# 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.”

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[].