solution(go,python,rust,scala): 115. Distinct Subsequences

115. Distinct Subsequences
- Go
- Python
- Rust
- Scala

Hard/115. Distinct Subsequences/Approach 1/sol.md

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+1. The function numDistinct is designed to determine the number of distinct subsequences of string s which equals string t.
+2. To achieve this, the function leverages a dynamic programming approach using a 2D array dp. The element dp[i][j] represents the number of distinct subsequences of the first i characters of s that equal the first j characters of t.
+3. The function initializes the first column of dp to 1 because there's always one way to form an empty subsequence from any string.
+4. For each character in s and t, the function updates the dp array based on the following conditions:
+5. If the current characters of s and t match, the number of subsequences would be the sum of the subsequences without the current character in both s and t (i.e., dp[i-1][j-1]) and the subsequences without the current character in s (i.e., dp[i-1][j]).
+6. If the characters don't match, the number of subsequences would be the same as the number of subsequences without the current character in s.
+7. After processing all characters, the function returns the value dp[m][n], which represents the total number of distinct subsequences of s that equal t.
+
+
+## Time Complexity:
+The time complexity of the numDistinct function is O(m * n), where m is the length of string s and n is the length of string t. This is because the function iterates through each character of s and t once to update the dp array.
+
+## Space Complexity:
+The space complexity is also O(m * n) due to the 2D array dp used to store the number of distinct subsequences at each position. The size of this array scales with the lengths of s and t.
+

Hard/115. Distinct Subsequences/Approach 1/solution.go

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+func numDistinct(s string, t string) int {
+    m := len(s)
+    n := len(t)
+
+    if m < n {
+        return 0
+    }
+
+    dp := make([][]int, m+1)
+    for i := range dp {
+        dp[i] = make([]int, n+1)
+        dp[i][0] = 1
+    }
+
+    for i := 1; i <= m; i++ {
+        for j := 1; j <= n; j++ {
+            if s[i-1] == t[j-1] {
+                dp[i][j] = dp[i-1][j-1] + dp[i-1][j]
+            } else {
+                dp[i][j] = dp[i-1][j]
+            }
+        }
+    }
+
+    return dp[m][n]
+}

Hard/115. Distinct Subsequences/Approach 1/solution.py

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+class Solution:
+    def numDistinct(self, s: str, t: str) -> int:
+        m, n = len(s), len(t)
+        dp = [[0] * (n + 1) for _ in range(m + 1)]
+
+        for i in range(m + 1):
+            dp[i][0] = 1
+
+        for i in range(1, m + 1):
+            for j in range(1, n + 1):
+                if s[i - 1] == t[j - 1]:
+                    dp[i][j] = dp[i - 1][j - 1] + dp[i - 1][j]
+                else:
+                    dp[i][j] = dp[i - 1][j]
+
+        return dp[m][n]

Hard/115. Distinct Subsequences/Approach 1/solution.rust

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+impl Solution {
+    pub fn num_distinct(s: String, t: String) -> i32 {
+        let m = s.len();
+        let n = t.len();
+        let s_bytes = s.as_bytes();
+        let t_bytes = t.as_bytes();
+
+        if m < n {
+            return 0;
+        }
+
+        let mut dp = vec![vec![0; n + 1]; m + 1];
+
+        for i in 0..=m {
+            dp[i][0] = 1;
+        }
+
+        for i in 1..=m {
+            for j in 1..=n {
+                if s_bytes[i - 1] == t_bytes[j - 1] {
+                    dp[i][j] = dp[i - 1][j - 1] + dp[i - 1][j];
+                } else {
+                    dp[i][j] = dp[i - 1][j];
+                }
+            }
+        }
+
+        dp[m][n]
+    }
+}

Hard/115. Distinct Subsequences/Approach 1/solution.scala

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+object Solution {
+    def numDistinct(s: String, t: String): Int = {
+        val m = s.length
+        val n = t.length
+
+        if (m < n) {
+            return 0
+        }
+
+        val dp: Array[Array[Int]] = Array.fill(m + 1, n + 1)(0)
+        for (i <- 0 to m) {
+            dp(i)(0) = 1
+        }
+
+        for (i <- 1 to m) {
+            for (j <- 1 to n) {
+                if (s(i-1) == t(j-1)) {
+                    dp(i)(j) = dp(i-1)(j-1) + dp(i-1)(j)
+                } else {
+                    dp(i)(j) = dp(i-1)(j)
+                }
+            }
+        }
+
+        dp(m)(n)
+    }
+}