Cost required to make all array elements equal to 1

Given a binary array arr[] of size N, the task is to find the total cost required to make all array elements equal to 1, where the cost of converting any 0 to 1 is equal to the count of 1s present before that 0.

Examples:

Input: arr[] = {1, 0, 1, 0, 1, 0}
Output: 9
Explanation:
Following operations are performed:

1. Converting arr[1] to 1 modifies arr[] to {1, 1, 1, 0, 1, 0}. Cost = 1.
2. Converting arr[3] to 1 modifies arr[] to {1, 1, 1, 1, 1, 0}. Cost = 3.
3. Converting arr[5] to 1 modifies arr[] to {1, 1, 1, 1, 1, 5}. Cost = 5.

Therefore, the total cost is 1 + 3 + 5 = 9.

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

Naive Approach: The simplest approach to solve the given problem is to traverse the array arr[] and count the numbers of 1s present before every index containing 0 and print the sum of all the costs obtained. 

Implementation:

C++

#include <iostream>
using namespace std;

int getTotalCost(int arr[],int N) {
   int countones = 0;
  int cost=0;
   for (int i = 0; i <N; i++) {
       if(arr[i]==1)
       {
           countones++;
           continue;
       }
       if (arr[i] == 0) {
           cost += countones;
         countones++;
       }
   }
   return cost;
}

int main() {
   int arr[] = {1,0,1,0,1,0};

   int N = sizeof(arr) / sizeof(arr[0]);
   cout <<getTotalCost(arr,N)<<endl;

   return 0;
}

Output

9

Time Complexity: O(N), where N is the size of the array.
Auxiliary Space: O(1), as we are not using any extra array.

Efficient Approach: The above approach can be optimized by observing the fact that after converting every 0 to 1, the count of 1s present before every 0 is given by the index at which 0 occurs. Therefore, the task is to traverse the given array and print all the sum of all the indices having 0s in the array arr[].

Below is the implementation of the above approach: 

C++

// C++ program for the above approach

#include <bits/stdc++.h>
using namespace std;

// Function to calculate the cost required
// to make all array elements equal to 1
int findCost(int A[], int N)
{
    // Stores the total cost
    int totalCost = 0;

    // Traverse the array arr[]
    for (int i = 0; i < N; i++) {

        // If current element is 0
        if (A[i] == 0) {

            // Convert 0 to 1
            A[i] = 1;

            // Add the cost
            totalCost += i;
        }
    }

    // Return the total cost
    return totalCost;
}

// Driver Code
int main()
{
    int arr[] = { 1, 0, 1, 0, 1, 0 };
    int N = sizeof(arr) / sizeof(arr[0]);
    cout << findCost(arr, N);

    return 0;
}

Java

// Java program for the above approach

class GFG{

// Function to calculate the cost required
// to make all array elements equal to 1
static int findCost(int[] A, int N)
{

    // Stores the total cost
    int totalCost = 0;

    // Traverse the array arr[]
    for(int i = 0; i < N; i++)
    {

        // If current element is 0
        if (A[i] == 0)
        {

            // Convert 0 to 1
            A[i] = 1;

            // Add the cost
            totalCost += i;
        }
    }

    // Return the total cost
    return totalCost;
}

// Driver Code
public static void main(String[] args)
{
    int[] arr = { 1, 0, 1, 0, 1, 0 };
    int N = arr.length;

    System.out.println(findCost(arr, N));
}
}

// This code is contributed by ukasp

Python3

# Python3 program for the above approach

# Function to calculate the cost required
# to make all array elements equal to 1
def findCost(A, N):

    # Stores the total cost
    totalCost = 0

    # Traverse the array arr[]
    for i in range(N):

        # If current element is 0
        if (A[i] == 0):

            # Convert 0 to 1
            A[i] = 1

            # Add the cost
            totalCost += i

    # Return the total cost
    return totalCost

# Driver Code
if __name__ == '__main__':

    arr = [ 1, 0, 1, 0, 1, 0 ]
    N = len(arr)

    print(findCost(arr, N))

# This code is contributed by Shivam Singh

C#

// C# program for the above approach
using System;
using System.Collections.Generic;

class GFG{

// Function to calculate the cost required
// to make all array elements equal to 1
static int findCost(int []A, int N)
{

    // Stores the total cost
    int totalCost = 0;

    // Traverse the array arr[]
    for(int i = 0; i < N; i++)
    {

        // If current element is 0
        if (A[i] == 0)
        {

            // Convert 0 to 1
            A[i] = 1;

            // Add the cost
            totalCost += i;
        }
    }

    // Return the total cost
    return totalCost;
}

// Driver Code
public static void Main()
{
    int []arr = { 1, 0, 1, 0, 1, 0 };
    int N = arr.Length;

    Console.Write(findCost(arr, N));
}
}

// This code is contributed by SURENDRA_GANGWAR

Javascript

<script>


// Javascript program for the above approach

// Function to calculate the cost required
// to make all array elements equal to 1
function findCost(A, N)
{
    // Stores the total cost
    var totalCost = 0;

    var i;
    // Traverse the array arr[]
    for (i = 0; i < N; i++) {

        // If current element is 0
        if (A[i] == 0) {

            // Convert 0 to 1
            A[i] = 1;

            // Add the cost
            totalCost += i;
        }
    }

    // Return the total cost
    return totalCost;
}

// Driver Code
    var arr = [1, 0, 1, 0, 1, 0]
    var N = arr.length
    document.write(findCost(arr, N));

</script>

Output:

9

Time Complexity: O(N)
Auxiliary Space: O(1)