Ways to divide a binary array into sub-arrays such that each sub-array contains exactly one 1

Give an integer array arr[] consisting of elements from the set {0, 1}. The task is to print the number of ways the array can be divided into sub-arrays such that each sub-array contains exactly one 1.

Examples:

Input: arr[] = {1, 0, 1, 0, 1}
Output: 4
Below are the possible ways:



  • {1, 0}, {1, 0}, {1}
  • {1}, {0, 1, 0}, {1}
  • {1, 0}, {1}, {0, 1}
  • {1}, {0, 1}, {0, 1}

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

Approach:

  • When all the elements of the array are 0 then the result will be zero.
  • Else, between two adjacent ones we must have only one separation. So, answer equals to product of values posi + 1 – posi (for all valid pairs) where posi is the position of ith 1.

Below is the implementation of the above approach:

C++

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// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
  
// Function to return the number of ways
// the array can be divided into sub-arrays
// satisfying the given condition
int countWays(int arr[], int n)
{
  
    int pos[n], p = 0, i;
  
    // for loop for saving the positions of all 1s
    for (i = 0; i < n; i++) {
        if (arr[i] == 1) {
            pos[p] = i + 1;
            p++;
        }
    }
  
    // If array contains only 0s
    if (p == 0)
        return 0;
  
    int ways = 1;
    for (i = 0; i < p - 1; i++) {
        ways *= pos[i + 1] - pos[i];
    }
  
    // Return the total ways
    return ways;
}
  
// Driver code
int main()
{
    int arr[] = { 1, 0, 1, 0, 1 };
    int n = sizeof(arr) / sizeof(arr[0]);
    cout << countWays(arr, n);
    return 0;
}

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Java

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// Java implementation of the approach
class GFG
{
      
// Function to return the number of ways
// the array can be divided into sub-arrays
// satisfying the given condition
static int countWays(int arr[], int n)
{
    int pos[] = new int[n]; 
    int p = 0, i;
  
    // for loop for saving the 
    // positions of all 1s
    for (i = 0; i < n; i++) 
    {
        if (arr[i] == 1
        {
            pos[p] = i + 1;
            p++;
        }
    }
  
    // If array contains only 0s
    if (p == 0)
        return 0;
  
    int ways = 1;
    for (i = 0; i < p - 1; i++) 
    {
        ways *= pos[i + 1] - pos[i];
    }
  
    // Return the total ways
    return ways;
}
  
// Driver code
public static void main(String args[])
{
    int[] arr = { 1, 0, 1, 0, 1 };
    int n = arr.length;
    System.out.println(countWays(arr, n));
}
}
  
// This code is contributed 
// by Akanksha Rai

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Python3

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# Python 3 implementation of the approach
  
# Function to return the number of ways
# the array can be divided into sub-arrays
# satisfying the given condition
def countWays(are, n):
    pos = [0 for i in range(n)]
    p = 0
  
    # for loop for saving the positions
    # of all 1s
    for i in range(n):
        if (arr[i] == 1):
            pos[p] = i + 1
            p += 1
  
    # If array contains only 0s
    if (p == 0):
        return 0
  
    ways = 1
    for i in range(p - 1):
        ways *= pos[i + 1] - pos[i]
  
    # Return the total ways
    return ways
  
# Driver code
if __name__ == '__main__':
    arr = [1, 0, 1, 0, 1]
    n = len(arr)
    print(countWays(arr, n))
      
# This code is contributed by
# Surendra_Gangwar

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C#

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// C# implementation of the approach
using System;
  
class GFG
{
      
// Function to return the number of ways
// the array can be divided into sub-arrays
// satisfying the given condition
static int countWays(int[] arr, int n)
{
    int[] pos = new int[n]; 
    int p = 0, i;
  
    // for loop for saving the positions
    // of all 1s
    for (i = 0; i < n; i++) 
    {
        if (arr[i] == 1) 
        {
            pos[p] = i + 1;
            p++;
        }
    }
  
    // If array contains only 0s
    if (p == 0)
        return 0;
  
    int ways = 1;
    for (i = 0; i < p - 1; i++) 
    {
        ways *= pos[i + 1] - pos[i];
    }
  
    // Return the total ways
    return ways;
}
  
// Driver code
public static void Main()
{
    int[] arr = { 1, 0, 1, 0, 1 };
    int n = arr.Length;
    Console.Write(countWays(arr, n));
}
}
  
// This code is contributed 
// by Akanksha Rai

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PHP

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<?php
// PHP implementation of the approach 
  
// Function to return the number of ways 
// the array can be divided into sub-arrays 
// satisfying the given condition 
function countWays($arr, $n
    $pos = array_fill(0, $n, 0); 
    $p = 0 ;
  
    // for loop for saving the positions
    // of all 1s 
    for ($i = 0; $i < $n; $i++)
    
        if ($arr[$i] == 1) 
        
            $pos[$p] = $i + 1; 
            $p++; 
        
    
  
    // If array contains only 0s 
    if ($p == 0) 
        return 0; 
  
    $ways = 1; 
    for ($i = 0; $i < $p - 1; $i++) 
    
        $ways *= $pos[$i + 1] - $pos[$i]; 
    
  
    // Return the total ways 
    return $ways
  
// Driver code 
$arr = array(1, 0, 1, 0, 1); 
$n = sizeof($arr); 
echo countWays($arr, $n); 
  
// This code is contributed by Ryuga
?>

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Output:

4


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