Flip String to Monotone Increasing

LeetCode 926, Medium. Topics: String, Dynamic Programming, Greedy. View on LeetCode. Generate this problem as a practice environment: tested reference solution, 16 parametrized pytest cases, and a playground notebook:

lcpy gen -n 926   # by problem number
lcpy gen -s flip_string_to_monotone_increasing   # by problem name

Problem

A binary string is monotone increasing if it consists of some number of <code>0</code>‘s (possibly none), followed by some number of <code>1</code>‘s (also possibly none). You are given a binary string <code>s</code>. You can flip <code>s[i]</code> changing it from <code>0</code> to <code>1</code> or from <code>1</code> to <code>0</code>. Return the minimum number of flips to make <code>s</code> monotone increasing.

Examples

Input: s = "00110"
Output: 1
Explanation: We flip the last digit to get 00111.

Input: s = "010110"
Output: 2
Explanation: We flip to get 011111, or alternatively 000111.

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

Constraints

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

Solution

Reference implementation from solution.py on GitHub, full suite in test_solution.py:

class Solution:
    # Time: O(?)
    # Space: O(?)
    def min_flips_mono_increasing(self, s: str) -> int:
        ones = 0
        flips = 0
        for char in s:
            if char == "1":
                ones += 1
            else:
                # Either flip this 0 to 1, or flip all 1s seen so far to 0
                flips = min(flips + 1, ones)
        return flips

Complexity

Time	Space
O(?)	O(?)

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Flip String to Monotone Increasing

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