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'
.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:
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.
Iteration: We iterate through the characters of the target
string.
Flip Check: For each character in target
:
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.count
(representing a flip operation).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.