Maximize sum by picking Array element to left of each '1' of a Binary String

Given a binary string S and an array arr[] each of size N, we can pick any element from the Array which is to the left of (or at the same position) the indices of '1's in the given binary string. The task is to find the maximum possible sum.

Examples:

Input: arr[] = {20, 10, 30, 9, 20, 9}, string S = "011011", N = 6
Output: 80
Explanation: Pick 20, 10, 30 and 20 in Sum, so, Sum = 80.

Input:  arr[] = {30, 20, 10}, string S = "000", N = 3.
Output: 0

Approach: The given problem can be solved by using a priority queue based on the following idea:

Say there are K occurrences of '1' in string S. It can be seen that we can arrange the characters in a way such that we can pick the K maximum elements from the array which are to the left of the last occurrence of '1' in S. So we can use a priority queue to get these K maximum elements.

Follow the steps to solve this problem:

• Initialize variable Sum = 0, Cnt = 0.
• Create a priority queue (max heap) and traverse from i = 0 to N-1:
  • If S[i] is '1', increment Cnt by 1.
  • Else, while Cnt > 0, add the topmost element of the priority queue and decrement Cnt by 1.
  • Push the i^th element of the array into the priority queue.
• After executing the loop, while Cnt > 0, add the topmost element of the priority queue and decrement Cnt by 1.
• At last, return the Sum as the required answer.

Below is the implementation of the above approach.

// C++ code to implement the approach

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

// Function to find maximum Sum
int findMaxSum(int* arr, string s, int n)
{
    // Initialize variables
    int Cnt = 0, Sum = 0;

    priority_queue<int> pq;

    // Traverse the string
    for (int i = 0; i < n; i++) {
        if (s[i] == '1') {
            Cnt++;
        }
        else {
            while (Cnt != 0) {
                Sum += pq.top();
                pq.pop();
                Cnt--;
            }
        }

        // Push the element of array in pq
        pq.push(arr[i]);
    }

    while (Cnt != 0) {
        Sum += pq.top();
        pq.pop();
        Cnt--;
    }

    // Return Max Sum
    return Sum;
}

// Driver Code
int main()
{
    int N = 6;
    string S = "011011";
    int arr[] = { 20, 10, 30, 9, 20, 9 };

    // Function Call
    cout << findMaxSum(arr, S, N) << endl;

    return 0;
}

// Java code to implement the approach

import java.io.*;
import java.util.*;

public class GFG 
{
  
  // Function to find maximum Sum
  static int findMaxSum(int[] arr, String s, int n)
  {
    
    // Initialize variables
    int Cnt = 0, Sum = 0;
    PriorityQueue<Integer> pq
      = new PriorityQueue<Integer>(
      Collections.reverseOrder());
    
    // Traverse the string
    for (int i = 0; i < n; i++) {
      if (s.charAt(i) == '1') {
        Cnt++;
      }
      else {
        while (Cnt != 0) {
          Sum += pq.peek();
          pq.poll();
          Cnt--;
        }
      }

      // Push the element of array in pq
      pq.add(arr[i]);
    }

    while (Cnt != 0) {
      Sum += pq.peek();
      pq.poll();
      Cnt--;
    }

    // Return Max Sum
    return Sum;
  }

  // Driver Code
  public static void main(String[] args)
  {
    int N = 6;
    String S = "011011";
    int[] arr = { 20, 10, 30, 9, 20, 9 };

    // Function Call
    System.out.println(findMaxSum(arr, S, N));

    return;
  }
}

// This code is contributed by garg28harsh.

# Python code to implement the approach
import heapq

# Function to find maximum Sum
def findMaxSum(arr, s, n):
  
    # Initialize variables
    Cnt, Sum = 0, 0
    pq = []
    heapq._heapify_max(pq)

    # Traverse the string
    for i in range(n):
        if(s[i] == '1'):
            Cnt += 1
        else:
            while(Cnt is not 0):
                Sum += heapq.heappop(pq)
                heapq._heapify_max(pq)
                Cnt -= 1

        # Push the element of array in pq
        heapq.heappush(pq, arr[i])
        heapq._heapify_max(pq)

    while(Cnt is not 0):
        Sum += heapq.heappop(pq)
        heapq._heapify_max(pq)
        Cnt -= 1

    # Return Max Sum
    return Sum

N = 6
S = "011011"
arr = [20, 10, 30, 9, 20, 9]

# Function call
print(findMaxSum(arr, S, N))

# This code is contributed by lokesh

// C# code to implement the approach
using System;
using System.Collections.Generic;
using System.Linq;

class Program {
    // Function to find maximum Sum
    static int findMaxSum(int[] arr, string s, int n)
    {
        // Initialize variables
        int Cnt = 0, Sum = 0;
        List<int> pq = new List<int>();

        // Traverse the string
        for (int i = 0; i < n; i++) {
            pq.Sort((a, b) => b.CompareTo(a));
            if (s[i] == '1') {
                Cnt++;
            }
            else {
                while (Cnt != 0) {
                    pq.Sort((a, b) => b.CompareTo(a));
                    Sum += pq[0];
                    pq.RemoveAt(0);
                    Cnt--;
                }
            }

            // Push the element of array in pq
            pq.Add(arr[i]);
        }

        while (Cnt != 0) {
            pq.Sort((a, b) => b.CompareTo(a));
            Sum += pq[0];
            pq.RemoveAt(0);
            Cnt--;
        }

        // Return Max Sum
        return Sum;
    }

    // Driver Code
    public static void Main(string[] args)
    {
        int N = 6;
        string S = "011011";
        int[] arr = { 20, 10, 30, 9, 20, 9 };

        // Function Call
        Console.WriteLine(findMaxSum(arr, S, N));
    }
}

// This code is contributed by Tapesh(tapeshdua420)

    // Javascript code to implement the approach
    
    // Function to find maximum Sum
    function findMaxSum(arr, s, n)
    {
        // Initialize variables
        let Cnt = 0;
        let Sum = 0;
    
        pq=[];
    
        // Traverse the string
        for (let i = 0; i < n; i++) {
            if (s[i] == '1') {
                Cnt++;
            }
            else {
                while (Cnt != 0) {
                    Sum += pq[pq.length-1];
                    pq.pop();
                    Cnt--;
                }
            }
    
            // Push the element of array in pq
            pq.push(arr[i]);
            pq.sort((a,b)=>a-b);
        }
    
        while (Cnt != 0) {
            Sum += pq[pq.length-1];
            pq.pop();
            Cnt--;
        }
    
        // Return Max Sum
        return Sum;
    }
    
    // Driver Code
        let N = 6;
        let S = "011011";
        let arr = [ 20, 10, 30, 9, 20, 9 ];
    
        // Function Call
        console.log(findMaxSum(arr, S, N));
        
        // This code is contributed by Pushpesh Raj.
        

80

Time Complexity: O(N * log N)
Auxiliary Space: O(N)