Is Flip String to Monotone Increasing easy or hard?

Flip String to Monotone Increasing is classified as a Medium problem. The challenge comes from recognizing the optimal greedy dynamic programming strategy instead of trying all possible flips. Once the prefix-based decision logic is understood, the implementation becomes short and efficient.

Flip String to Monotone Increasing Python/Java solution

In Python or Java, the optimal implementation uses two integer variables: one for the number of ones seen so far and one for the minimum flips required. Iterate through the string characters, update counters based on whether the character is '0' or '1', and compute the minimum flips using a simple min operation. The implementation runs in O(n) time and O(1) space.

How to solve Flip String to Monotone Increasing in O(n)?

Iterate through the string while tracking two variables: the number of '1's seen so far and the minimum flips required. When encountering a '0', choose the cheaper option between flipping that '0' to '1' or flipping all previous '1's to '0'. Update the running minimum using min(flips + 1, ones). This single-pass dynamic programming method achieves O(n) time.

What is the best approach for Flip String to Monotone Increasing?

The Dynamic Programming approach is typically the best solution. It scans the string once while maintaining the number of ones seen and the minimum flips required so far. Each time a '0' appears after some '1's, you decide whether to flip the current '0' or flip previous '1's. This achieves O(n) time and O(1) space.

Is Flip String to Monotone Increasing asked at Google/Amazon/Meta?

Flip String to Monotone Increasing appears in interviews at companies that emphasize string processing and dynamic programming patterns. Variations of the problem have been reported in interviews at companies like Amazon, Google, and Meta because it tests greedy reasoning and prefix-based DP optimization.

What data structure is used in Flip String to Monotone Increasing?

The problem mainly relies on string traversal and counting rather than complex data structures. Solutions typically use prefix sum arrays or constant-space counters to track the number of ones and flips. The key technique is dynamic programming on prefixes of the string.

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

The optimal solutions run in O(n) time where n is the length of the string. Both the Prefix Sum method and the Dynamic Programming approach process the string linearly. The prefix sum approach may use O(n) extra space, while the optimized DP solution only uses O(1) space.

Description Solution Video 15:05

926. Flip String to Monotone Increasing

Medium61.5% acceptance5 companies

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.

Example 3:

Input: s = "00011000"
Output: 2
Explanation: We flip to get 00000000.

Constraints:

1 <= s.length <= 10⁵
s[i] is either '0' or '1'.

Asked at 5 companies

Expedia

IBM Amazon

Google Meta

Topics

Dynamic Programming String

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926. Flip String to Monotone Increasing

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