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Php Program to Count 1’s in a sorted binary array

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Given a binary array sorted in non-increasing order, count the number of 1’s in it. 

Examples: 

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

Input: arr[] = {1, 1, 1, 1, 1, 1, 1}
Output: 7

Input: arr[] = {0, 0, 0, 0, 0, 0, 0}
Output: 0

A simple solution is to linearly traverse the array. The time complexity of the simple solution is O(n). We can use Binary Search to find count in O(Logn) time. The idea is to look for last occurrence of 1 using Binary Search. Once we find the index last occurrence, we return index + 1 as count.
The following is the implementation of above idea. 

PHP




<?php
// PHP program to count one's in a
// boolean array
  
/* Returns counts of 1's in arr[low..high].
The array is assumed to be sorted in 
non-increasing order */
function countOnes( $arr, $low, $high)
{
    if ($high >= $low)
    {
        // get the middle index
        $mid = $low + ($high - $low)/2;
      
        // check if the element at middle
        // index is last 1
        if ( ($mid == $high or $arr[$mid+1] == 0) 
                           and ($arr[$mid] == 1))
            return $mid+1;
      
        // If element is not last 1, recur for 
        // right side
        if ($arr[$mid] == 1)
            return countOnes($arr, ($mid + 1),
                                          $high);
      
        // else recur for left side
        return countOnes($arr, $low, ($mid -1));
    }
      
    return 0;
}
  
/* Driver code */
$arr = array(1, 1, 1, 1, 0, 0, 0);
$n = count($arr);
echo "Count of 1's in given array is "
                      countOnes($arr, 0, $n-1);
  
// This code is contributed by anuj_67.
?>


Output

Count of 1's in given array is 4

Time complexity of the above solution is O(Logn)

Space complexity o(log n) (function call stack)

Please refer complete article on Count 1’s in a sorted binary array for more details!


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Last Updated : 27 Dec, 2021
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