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PHP Program to Count Sets of 1s and 0s in a Binary Matrix

Last Updated : 22 Jul, 2024

Given a N x M Binary Matrix, count the number of sets where a set can be formed one or more same values in a row or column.

Examples:

Input: [[ 1, 0, 1 ],
           [ 0, 1, 0 ]] 
Output: 8 
Explanation: There are six one-element sets (three 1s and three 0s). 
There are two two - element sets, the first one consists of the first 
and the third cells of the first row. The second one consists of the 
first and the third cells of the second row. 

Input: [[ 1, 0 ],
             [ 1, 1 ]] 
Output: 6

The number of non-empty subsets of x elements is 2^x – 1. We traverse every row and calculate numbers of 1’s and 0’s cells. For every u zeros and v ones, total sets is 2^u – 1 + 2^v – 1. We then traverse all columns and compute same values and compute overall sum. We finally subtract m x n from the overall sum as single elements are considered twice.

PHP

<?php
// PHP program to compute number of sets
// in a binary matrix.

// Number of columns
$m = 3; 

// Number of rows
$n = 2; 

// Function to calculate the number 
// of non empty sets of cell
function countSets($a) { 
    global $m, $n;
    
    // Stores the final answer 
    $res = 0;
    
    // Traverses row-wise 
    for ($i = 0; $i < $n; $i++) {
        $u = 0; $v = 0; 
        for ( $j = 0; $j < $m; $j++) 
            $a[$i][$j] ? $u++ : $v++;     
        $res += pow(2, $u) - 1 + pow(2, $v) - 1; 
    } 
    
    // Traverses column wise 
    for ($i = 0; $i < $m; $i++) {
        $u = 0;$v = 0; 
        for ($j = 0; $j < $n; $j++) 
            $a[$j][$i] ? $u++ : $v++; 
        $res += pow(2, $u) - 1 + 
                pow(2, $v) - 1; 
    }
    
    // At the end subtract
    // n*m as no of single
    // sets have been added 
    // twice.
    return $res-($n*$m);
}

// Driver Code
$a = array(array(1, 0, 1),
           array(0, 1, 0));
    
echo countSets($a); 
    
?>

Output

Time Complexity: O(n * m)

Space Complexity: O(1) as no extra space has been taken.

Please refer complete article on Counting sets of 1s and 0s in a binary matrix for more details!

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