Construct an array from its pair-sum array

Given a pair-sum array and size of the original array (n), construct the original array.

A pair-sum array for an array is the array that contains sum of all pairs in ordered form. For example pair-sum array for arr[] = {6, 8, 3, 4} is {14, 9, 10, 11, 12, 7}.

In general, pair-sum array for arr[0..n-1] is {arr[0]+arr[1], arr[0]+arr[2], ……., arr[1]+arr[2], arr[1]+arr[3], ……., arr[2]+arr[3], arr[2]+arr[4], …., arr[n-2]+arr[n-1}.

“Given a pair-sum array, construct the original array.”

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Let the given array be “pair[]” and let there be n elements in original array. If we take a look at few examples, we can observe that arr[0] is half of pair[0] + pair[1] – pair[n-1]. Note that the value of pair[0] + pair[1] – pair[n-1] is (arr[0] + arr[1]) + (arr[0] + arr[2]) – (arr[1] + arr[2]).
Once we have evaluated arr[0], we can evaluate other elements by subtracting arr[0]. For example arr[1] can be evaluated by subtracting arr[0] from pair[0], arr[2] can be evaluated by subtracting arr[0] from pair[1].

Following is the implementation of the above idea.

C++

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#include <bits/stdc++.h>
using namespace std;
  
// Fills element in arr[] from its pair sum array pair[]. 
// n is size of arr[]
void constructArr(int arr[], int pair[], int n)
{
    arr[0] = (pair[0]+pair[1]-pair[n-1]) / 2;
    for (int i=1; i<n; i++)
        arr[i] = pair[i-1]-arr[0];
}
  
// Driver program to test above function
int main()
{
    int pair[] = {15, 13, 11, 10, 12, 10, 9, 8, 7, 5};
    int n = 5;
    int arr[n];
    constructArr(arr, pair, n);
    for (int i = 0; i < n; i++)
        cout << arr[i] << " ";
    return 0;
}

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Java














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import java.io.*; 


  


class PairSum { 


      


    // Fills element in arr[] from its pair sum array pair[].  


    // n is size of arr[] 


    static void constructArr(int arr[], int pair[], int n) 


    { 


        arr[0] = (pair[0]+pair[1]-pair[n-1]) / 2; 


        for (int i=1; i<n; i++) 


            arr[i] = pair[i-1]-arr[0]; 


    } 


      


    // Driver program to test above function 


    public static void main(String[] args) 


    { 


        int pair[] = {15, 13, 11, 10, 12, 10, 9, 8, 7, 5}; 


        int n = 5; 


        int[] arr = new int[n]; 


        constructArr(arr, pair, n); 


        for (int i = 0; i < n; i++) 


            System.out.print(arr[i]+" ");         


    } 


} 


/* This code is contributed by Devesh Agrawal */



















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Python3














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# Fills element in arr[] from its  


# pair sum array pair[].  


# n is size of arr[]  


  


def constructArr(arr,pair,n): 


    arr [0] = (pair[0]+pair[1]-pair[n-1])//2


    for i in range(1,n): 


        arr[i] = pair[i-1]-arr[0] 


  


# Driver code 


if __name__=='__main__': 


    pair = [15, 13, 11, 10, 12, 10, 9, 8, 7, 5] 


    n =5


    arr = [0]*n 


    constructArr(arr,pair,n) 


    for i in range(n): 


        print(arr[i],end =" ") 


  


# This code is contributed by  


# Shrikant13 



















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C#














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// C# program to construct an 


// array from its pair-sum array 


using System; 


  


class PairSum  


{ 


    // Fills element in arr[] from its 


    // pair sum array pair[].  


    // n is size of arr[] 


    static void constructArr(int []arr, int []pair, 


                                             int n) 


    { 


        arr[0] = (pair[0] + pair[1] - pair[n - 1]) / 2; 


        for (int i = 1; i < n; i++) 


            arr[i] = pair[i - 1] - arr[0]; 


    } 


      


    // Driver program to test above function 


    public static void Main() 


    { 


        int []pair = {15, 13, 11, 10, 12, 


                         10, 9, 8, 7, 5}; 


        int n = 5; 


        int []arr = new int[n]; 


        constructArr(arr, pair, n); 


        for (int i = 0; i < n; i++) 


            Console.Write(arr[i] + " ");      


    } 


} 


  


// This code is contributed by nitin mittal 



















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PHP














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<?php 


// Fills element in arr[] from   


// its pair sum array pair[].  


// n is size of arr[] 


function constructArr($pair) 


{ 


    $arr = array(); 


    $n = 5; 


    $arr[0] = intval(($pair[0] + $pair[1] -  


                      $pair[$n - 1]) / 2); 


    for ($i = 1; $i < $n; $i++) 


        $arr[$i] = $pair[$i - 1] - $arr[0]; 


          


    for ($i = 0; $i < $n; $i++) 


        echo $arr[$i] . " ";  


} 


  


// Driver Code 


$pair = array(15, 13, 11, 10,  


              12, 10, 9, 8, 7, 5); 


constructArr($pair); 


  


// This code is contributed by Sam007 


?> 



















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Output :


 8 7 5 3 2 


Time complexity of constructArr() is O(n) where n is number of elements in arr[].


This article is contributed by Abhishek. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.


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