How do you solve Flip String to Monotone Increasing on LeetCode?

Flip String to Monotone Increasing (LeetCode #926) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(1) space complexity. Key insight: The key to solving this problem is recognizing that you can count the number of flips needed efficiently by maintaining a running total of 1's and 0's.

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

The optimal solution for Flip String to Monotone Increasing runs in O(n) time and uses O(1) space. This approach runs in linear time because we only make a single pass through the string, maintaining a constant amount of extra space.

What is the brute force solution for Flip String to Monotone Increasing?

The brute force approach for Flip String to Monotone Increasing is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves checking every possible way to flip bits in the string to see how many flips are needed to make it monotone increasing. This is straightforward but inefficient. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Flip String to Monotone Increasing?

Flip String to Monotone Increasing uses the following concepts: String, Dynamic Programming. The recommended patterns to study are: Two Pointers, Dynamic Programming.

What are the interview tips for Flip String to Monotone Increasing?

Always start with a brute force solution to understand the problem better before optimizing. Explain your thought process clearly to the interviewer as you work through the problem. Practice writing clean and efficient code, as this will help you avoid common pitfalls during interviews.

What are common mistakes when solving Flip String to Monotone Increasing?

Students often forget to consider the edge cases where the string is already monotone increasing. Some may miscalculate the number of flips needed at each split point in the brute force method, leading to incorrect results.

#926

Flip String to Monotone Increasing

Medium

StringDynamic ProgrammingTwo PointersDynamic Programming

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(1)

💡

Intuition

Time O(n)Space O(1)

The optimal approach uses a single pass to count the number of flips needed to convert the string into a monotone increasing format. This is efficient because we only need to keep track of the number of 1's and 0's as we iterate through the string.

⚙️

Algorithm

4 steps

1Step 1: Initialize two counters: one for the number of 1's seen so far and another for the total flips needed.
2Step 2: Iterate through the string, updating the count of 1's and calculating the flips needed if the current character is 0.
3Step 3: At each character, calculate the total flips required if we decide to make all characters to the left 0's and all characters to the right 1's.
4Step 4: Keep track of the minimum flips encountered during the iteration.

solution.py13 lines

1# Full working Python code
2
3def minFlipsMonoIncr(s):
4    count1 = 0
5    flips = 0
6    min_flips = float('inf')
7    for char in s:
8        if char == '1':
9            count1 += 1
10        else:
11            flips += 1
12        min_flips = min(min_flips, flips + count1)
13    return min_flips

ℹ

Complexity note: This approach runs in linear time because we only make a single pass through the string, maintaining a constant amount of extra space.

1The key to solving this problem is recognizing that you can count the number of flips needed efficiently by maintaining a running total of 1's and 0's.
2The optimal solution leverages the idea of cumulative counts to minimize the number of passes through the string.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.