Given ‘N’ number of sticks of length a1, a2, a3…an. The task is to count the number of squares and rectangles possible.
Note: One stick should be used only once i.e. either in any of the squares or rectangles.
Examples:
Input: arr[] = {1, 2, 1, 2} Output: 1 Rectangle with sides 1 1 2 2 Input: arr[] = {1, 2, 3, 4, 5, 6, 7, 8, 9} Output: 0 No square or rectangle is possible
Approach: Below is the step by step algorithm to solve this problem :
- Initialize the number of sticks.
- Initialize all the sticks with it’s lengths in an array.
- Sort the array in an increasing order.
- Calculate the number of pairs of sticks with the same length.
- Divide the total number of pairs by 2, which will be the total possible rectangle and square.
Below is the implementation of above approach:
C++
// C++ implementation of above approach #include <bits/stdc++.h> using namespace std;
// Function to find the possible // rectangles and squares int rectangleSquare( int arr[], int n)
{ // sort all the sticks
sort(arr, arr + n);
int count = 0;
// calculate all the pair of
// sticks with same length
for ( int i = 0; i < n - 1; i++) {
if (arr[i] == arr[i + 1]) {
count++;
i++;
}
}
// divide the total number of pair
// which will be the number of possible
// rectangle and square
return count / 2;
} // Driver code int main()
{ // initialize all the stick lengths
int arr[] = { 2, 2, 4, 4, 4, 4, 6, 6, 6, 7, 7, 9, 9 };
int n = sizeof (arr) / sizeof (arr[0]);
cout << rectangleSquare(arr, n);
return 0;
} |
Java
// Java implementation of above approach import java.util.Arrays;
class GFG
{ // Function to find the possible
// rectangles and squares
static int rectangleSquare( int arr[], int n)
{
// sort all the sticks
Arrays.sort(arr);
int count = 0 ;
// calculate all the pair of
// sticks with same length
for ( int i = 0 ; i < n - 1 ; i++)
{
if (arr[i] == arr[i + 1 ])
{
count++;
i++;
}
}
// divide the total number of pair
// which will be the number of possible
// rectangle and square
return count / 2 ;
}
// Driver code
public static void main(String[] args)
{
// initialize all the stick lengths
int arr[] = { 2 , 2 , 4 , 4 , 4 , 4 , 6 , 6 , 6 , 7 , 7 , 9 , 9 };
int n = arr.length;
System.out.println(rectangleSquare(arr, n));
}
} // This code is contributed // by PrinciRaj1992 |
Python3
# Python3 implementation of above approach # Function to find the possible # rectangles and squares def rectangleSquare( arr, n):
# sort all the sticks
arr.sort()
count = 0
#print(" xx",arr[6])
# calculate all the pair of
# sticks with same length
k = 0
for i in range (n - 1 ):
if (k = = 1 ):
k = 0
continue
if (arr[i] = = arr[i + 1 ]):
count = count + 1
k = 1
# divide the total number of pair
# which will be the number of possible
# rectangle and square
return count / 2
# Driver code if __name__ = = '__main__' :
# initialize all the stick lengths arr = [ 2 , 2 , 4 , 4 , 4 , 4 , 6 , 6 , 6 , 7 , 7 , 9 , 9 ]
n = len (arr)
print (rectangleSquare(arr, n))
# this code is written by ash264 |
C#
// C# implementation of above approach using System;
class GFG
{ // Function to find the possible
// rectangles and squares
static int rectangleSquare( int []arr, int n)
{
// sort all the sticks
Array.Sort(arr);
int count = 0;
// calculate all the pair of
// sticks with same length
for ( int i = 0; i < n - 1; i++)
{
if (arr[i] == arr[i + 1])
{
count++;
i++;
}
}
// divide the total number of pair
// which will be the number of possible
// rectangle and square
return count / 2;
}
// Driver code
public static void Main(String[] args)
{
// initialize all the stick lengths
int []arr = {2, 2, 4, 4, 4, 4, 6,
6, 6, 7, 7, 9, 9};
int n = arr.Length;
Console.WriteLine(rectangleSquare(arr, n));
}
} // This code has been contributed // by Rajput-Ji |
PHP
<?php // PHP implementation of above approach // Function to find the possible // rectangles and squares function rectangleSquare( $arr , $n )
{ // sort all the sticks
sort( $arr );
$count = 0;
// calculate all the pair of
// sticks with same length
for ( $i = 0; $i < $n - 1; $i ++)
{
if ( $arr [ $i ] == $arr [ $i + 1])
{
$count ++;
$i ++;
}
}
// divide the total number of pair
// which will be the number of possible
// rectangle and square
return ( $count / 2);
} // Driver code // initialize all the stick lengths $arr = array (2, 2, 4, 4, 4, 4, 6,
6, 6, 7, 7, 9, 9 );
$n = sizeof( $arr );
echo rectangleSquare( $arr , $n );
// This code is contributed by Sachin. ?> |
Javascript
<script> // javascript implementation of above approach // Function to find the possible // rectangles and squares function rectangleSquare(arr , n)
{ // sort all the sticks
arr.sort();
var count = 0;
// calculate all the pair of
// sticks with same length
for (i = 0; i < n - 1; i++)
{
if (arr[i] == arr[i + 1])
{
count++;
i++;
}
}
// divide the total number of pair
// which will be the number of possible
// rectangle and square
return count / 2;
} // Driver code // initialize all the stick lengths var arr = [2, 2, 4, 4, 4, 4, 6, 6, 6, 7, 7, 9, 9];
var n = arr.length;
document.write(rectangleSquare(arr, n)); // This code is contributed by 29AjayKumar </script> |
Output
3
Complexity Analysis:
- Time Complexity: O(n*log n) where n is the size of the array.
- Auxiliary Space: O(1)