diff --git a/dsa-problems/leetcode-problems/0600-0699.md b/dsa-problems/leetcode-problems/0600-0699.md index fd7ca7675..fdb7435b1 100644 --- a/dsa-problems/leetcode-problems/0600-0699.md +++ b/dsa-problems/leetcode-problems/0600-0699.md @@ -591,7 +591,7 @@ export const problems = [ "problemName": "696. Count Binary Substrings", "difficulty": "Easy", "leetCodeLink": "https://leetcode.com/problems/count-binary-substrings", - "solutionLink": "#" + "solutionLink": "/dsa-solutions/lc-solutions/0600-0699/count-binary-substrings" }, { "problemName": "697. Degree of an Array", diff --git a/dsa-solutions/lc-solutions/0600-0699/0696-count-binary -ubstrings.md b/dsa-solutions/lc-solutions/0600-0699/0696-count-binary -ubstrings.md new file mode 100644 index 000000000..8aeef769e --- /dev/null +++ b/dsa-solutions/lc-solutions/0600-0699/0696-count-binary -ubstrings.md @@ -0,0 +1,184 @@ +--- +id: count-binary-substrings +title: Count Binary Substrings +sidebar_label: 0696 - Count Binary Substrings +tags: + - String + - Two Pointers + - Sliding Window +description: "This is a solution to the Count Binary Substrings problem on LeetCode." +--- + +## Problem Description + +Given a binary string `s`, return the number of non-empty substrings that have the same number of `0`'s and `1`'s, and all the `0`'s and all the `1`'s in these substrings are grouped consecutively. + +Substrings that occur multiple times are counted the number of times they occur. + +### Examples + +**Example 1:** + +``` +Input: s = "00110011" +Output: 6 +Explanation: There are 6 substrings that have equal number of consecutive 1's and 0's: "0011", "01", "1100", "10", "0011", and "01". +Notice that some of these substrings repeat and are counted the number of times they occur. +Also, "00110011" is not a valid substring because all the 0's (and 1's) are not grouped together. +``` + +**Example 2:** + +``` +Input: s = "10101" +Output: 4 +Explanation: There are 4 substrings: "10", "01", "10", "01" that have equal number of consecutive 1's and 0's. +``` + +### Constraints + +- $1 <= s.length <= 10^5$ +- `s[i]` is either `'0'` or `'1'`. + +## Solution for Count Binary Substrings + +### Approach 1: Group By Character +#### Intuition + +We can convert the string `s` into an array groups that represents the length of same-character contiguous blocks within the string. For example, if `s = "110001111000000"`, then `groups = [2, 3, 4, 6]`. + +For every binary string of the form `'0' * k + '1' * k` or `'1' * k + '0' * k`, the middle of this string must occur between two groups. + +Let's try to count the number of valid binary strings between `groups[i]` and `groups[i+1]`. If we have `groups[i] = 2, groups[i+1] = 3`, then it represents either "00111" or "11000". We clearly can make `min(groups[i], groups[i+1])` valid binary strings within this string. Because the binary digits to the left or right of this string must change at the boundary, our answer can never be larger. + +#### Algorithm + +Let's create `groups` as defined above. The first element of `s` belongs in its own group. From then on, each element either doesn't match the previous element, so that it starts a new group of size 1, or it does match, so that the size of the most recent group increases by 1. + +Afterward, we will take the sum of `min(groups[i-1], groups[i])`. + +## Code in Different Languages + + + + + +```java +class Solution { + public int countBinarySubstrings(String s) { + int[] groups = new int[s.length()]; + int t = 0; + groups[0] = 1; + for (int i = 1; i < s.length(); i++) { + if (s.charAt(i-1) != s.charAt(i)) { + groups[++t] = 1; + } else { + groups[t]++; + } + } + + int ans = 0; + for (int i = 1; i <= t; i++) { + ans += Math.min(groups[i-1], groups[i]); + } + return ans; + } +} +``` + + + + + +```python +class Solution(object): + def countBinarySubstrings(self, s): + groups = [1] + for i in xrange(1, len(s)): + if s[i-1] != s[i]: + groups.append(1) + else: + groups[-1] += 1 + + ans = 0 + for i in xrange(1, len(groups)): + ans += min(groups[i-1], groups[i]) + return ans +``` + + + +## Complexity Analysis + +### Time Complexity: $O(N)$ + +> **Reason**: where N is the length of s. Every loop is through $O(N)$ items with $O(1)$ work inside the for-block. + +### Space Complexity: $O(N)$ + +> **Reason**: the space used by `groups`. + +### Approach 2: Linear Scan +#### Intuition and Algorithm + +We can amend our Approach #1 to calculate the answer on the fly. Instead of storing `groups`, we will remember only `prev = groups[-2]` and `cur = groups[-1]`. Then, the answer is the sum of `min(prev, cur)` over each different final `(prev, cur)` we see. + +## Code in Different Languages + + + + + +```java +class Solution { + public int countBinarySubstrings(String s) { + int ans = 0, prev = 0, cur = 1; + for (int i = 1; i < s.length(); i++) { + if (s.charAt(i-1) != s.charAt(i)) { + ans += Math.min(prev, cur); + prev = cur; + cur = 1; + } else { + cur++; + } + } + return ans + Math.min(prev, cur); + } +} +``` + + + + + +```python +class Solution(object): + def countBinarySubstrings(self, s): + ans, prev, cur = 0, 0, 1 + for i in xrange(1, len(s)): + if s[i-1] != s[i]: + ans += min(prev, cur) + prev, cur = cur, 1 + else: + cur += 1 + + return ans + min(prev, cur) +``` + + + +## Complexity Analysis + +### Time Complexity: $O(N)$ + +> **Reason**: where N is the length of s. Every loop is through $O(N)$ items with $O(1)$ work inside the for-block. + +### Space Complexity: $O(1)$ + +> **Reason**: the space used by `prev`, `cur`, and `ans`. + +## References + +- **LeetCode Problem**: [Count Binary Substrings](https://leetcode.com/problems/count-binary-substrings/description/) + +- **Solution Link**: [Count Binary Substrings](https://leetcode.com/problems/count-binary-substrings/solutions/)