Minimum Operations to Equalize Binary String — Algorithm Visualization & Coding Challenge

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Understanding Minimum Operations to Equalize Binary String

Detailed explanation and reference materials

Problem Overview

🔥 Minimum Operations to Equalize Binary String

Difficulty: 🔴 Hard
Topics: • Greedy • Parity

🧠 Problem Statement

You are given:

A binary string s
An integer k

⚙️ Operation Rule

In one operation, you must:

Choose exactly k different indices
Flip each selected character:
- '0' → '1'
- '1' → '0'

🎯 Goal

Return the minimum number of operations required to make all characters equal to '1'.

If it is not possible, return:

-1

📌 Example 1

Input

s = "110"
k = 1

Output

Explanation

There is one '0' in the string.

Since k = 1, we can flip it directly in one operation.

📌 Example 2

Input

s = "0101"
k = 3

Output

Explanation

One optimal sequence:

Operation 1:
Flip indices [0, 1, 3]

"0101" → "1000"

Operation 2:
Flip indices [1, 2, 3]

"1000" → "1111"

✅ Minimum operations = 2

📌 Example 3

Input

s = "101"
k = 2

Output

-1

Explanation

There is only one '0', but each operation must flip exactly 2 indices.

⚠️ Impossible to make all characters '1'.

📊 Constraints

1 <= s.length <= 10^5
s[i] is either '0' or '1'
1 <= k <= s.length

💡 Key Insight Hint

Each operation flips exactly k bits.

Think in terms of:

Number of zeros
Parity (even/odd flips)
Mathematical feasibility

💻 Java Implementation

java

public class Main {

    public static int minimumOperations(String s, int k) {

        int n = s.length();
        int zeroCount = 0;

        // Count number of zeros
        for (int i = 0; i < n; i++) {
            if (s.charAt(i) == '0') {
                zeroCount++;
            }
        }

        // If already all 1s
        if (zeroCount == 0) {
            return 0;
        }

        // Try possible number of operations
        for (int t = 1; t <= n; t++) {

            int totalFlips = t * k;

            // Condition 1: must flip at least all zeros
            if (totalFlips < zeroCount) continue;

            // Condition 2: extra flips must be even
            if ((totalFlips - zeroCount) % 2 == 0) {
                return t;
            }
        }

        return -1;
    }

    public static void main(String[] args) {

        // Hardcoded test cases

        String s1 = "110";
        int k1 = 1;

        String s2 = "0101";
        int k2 = 3;

        String s3 = "101";
        int k3 = 2;
        int ans1 = minimumOperations(s1, k1);
        int ans2 = minimumOperations(s1, k1);
        int ans3 = minimumOperations(s1, k1);
        System.out.println("Example 1 Output: " + ans1);
        System.out.println("Example 2 Output: " + ans2);
        System.out.println("Example 3 Output: " + ans3);
    }
}

— Written by Saurabh Patil • B.Tech CSE • Software Developer

Reference Link

https://leetcode.com/problems/minimum-operations-to-equalize-binary-string/description/

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Minimum Operations to Equalize Binary String — Algorithm Visualization & Coding Challenge

Choose Your Learning Path

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🎯 Challenge Mode

Watch algorithms run step by step.

Understanding Minimum Operations to Equalize Binary String

Problem Overview

🔥 Minimum Operations to Equalize Binary String

🧠 Problem Statement

⚙️ Operation Rule

🎯 Goal

📌 Example 1

Input

Output

Explanation

📌 Example 2

Input

Output

Explanation

📌 Example 3

Input

Output

Explanation

📊 Constraints

💡 Key Insight Hint

💻 Java Implementation

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