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PHP Program to Count number of binary strings without consecutive 1’s

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  • Last Updated : 16 Jun, 2022

Given a positive integer N, count all possible distinct binary strings of length N such that there are no consecutive 1’s.

Examples:

Input:  N = 2
Output: 3
// The 3 strings are 00, 01, 10

Input: N = 3
Output: 5
// The 5 strings are 000, 001, 010, 100, 101

Recommended: Please solve it on “PRACTICE ” first, before moving on to the solution.

PHP




<?php
// PHP program to count all distinct
// binary stringswithout two
// consecutive 1's
 
function countStrings($n)
{
    $a[$n] = 0;
    $b[$n] = 0;
    $a[0] = $b[0] = 1;
    for ($i = 1; $i < $n; $i++)
    {
        $a[$i] = $a[$i - 1] +
                 $b[$i - 1];
        $b[$i] = $a[$i - 1];
    }
    return $a[$n - 1] +
           $b[$n - 1];
}
 
    // Driver Code
    echo countStrings(3) ;
 
// This code is contributed by nitin mittal
?>

Output:

5

Time Complexity: O(n)
Auxiliary Space: O(n)

Please refer complete article on Count number of binary strings without consecutive 1’s for more details!

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