Minimum number of deletions from front and back of given Array to make count of 0 and 1 equal

Given an array arr[] consisting of only 0 and 1. The task is to find the minimum number of deletions from the front and back of the array, such that the new modified array consists of an equal number of 0’s and 1’s.

Examples:

Input: arr[] = {1, 1, 0, 1}
Output: 2
Explanation: Two ones from the starting or first and last element can be removed
Input: arr[] = {0, 1, 1, 1, 0}
Output: 3
Explanation: First three elements can be removed or last three elements

Approach: The problem can be solved using greedy approach. As each element of the array can be either 0 or 1, so consider 0 as -1 and 1 as 1 itself. Then find the largest subarray that consists of an equal number of 1s and 0s. Then subtract the size of this subarray from the total size of the array. This approach works because at any moment the approach tries to keep the size of the subarray as large as possible so that only a minimum number of elements from the ends can be removed. See the following diagram for a better understanding.

As it can be seen from the diagram, as the size of middle part y increases which consists of an equal number of 0s and 1s, automatically the size of part (x + z) decreases.

Below is the implementation of the above approach.

C++

// C++ code for the above approach
#include <bits/stdc++.h>
using namespace std;
 
// Function to calculate
// the minimum number of deletions
int solve(vector<int> arr)
{
 
    // Size of the array
    int sz = arr.size();
 
    // Store running sum of array
    int summe = 0;
 
    // To store index of the sum
    unordered_map<int, int> index;
 
    // Initially sum is 0 with index -1
    index[summe] = -1;
 
    // Store length of largest subarray
    int ans = 0, curr_len = 0;
 
    for (int i = 0; i < sz; i++) {
 
        // If curr_element is 0, add -1
        if (arr[i] == 0)
            summe -= 1;
 
        // If curr_element is 1, add 1
        else
            summe += 1;
 
        // Check if sum already occurred
        if (index.find(summe) != index.end()) {
 
            // Calculate curr subarray length
            curr_len = i - index[summe];
 
            // Store the maximum value
            // in the ans
            ans = max(ans, curr_len);
        }
 
        // Sum occurring for the first time
        // So store this sum with current index
        else
            index[summe] = i;
    }
 
    // Return diff between size
    // and largest subarray
    return (sz - ans);
}
 
// Driver code
int main()
{
    vector<int> arr = { 1, 1, 0, 1 };
    int val = solve(arr);
    cout << val;
}
 
// This code is contributed by Samim Hossain Mondal.

Java

// Java code for the above approach
import java.util.*;
 
class GFG{
 
  // Function to calculate
  // the minimum number of deletions
  static int solve(int[] arr)
  {
 
    // Size of the array
    int sz = arr.length;
 
    // Store running sum of array
    int summe = 0;
 
    // To store index of the sum
    HashMap<Integer,Integer> index = new HashMap<Integer,Integer>();
 
    // Initially sum is 0 with index -1
    index.put(summe, -1);
 
    // Store length of largest subarray
    int ans = 0, curr_len = 0;
 
    for (int i = 0; i < sz; i++) {
 
      // If curr_element is 0, add -1
      if (arr[i] == 0)
        summe -= 1;
 
      // If curr_element is 1, add 1
      else
        summe += 1;
 
      // Check if sum already occurred
      if (index.containsKey(summe) ) {
 
        // Calculate curr subarray length
        curr_len = i - index.get(summe);
 
        // Store the maximum value
        // in the ans
        ans = Math.max(ans, curr_len);
      }
 
      // Sum occurring for the first time
      // So store this sum with current index
      else
        index.put(summe, i);
    }
 
    // Return diff between size
    // and largest subarray
    return (sz - ans);
  }
 
  // Driver code
  public static void main(String[] args)
  {
    int []arr = { 1, 1, 0, 1 };
    int val = solve(arr);
    System.out.print(val);
  }
}
 
// This code is contributed by 29AjayKumar

Python3

# Python code to implement the given approach
from collections import defaultdict
 
class Solution:
     
    # Function to calculate
    # the minimum number of deletions
    def solve(self, arr):
 
        # Size of the array
        size = len(arr)
 
        # Store running sum of array
        summe = 0
 
        # To store index of the sum
        index = defaultdict(int)
 
        # Initially sum is 0 with index -1
        index[summe] = -1
 
        # Store length of largest subarray
        ans = 0
 
        for i in range(size):
 
            # If curr_element is 0, add -1
            if (arr[i] == 0):
                summe -= 1
 
            # If curr_element is 1, add 1
            else:
                summe += 1
 
            # Check if sum already occurred
            if (summe in index):
 
                # Calculate curr subarray length
                curr_len = i - index[summe]
 
                # Store the maximum value
                # in the ans
                ans = max(ans, curr_len)
 
            # Sum occurring for the first time
            # So store this sum with current index
            else:
                index[summe] = i
 
        # Return diff between size
        # and largest subarray
        return (size - ans)
 
 
if __name__ == "__main__":
    arr = [1, 1, 0, 1]
    obj = Solution()
    val = obj.solve(arr)
    print(val)

C#

// C# code for the above approach
using System;
using System.Collections.Generic;
class GFG{
 
  // Function to calculate
  // the minimum number of deletions
  static int solve(int[] arr)
  {
 
    // Size of the array
    int sz = arr.Length;
 
    // Store running sum of array
    int summe = 0;
 
    // To store index of the sum
    Dictionary<int,int> index = new Dictionary<int, int>();
 
    // Initially sum is 0 with index -1
    index.Add(summe, -1);
 
    // Store length of largest subarray
    int ans = 0, curr_len = 0;
 
    for (int i = 0; i < sz; i++) {
 
      // If curr_element is 0, add -1
      if (arr[i] == 0)
        summe -= 1;
 
      // If curr_element is 1, add 1
      else
        summe += 1;
 
      // Check if sum already occurred
      if (index.ContainsKey(summe) ) {
 
        // Calculate curr subarray length
        curr_len = i - index[summe];
 
        // Store the maximum value
        // in the ans
        ans = Math.Max(ans, curr_len);
      }
 
      // Sum occurring for the first time
      // So store this sum with current index
      else
        index[summe] = i;
    }
 
    // Return diff between size
    // and largest subarray
    return (sz - ans);
  }
 
  // Driver code
  public static void Main()
  {
    int []arr = { 1, 1, 0, 1 };
    int val = solve(arr);
    Console.Write(val);
  }
}
 
// This code is contributed by gfgking

Javascript

<script>
        // JavaScript code for the above approach
 
        // Function to calculate
        // the minimum number of deletions
        function solve(arr)
        {
 
            // Size of the array
            size = arr.length
             
            // Store running sum of array
            let summe = 0
 
            // To store index of the sum
            index = new Map();
 
            // Initially sum is 0 with index -1
            index.set(summe, -1);
 
            // Store length of largest subarray
            ans = 0
 
            for (let i = 0; i < size; i++) {
 
                // If curr_element is 0, add -1
                if (arr[i] == 0)
                    summe -= 1
 
                // If curr_element is 1, add 1
                else
                    summe += 1
 
                // Check if sum already occurred
                if (index.has(summe)) {
 
                    // Calculate curr subarray length
                    curr_len = i - index.get(summe)
 
                    // Store the maximum value
                    // in the ans
                    ans = Math.max(ans, curr_len)
                }
                 
                // Sum occurring for the first time
                // So store this sum with current index
                else
                    index.set(summe, i)
            }
             
            // Return diff between size
            // and largest subarray
            return (size - ans)
        }
 
        // Driver code
        arr = [1, 1, 0, 1]
        val = solve(arr)
        document.write(val)
 
  // This code is contributed by Potta Lokesh
    </script>