What is the time complexity of Flip String to Monotone Increasing?

The optimal solution has a time complexity of O(n).

What data structures are used to solve Flip String to Monotone Increasing?

This problem uses String, Dynamic Programming. Understanding these concepts is essential for solving this Medium problem efficiently.

What are the key insights for solving Flip String to Monotone Increasing?

Insight 1: The core idea is to iterate through the string and, for each position, consider it as the potential boundary between the 0s and the 1s. We can calculate the flips needed if we make all characters before this position '0' and all characters after it '1'. Insight 2: We can maintain two variables: one to track the number of '1's encountered so far (representing the cost of flipping them to '0's) and another to track the minimum number of flips needed so far.

Which companies ask LeetCode 926. Flip String to Monotone Increasing in interviews?

This problem is frequently asked at IBM, Snap.

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Flip String to Monotone Increasing - LeetCode 926 Solution

Flip String to Monotone Increasing - Complete Solution Guide

Flip String to Monotone Increasing is LeetCode problem 926, a Medium level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3, java, cpp, c.

Problem Statement

A binary string is monotone increasing if it consists of some number of 0 's (possibly none), followed by some number of 1 's (also possibly none). You are given a binary string s . You can flip s[i] changing it from 0 to 1 or from 1 to 0 . Return the minimum number of flips to make s monotone increasing . Example 1: Input: s = "00110" Output: 1 Explanation: We flip the last digit to get 00111. Example 2: Input: s = "010110" Output: 2 Explanation: We flip to get 011111, or alternatively 000111.

Detailed Explanation

The problem asks us to find the minimum number of flips required to transform a given binary string `s` into a monotone increasing string. A monotone increasing binary string consists of a sequence of 0s (possibly none) followed by a sequence of 1s (also possibly none). We are allowed to flip any character in the string, changing a '0' to a '1' or a '1' to a '0'. The goal is to minimize the total number of flips needed to achieve the monotone increasing property.

Solution Approach

The solution uses a dynamic programming approach with constant space. It iterates through the string, maintaining a count of '1's encountered so far (`ones_count`) and the minimum flips required (`flips_count`). When a '0' is encountered, it means we have two options: either flip the current '0' to a '1' or flip all the preceding '1's to '0's. We choose the option that results in the minimum number of flips.

Step-by-Step Algorithm

Step 1: Initialize `ones_count` and `flips_count` to 0.
Step 2: Iterate through the input string `s` character by character.
Step 3: If the current character is '1', increment `ones_count`.
Step 4: If the current character is '0', update `flips_count` by taking the minimum of `flips_count + 1` (flipping the current '0' to '1') and `ones_count` (flipping all preceding '1's to '0').
Step 5: After iterating through the entire string, return `flips_count`.

Key Insights

Insight 1: The core idea is to iterate through the string and, for each position, consider it as the potential boundary between the 0s and the 1s. We can calculate the flips needed if we make all characters before this position '0' and all characters after it '1'.
Insight 2: We can maintain two variables: one to track the number of '1's encountered so far (representing the cost of flipping them to '0's) and another to track the minimum number of flips needed so far.
Insight 3: The minimum flips at any point is either flipping the current '0' to a '1' (increasing the `flips_count`) or flipping all preceding '1's to '0's (represented by `ones_count`). We always choose the minimum of the two.

Complexity Analysis

Time Complexity: O(n)

Space Complexity: O(1)

Topics

This problem involves: String, Dynamic Programming.

Companies

Asked at: IBM, Snap.

Flip String to Monotone Increasing | LeetCode 926

Medium

String Dynamic Programming

Time: O(n)Space: O(1)

Solution Code

Available in:

class Solution {
    public int minFlipsMonoIncr(String s) {
        int ones_count = 0;
        int flips_count = 0;
        for (char charr : s.toCharArray()) {
            if (charr == '1') {
                ones_count += 1;
            } else {
                flips_count = Math.min(flips_count + 1, ones_count);
            }
        }
        return flips_count;
    }
}

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Problem Info

Description

Problem 926: Flip String to Monotone Increasing - Detailed explanation and solution approaches.

Topics

String Dynamic Programming

Companies

IBMSnap

Stats

Difficulty:Medium

Languages:4

Companies:2

Problem #:926

Problem Explanation

💡

Think Before You Code

🤔 Ask Yourself

→What is the input? What output do I need?
→Can I solve a smaller version of this problem first?
→What patterns have I seen in similar problems?

✏️ Try This First

Before looking at the solution, try to solve it on paper with a simple example!

🚀 Try on LeetCode

Solution Approach

📋

Step-by-Step Solution

5 steps

1
Step 1: Initialize `ones_count` and `flips_count` to 0.
2
Step 2: Iterate through the input string `s` character by character.
3
Step 3: If the current character is '1', increment `ones_count`.
4
Step 4: If the current character is '0', update `flips_count` by taking the minimum of `flips_count + 1` (flipping the current '0' to '1') and `ones_count` (flipping all preceding '1's to '0').
5
Step 5: After iterating through the entire string, return `flips_count`.

💡

Pro Tip for Students

Try tracing through each step with a small example on paper before coding. Understanding "why" each step happens is more important than memorizing the code!

⚡

Complexity Analysis

⏱️

Time Complexity

O(n)

👍 Linear - Good! Visits each element once.

💾

Space Complexity

O(1)

💪 Constant space - Uses same memory regardless of input!

📝

Why?

The time complexity is O(n) because the algorithm iterates through each character of the input string once. The space complexity is O(1) because only two integer variables are used, regardless of the size of the input string.

📖New to Big O? Click to learn more

Big O Notation - Quick Guide

O(1)Best - Instant

O(log n)Excellent - Binary Search

O(n)Good - One loop

O(n log n)OK - Sorting

O(n²)Slow - Nested loops

O(2ⁿ)Very Slow - Recursion

Alternative Approaches

Dynamic Programming with 2D array

We can create a 2D DP array where dp[i][0] stores the minimum flips needed to make the first i characters monotone increasing ending with '0', and dp[i][1] stores the minimum flips needed to make the first i characters monotone increasing ending with '1'.

Time: O(n)Space: O(n)

Trade-offs: This approach uses O(n) space compared to O(1) space of the optimal solution. It might be easier to understand for some, but less efficient in terms of space.

✨

Key Insights

1Insight 1: The core idea is to iterate through the string and, for each position, consider it as the potential boundary between the 0s and the 1s. We can calculate the flips needed if we make all characters before this position '0' and all characters after it '1'.
2Insight 2: We can maintain two variables: one to track the number of '1's encountered so far (representing the cost of flipping them to '0's) and another to track the minimum number of flips needed so far.
3Insight 3: The minimum flips at any point is either flipping the current '0' to a '1' (increasing the `flips_count`) or flipping all preceding '1's to '0's (represented by `ones_count`). We always choose the minimum of the two.

📚

Key Terms Explained

For Students

Dynamic Programming

Breaking complex problems into smaller subproblems and storing results.

String

A sequence of characters. Like a word or sentence in programming!

Edge Cases

Edge case 1: Empty string. The code implicitly handles this case because the loop won't execute, and the initial value of `flips_count` (0) will be returned, which is correct.
Edge case 2: String consisting only of '0's. In this case, `ones_count` remains 0 throughout, and `flips_count` increments in each iteration until it becomes 0. Then the min function always chooses zero. Therefore, the result is 0, which is correct.
Edge case 3: String consisting only of '1's. In this case, `flips_count` remains 0, and the result is 0, which is correct.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Not considering the case where flipping all preceding '1's to '0's might be better than flipping the current '0' to '1'.

✗Common mistake 2: Failing to initialize `flips_count` and `ones_count` to 0, leading to incorrect results.

✗Common mistake 3: Incorrectly implementing the minimum calculation, especially in languages without a built-in `min` function (as seen in the initial C code before edits).

✅

Learning Tip

Every mistake is a learning opportunity! When you make an error, understand why it happened before moving on.

🌍

Where is This Used in Real Life?

💼Real-world scenario 1: Data cleaning and preprocessing. When dealing with noisy binary data, this algorithm can be used to correct errors and enforce monotonicity.

🏦Real-world scenario 2: Signal processing. In signal processing, sometimes we want to approximate a signal with a monotone increasing or decreasing function. This problem provides a simplified version of this concept.

💡Understanding real-world applications helps you see the "why" behind algorithms. It's not just about passing interviews—these concepts power the apps and websites you use every day!

Author's Notes

💡 Key Insight

String problems often involve sliding windows or two pointers. Consider if the character set is limited (lowercase letters = only 26 possibilities).

🎯 Interview Tip

Consider multiple approaches before coding. Mentioning alternatives shows breadth of knowledge.

⚠️ Watch Out

Mutating strings directly in languages where strings are immutable. Use StringBuilder or arrays.

Written by Saswata Mondal

Software Engineer • Algorithms Enthusiast • Interview Coach

👨‍💻

About the Author

👨‍💻

Saswata MondalAuthor400+ LC Problems

B.Tech CSE, IEM Kolkata | LeetCode Rating: 1672 (Top 15%)

Certified: IBM Java Developer, NPTEL Programming in Java

Last updated: June 27, 2024LeetCode Profile GitHub

This solution has been crafted based on my experience solving 400+ LeetCode problems. Each explanation is designed to help you understand the underlying concepts, not just memorize the code.

Community Tips & Insights

The key insight here is recognizing the pattern. Once you see it, the solution becomes straightforward.

@AlgoMasterJul 14

I was asked this exact problem at my Google interview. The interviewer wanted me to optimize space complexity.

@InterviewProJul 7

❓

Frequently Asked Questions

How do I handle string manipulation efficiently?

In languages with immutable strings (Java, Python, C#), use StringBuilder/list to avoid O(n) concatenation cost. Consider using character arrays for in-place modifications. For pattern matching, consider KMP or Rabin-Karp for O(n+m) complexity.

How do I identify if a problem needs dynamic programming?

DP problems typically have: 1) Overlapping subproblems (same calculation repeated), 2) Optimal substructure (optimal solution uses optimal solutions to subproblems). Look for keywords like "minimum/maximum," "count ways," "is it possible," or "longest/shortest."

What techniques are commonly tested in medium-difficulty problems?

Medium problems often require combining multiple techniques: two-pointer with hash maps, BFS/DFS with state tracking, dynamic programming with optimization, or divide-and-conquer approaches. They test your ability to recognize patterns and choose the right combination of techniques.

How should I practice algorithm problems effectively?

Focus on understanding patterns rather than memorizing solutions. After solving a problem, review optimal solutions and understand the intuition. Group similar problems to recognize patterns. Practice explaining your approach out loud. Review problems after a few days to test retention.

What is the optimal approach for "Flip String to Monotone Increasing"?

For this medium-level String problem, the key is to identify the core pattern. Analyze the input constraints to determine acceptable time complexity. Consider whether dynamic programming techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

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