{x}
blog image

Minimum Suffix Flips

You are given a 0-indexed binary string target of length n. You have another binary string s of length n that is initially set to all zeros. You want to make s equal to target.

In one operation, you can pick an index i where 0 <= i < n and flip all bits in the inclusive range [i, n - 1]. Flip means changing '0' to '1' and '1' to '0'.

Return the minimum number of operations needed to make s equal to target.

 

Example 1:

Input: target = "10111"
Output: 3
Explanation: Initially, s = "00000".
Choose index i = 2: "00000" -> "00111"
Choose index i = 0: "00111" -> "11000"
Choose index i = 1: "11000" -> "10111"
We need at least 3 flip operations to form target.

Example 2:

Input: target = "101"
Output: 3
Explanation: Initially, s = "000".
Choose index i = 0: "000" -> "111"
Choose index i = 1: "111" -> "100"
Choose index i = 2: "100" -> "101"
We need at least 3 flip operations to form target.

Example 3:

Input: target = "00000"
Output: 0
Explanation: We do not need any operations since the initial s already equals target.

 

Constraints:

  • n == target.length
  • 1 <= n <= 105
  • target[i] is either '0' or '1'.

Solution Explanation

This problem can be solved efficiently using a greedy approach. The core idea is to track the current state (0 or 1) and flip the state only when necessary to match the target string.

Algorithm:

  1. Initialization: We start with a count (or ans in the code examples) initialized to 0. This variable keeps track of the number of flips performed. The initial state of the binary string s is all zeros.

  2. Iteration: We iterate through the characters of the target string.

  3. Flip Check: For each character in target:

    • We check if the current state (count % 2) is different from the character's value (0 or 1). The XOR operation (^) helps us concisely perform this comparison. If they are different, it means a flip is required.
    • If a flip is needed, we increment the count (representing a flip operation).
  4. Return: After iterating through the entire target string, the count variable will hold the minimum number of flip operations needed.

Time Complexity Analysis:

The algorithm iterates through the target string once. Therefore, the time complexity is O(n), where n is the length of the target string.

Space Complexity Analysis:

The algorithm uses a constant amount of extra space to store the count variable. Therefore, the space complexity is O(1).

Code Explanation (Python):

class Solution:
    def minFlips(self, target: str) -> int:
        ans = 0  # Initialize the flip count
        for v in target:  # Iterate through the target string
            v = int(v) #Convert the character to integer
            if (ans & 1) ^ v:  #Check if flip is required using XOR
                ans += 1  # Increment the flip count if needed
        return ans

The code in other languages (Java, C++, Go) follows the same logic with minor syntax differences to accommodate the respective language features. The core algorithmic approach remains identical, providing an efficient solution to the problem.