Given a N x N Chessboard. The task is to count distinct rectangles from the chessboard. For example, if the input is 8 then the output should be 36.
Examples:
Input: N = 4 Output: 10 Input: N = 6 Output: 21
Approach:
Suppose N = 8 i.e. 8 x 8 chessboard is given, So different rectangles that can be formed are:
1 x 1, 1 x 2, 1 x 3, 1 x 4, 1 x 5, 1 x 6, 1 x 7, 1 x 8 = 8
2 x 2, 2 x 3, 2 x 4, 2 x 5, 2 x 6, 2 x 7, 2 x 8 = 7
3 x 3, 3 x 4, 3 x 5, 3 x 6, 2 x 7, 3 x 8 = 6
4 x 4, 4 x 5, 4 x 6, 4 x 7, 4 x 8 = 5
5 x 5, 5 x 6, 5 x 7, 5 x 8 = 4
6 x 6, 6 x 7, 6 x 8 = 3
7 x 7, 7 x 8 = 2
8 x 8 = 1
So total unique rectangles formed = 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 36 which is the sum of the first 8 natural numbers. So in general, distinct rectangles that can be formed in N x N chessboard is:
Sum of the first N natural numbers = N*(N+1)/2
= 8*(8+1)/2
= 36
Below is the implementation of the above approach:
C++
// C++ code to count distinct rectangle in a chessboard#include <bits/stdc++.h> using namespace std; // Function to return the count // of distinct rectangles int count(int N){ int a = 0; a = (N * (N + 1)) / 2; return a;}// Driver Codeint main(){ int N = 4; cout<<count(N); }// This code is contributed by nidhi16bcs2007 |
Java
// Java program to count unique rectangles in a chessboardclass Rectangle { // Function to count distinct rectangles static int count(int N) { int a = 0; a = (N * (N + 1)) / 2; return a; } // Driver Code public static void main(String args[]) { int n = 4; System.out.print(count(n)); }} |
Python3
# Python code to count distinct rectangle in a chessboard# Function to return the count # of distinct rectangles def count(N): a = 0; a = (N * (N + 1)) / 2; return int(a);# Driver CodeN = 4;print(count(N)); # This code has been contributed by 29AjayKumar |
C#
// C# program to count unique rectangles in a chessboard using System;class Rectangle { // Function to count distinct rectangles static int count(int N) { int a = 0; a = (N * (N + 1)) / 2; return a; } // Driver Code public static void Main() { int n = 4; Console.Write(count(n)); } } // This code is contributed by AnkitRai01 |
Javascript
// Javascript program to count unique rectangles in a chessboard // Function to count distinct rectangles function count(N) { var a = 0; a = (N * (N + 1)) / 2; return a; } // Driver Code var n = 4; document.write(count(n)); // This code is contributed by bunnyram19. |
Output:
10
Time Complexity: O(1)
Auxiliary Space: O(1)
Feeling lost in the world of random DSA topics, wasting time without progress? It’s time for a change! Join our DSA course, where we’ll guide you on an exciting journey to master DSA efficiently and on schedule.
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!
… [Trackback]
[…] Read More to that Topic: geeksforgeeks.org/count-distinct-rectangles-in-n-n-chessboard/ […]
… [Trackback]
[…] Find More here to that Topic: geeksforgeeks.org/count-distinct-rectangles-in-n-n-chessboard/ […]