr[1] + arr[2]
     sum_array[2] = arr[1] + arr[2] + arr[3]
     sum_array[3] = arr[2] + arr[3] + arr[4]
     sum_array[4] = arr[3] + arr[4]

Input : arr[] = {2, 4, 3, 4, 2}, 
           m = 1
Output : sum_array = {2, 4, 3, 4, 2}
Explanation : sum_array[0] = arr[0] 
              sum_array[1] = arr[1]
              sum_array[2] = arr[2]
              sum_array[3] = arr[3]
              sum_array[4] = arr[4]



Basic Approach : As per problem statement, we calculate sum_array[i] by iterating over i-(m/2) to i+(m/2). According to this approach, we have a nested loop which will result into time complexity of O(n*m).

Efficient Approach : For calculating sum_array is to use sliding window concept and thus can easily save our time. For Sliding window, the time complexity is O(n).
Algorithm

  • calculate sum of first (m/2)+1 elements
  • sum_array[0] = sum
  • for i=1 to i<n
    • if( (i-(m/2)-1) >= 0 ) sum -= arr[(i-(m/2)-1)]
    • if( (i+m/2) < n) sum += arr[(i+m/2)]
    • sum_array[i] = sum
  • print sum_array

C++

filter_none

edit
close

play_arrow

link
brightness_4
code

// CPP Program to find sum array for a given
// array.
#include <bits/stdc++.h>
using namespace std;
  
// function to calc sum_array and print
void calcSum_array(int arr[], int n, int m)
{
    int sum = 0;
    int sum_array[n];
  
    // calc 1st m/2 + 1 element for 1st window
    for (int i = 0; i < m / 2 + 1; i++)
        sum += arr[i];
    sum_array[0] = sum;
  
    // use sliding window to
    // calculate rest of sum_array
    for (int i = 1; i < n; i++) {
        if (i - (m / 2) - 1 >= 0)
            sum -= arr[i - (m / 2) - 1];
        if (i + (m / 2) < n)
            sum += arr[i + (m / 2)];
        sum_array[i] = sum;
    }
  
    // print sum_array
    for (int i = 0; i < n; i++)
        cout << sum_array[i] << " ";
}
  
// driver program
int main()
{
    int arr[] = { 3, 6, 2, 7, 3, 8, 4, 
                      9, 1, 5, 0, 4 };
    int m = 5;
    int n = sizeof(arr) / sizeof(int);
    calcSum_array(arr, n, m);
    return 0;
}

chevron_right


Java

filter_none

edit
close

play_arrow

link
brightness_4
code

// Java Program to find sum array 
// for a given array.
class GFG 
{
    // function to calc sum_array and print
    static void calcSum_array(int arr[], int n, int m)
    {
        int sum = 0;
        int sum_array[] = new int[n];
      
        // calc 1st m/2 + 1 element
        // for 1st window
        for (int i = 0; i < m / 2 + 1; i++)
            sum += arr[i];
        sum_array[0] = sum;
      
        // use sliding window to
        // calculate rest of sum_array
        for (int i = 1; i < n; i++) 
        {
            if (i - (m / 2) - 1 >= 0)
                sum -= arr[i - (m / 2) - 1];
            if (i + (m / 2) < n)
                sum += arr[i + (m / 2)];
            sum_array[i] = sum;
        }
      
        // print sum_array
        for (int i = 0; i < n; i++)
            System.out.print(sum_array[i] + " ");
    }
      
    // Driver program
    public static void main(String[] args)
    {
        int arr[] = { 3, 6, 2, 7, 3, 8, 4, 9, 1, 5, 0, 4 };
        int m = 5;
        int n = arr.length;
        calcSum_array(arr, n, m);
    }
}
  
// This code is contributed by prerna saini.

chevron_right


Python3

filter_none

edit
close

play_arrow

link
brightness_4
code

# Python3 Program to find Sum array 
# for a given array.
import math as mt
  
# function to calc Sum_array and print
def calcSum_array(arr, n, m):
  
    Sum = 0
    Sum_array = [0 for i in range(n)]
  
    # calc 1st m/2 + 1 element for 1st window
    for i in range(m // 2 + 1):
        Sum += arr[i]
    Sum_array[0] = Sum
  
    # use sliding window to
    # calculate rest of Sum_array
    for i in range(1, n):
        if (i - (m // 2) - 1 >= 0):
            Sum -= arr[i - (m // 2) - 1]
        if (i + (m / 2) < n):
            Sum += arr[i + (m //2)]
        Sum_array[i] = Sum
      
    # prSum_array
    for i in range(n):
        print(Sum_array[i], end = " ")
  
# Driver Code
arr = [ 3, 6, 2, 7, 3, 8, 4, 9, 1, 5, 0, 4 ]
m = 5
n = len(arr)
calcSum_array(arr, n, m)
  
# This code is contributed by mohit kumar 29

chevron_right


C#

filter_none

edit
close

play_arrow

link
brightness_4
code

// C# Program to find sum array 
// for a given array.
using System;
  
class GFG 
{
    // function to calc sum_array and print
    static void calcSum_array(int []arr, int n, int m)
    {
        int sum = 0;
        int []sum_array = new int[n];
      
        // calc 1st m/2 + 1 element
        // for 1st window
        for (int i = 0; i < m / 2 + 1; i++)
            sum += arr[i];
        sum_array[0] = sum;
      
        // use sliding window to
        // calculate rest of sum_array
        for (int i = 1; i < n; i++) 
        {
            if (i - (m / 2) - 1 >= 0)
                sum -= arr[i - (m / 2) - 1];
            if (i + (m / 2) < n)
                sum += arr[i + (m / 2)];
            sum_array[i] = sum;
        }
      
        // print sum_array
        for (int i = 0; i < n; i++)
        Console.Write(sum_array[i] + " ");
    }
      
    // Driver program
    public static void Main()
    {
        int []arr = { 3, 6, 2, 7, 3, 8, 4, 9, 1, 5, 0, 4 };
        int m = 5;
        int n = arr.Length;
        calcSum_array(arr, n, m);
    }
}
  
// This code is contributed by vt_m.

chevron_right


PHP

filter_none

edit
close

play_arrow

link
brightness_4
code

<?php
// PHP Program to find sum array 
// for a given array.
  
// function to calc sum_array and print
function calcSum_array(&$arr, $n, $m)
{
    $sum = 0;
    $sum_array = array();
  
    // calc 1st m/2 + 1 element
    // for 1st window
    for ($i = 0; 
         $i < (int)($m / 2) + 1; $i++)
        $sum = $sum + $arr[$i];
    $sum_array[0] = $sum;
  
    // use sliding window to
    // calculate rest of sum_array
    for ($i = 1; $i < $n; $i++) 
    {
        if ($i - (int)($m / 2) - 1 >= 0)
            $sum = $sum - $arr[$i
                    (int)($m / 2) - 1];
        if ($i + (int)($m / 2) < $n)
            $sum = $sum + $arr[$i
                    (int)($m / 2)];
        $sum_array[$i] = $sum;
    }
  
    // print sum_array
    for ($i = 0; $i < $n; $i++)
        echo $sum_array[$i] . " ";
}
  
// Driver Code
$arr = array(3, 6, 2, 7, 3, 8, 
             4, 9, 1, 5, 0, 4 );
$m = 5;
$n = sizeof($arr);
calcSum_array($arr, $n, $m);
  
// This code is contributed by Mukul Singh
?>

chevron_right



Output:

11 18 21 26 24 31 25 27 19 19 10 9 


My Personal Notes arrow_drop_up

Discovering ways to develop a plane for soaring career goals

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.



Improved By : mohit kumar 29, Code_Mech



Article Tags :
Practice Tags :


Be the First to upvote.


Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.