Construct an array from its pair-sum array

2.6

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.”

We strongly recommend to minimize your browser and try this yourself.

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 are C++ and Java implementations of the above idea.

C++

#include <iostream>
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;
}

Java

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 */


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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