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++
#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 */ |
Python3
# 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 |
C#
// 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 |
PHP
<?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 ?> |
Output :
8 7 5 3 2
Time complexity of constructArr() is O(n) where n is number of elements in arr[].
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