# Count pairs from an array having product of their sum and difference equal to 1

Given an array **arr[]** of size **N**, the task is to count possible pairs of array elements **(arr[i], arr[j])** such that **(arr[i] + arr[j]) * (arr[i] â€“ arr[j])** is 1.

**Examples:**

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

The two possible pairs are:

- (arr[1] + arr[3]) * (arr[1] â€“ arr[3]) = 1
- (arr[2] + arr[3]) * (arr[2] â€“ arr[3]) = 1

Input:arr[] = {12, 0, 1, 1, 14, 0, 9, 0}Output:4Explanation:

The four possible pairs are as follows:

- (3, 6): (arr[3] + arr[6]) * (arr[3] â€“ arr[6]) = 1
- (4, 6): (arr[4] + arr[6]) * (arr[4] â€“ arr[6]) = 1
- (3, 8): (arr[3] + arr[8]) * (arr[3] â€“ arr[8]) = 1
- (3, 6): (arr[4] + arr[8]) * (arr[4] â€“ arr[8]) = 1

**Naive Approach:** The simplest approach is to traverse the array and generate all possible pairs from the given array and count those pairs whose product of sum and difference is 1. Finally, print the final count obtained after completing the above steps.

**Time Complexity:** O(N^{2})**Auxiliary Space:** O(N)

**Efficient Approach:** The given condition can be expressed for any pair of array elements **(arr[i], arr[j])** as:

(arr[i] + arr[j]) * (arr[i] – arr[j]) = 1

=> (arr[i]^{2}– arr[j]^{2}) = 1

Therefore, it can be concluded that the required conditions can be satisfied only by the pairs **arr[i] = 1** and **arr[j] = 0** and **i < j**. Follow the steps below to solve the problem:

- Initialize two variables,
**oneCount**and**desiredPairs**to store the count of 1s and required pairs respectively. - Traverse the given array and check the following:
**If arr[i] = 1:**Increment**oneCount**by**1**.**If arr[i] = 0:**Add the count of**1**s obtained so far to**desiredPairs**.

- After completing the above steps, print the value of
**desiredPairs**as the required answer.

Below is the implementation of the above approach:

## C++

`// C++ program for the above approach` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to count the desired` `// number of pairs` `int` `countPairs(` `int` `arr[], ` `int` `n)` `{` ` ` `// Initialize oneCount` ` ` `int` `oneCount = 0;` ` ` `// Initialize the desiredPair` ` ` `int` `desiredPair = 0;` ` ` `// Traverse the given array` ` ` `for` `(` `int` `i = 0; i < n; i++) {` ` ` `// If 1 is encountered` ` ` `if` `(arr[i] == 1) {` ` ` `oneCount++;` ` ` `}` ` ` `// If 0 is encountered` ` ` `if` `(arr[i] == 0) {` ` ` `// Update count of pairs` ` ` `desiredPair += oneCount;` ` ` `}` ` ` `}` ` ` `// Return the final count` ` ` `return` `desiredPair;` `}` `// Driver Code` `int` `main()` `{` ` ` `// Given array arr[]` ` ` `int` `arr[] = { 3, 1, 1, 0 };` ` ` `int` `N = ` `sizeof` `(arr) / ` `sizeof` `(arr[0]);` ` ` `// Function Call` ` ` `cout << countPairs(arr, N);` ` ` `return` `0;` `}` |

## Java

`// Java program for the above approach` `import` `java.io.*;` `class` `GFG{` `// Function to count the desired` `// number of pairs` `static` `int` `countPairs(` `int` `arr[], ` `int` `n)` `{` ` ` ` ` `// Initialize oneCount` ` ` `int` `oneCount = ` `0` `;` ` ` `// Initialize the desiredPair` ` ` `int` `desiredPair = ` `0` `;` ` ` `// Traverse the given array` ` ` `for` `(` `int` `i = ` `0` `; i < n; i++)` ` ` `{` ` ` ` ` `// If 1 is encountered` ` ` `if` `(arr[i] == ` `1` `)` ` ` `{` ` ` `oneCount++;` ` ` `}` ` ` `// If 0 is encountered` ` ` `if` `(arr[i] == ` `0` `)` ` ` `{` ` ` ` ` `// Update count of pairs` ` ` `desiredPair += oneCount;` ` ` `}` ` ` `}` ` ` `// Return the final count` ` ` `return` `desiredPair;` `}` `// Driver Code` `public` `static` `void` `main(String[] args)` `{` ` ` ` ` `// Given array arr[]` ` ` `int` `arr[] = { ` `3` `, ` `1` `, ` `1` `, ` `0` `};` ` ` `int` `N = arr.length;` ` ` `// Function call` ` ` `System.out.println(countPairs(arr, N));` `}` `}` `// This code is contributed by sanjoy_62` |

## Python3

`# Python3 program for the above approach` `# Function to count the desired` `# number of pairs` `def` `countPairs(arr, n):` ` ` ` ` `# Initialize oneCount` ` ` `oneCount ` `=` `0` ` ` `# Initialize the desiredPair` ` ` `desiredPair ` `=` `0` ` ` `# Traverse the given array` ` ` `for` `i ` `in` `range` `(n):` ` ` `# If 1 is encountered` ` ` `if` `(arr[i] ` `=` `=` `1` `):` ` ` `oneCount ` `+` `=` `1` ` ` `# If 0 is encountered` ` ` `if` `(arr[i] ` `=` `=` `0` `):` ` ` `# Update count of pairs` ` ` `desiredPair ` `+` `=` `oneCount` ` ` `# Return the final count` ` ` `return` `desiredPair` `# Driver Code` `if` `__name__ ` `=` `=` `'__main__'` `:` ` ` ` ` `# Given array arr[]` ` ` `arr ` `=` `[ ` `3` `, ` `1` `, ` `1` `, ` `0` `]` ` ` `N ` `=` `len` `(arr)` ` ` ` ` `# Function call` ` ` `print` `(countPairs(arr, N))` `# This code is contributed by mohit kumar 29` |

## C#

`// C# program for the above approach` `using` `System;` `class` `GFG{` `// Function to count the desired` `// number of pairs` `static` `int` `countPairs(` `int` `[]arr, ` `int` `n)` `{` ` ` ` ` `// Initialize oneCount` ` ` `int` `oneCount = 0;` ` ` `// Initialize the desiredPair` ` ` `int` `desiredPair = 0;` ` ` `// Traverse the given array` ` ` `for` `(` `int` `i = 0; i < n; i++)` ` ` `{` ` ` ` ` `// If 1 is encountered` ` ` `if` `(arr[i] == 1)` ` ` `{` ` ` `oneCount++;` ` ` `}` ` ` `// If 0 is encountered` ` ` `if` `(arr[i] == 0)` ` ` `{` ` ` ` ` `// Update count of pairs` ` ` `desiredPair += oneCount;` ` ` `}` ` ` `}` ` ` `// Return the readonly count` ` ` `return` `desiredPair;` `}` `// Driver Code` `public` `static` `void` `Main(String[] args)` `{` ` ` ` ` `// Given array []arr` ` ` `int` `[]arr = { 3, 1, 1, 0 };` ` ` `int` `N = arr.Length;` ` ` `// Function call` ` ` `Console.WriteLine(countPairs(arr, N));` `}` `}` `// This code is contributed by gauravrajput1` |

## Javascript

`<script>` `// Javascript program for the above approach` `// Function to count the desired` `// number of pairs` `function` `countPairs(arr, n)` `{` ` ` ` ` `// Initialize oneCount` ` ` `let oneCount = 0;` ` ` ` ` `// Initialize the desiredPair` ` ` `let desiredPair = 0;` ` ` ` ` `// Traverse the given array` ` ` `for` `(let i = 0; i < n; i++)` ` ` `{` ` ` ` ` `// If 1 is encountered` ` ` `if` `(arr[i] == 1)` ` ` `{` ` ` `oneCount++;` ` ` `}` ` ` ` ` `// If 0 is encountered` ` ` `if` `(arr[i] == 0)` ` ` `{` ` ` ` ` `// Update count of pairs` ` ` `desiredPair += oneCount;` ` ` `}` ` ` `}` ` ` ` ` `// Return the final count` ` ` `return` `desiredPair;` `}` `// Driver Code` `// Given array arr[]` `let arr = [ 3, 1, 1, 0 ];` `let N = arr.length;` `// Function call` `document.write(countPairs(arr, N));` `// This code is contributed by target_2` `</script>` |

**Output:**

2

**Time Complexity:** O(N)**Auxiliary Space:** O(N)