3258. Count Substrings That Satisfy K-Constraint I
Description
You are given a binary string s
and an integer k
.
A binary string satisfies the k-constraint if either of the following conditions holds:
- The number of
0
's in the string is at mostk
. - The number of
1
's in the string is at mostk
.
Return an integer denoting the number of substrings of s
that satisfy the k-constraint.
Example 1:
Input: s = "10101", k = 1
Output: 12
Explanation:
Every substring of s
except the substrings "1010"
, "10101"
, and "0101"
satisfies the k-constraint.
Example 2:
Input: s = "1010101", k = 2
Output: 25
Explanation:
Every substring of s
except the substrings with a length greater than 5 satisfies the k-constraint.
Example 3:
Input: s = "11111", k = 1
Output: 15
Explanation:
All substrings of s
satisfy the k-constraint.
Constraints:
1 <= s.length <= 50
1 <= k <= s.length
s[i]
is either'0'
or'1'
.
Solutions
Solution 1: Sliding Window
We use two variables $\textit{cnt0}$ and $\textit{cnt1}$ to record the number of $0$s and $1$s in the current window, respectively. We use $\textit{ans}$ to record the number of substrings that satisfy the $k$ constraint, and $l$ to record the left boundary of the window.
When we move the window to the right, if the number of $0$s and $1$s in the window both exceed $k$, we need to move the window to the left until the number of $0$s and $1$s in the window are both no greater than $k$. At this point, all substrings in the window satisfy the $k$ constraint, and the number of such substrings is $r - l + 1$, where $r$ is the right boundary of the window. We add this count to $\textit{ans}$.
Finally, we return $\textit{ans}$.
The time complexity is $O(n)$, where $n$ is the length of the string $s$. The space complexity is $O(1)$.
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