Problem
Given strings s and t, count the number of distinct subsequences of s that equal t.
Example
Input: s = "rabbbit", t = "rabbit"
Output: 3Solution
2D DP. dp[i][j] = ways to form t[:j] from s[:i]. If chars match, sum of include and skip; else just skip.
def num_distinct(s, t):
m, n = len(s), len(t)
if n > m: return 0
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):
dp[i][j] = dp[i-1][j]
if s[i-1] == t[j-1]: dp[i][j] += dp[i-1][j-1]
return dp[m][n]function numDistinct(s, t) {
const m = s.length, n = t.length;
if (n > m) return 0;
const dp = Array.from({length: m + 1}, () => new Array(n + 1).fill(0));
for (let i = 0; i <= m; i++) dp[i][0] = 1;
for (let i = 1; i <= m; i++) {
for (let j = 1; j <= n; j++) {
dp[i][j] = dp[i-1][j];
if (s[i-1] === t[j-1]) dp[i][j] += dp[i-1][j-1];
}
}
return dp[m][n];
}int numDistinct(string s, string t) {
int m = s.size(), n = t.size();
if (n > m) return 0;
vector<vector<long>> dp(m + 1, vector<long>(n + 1, 0));
for (int i = 0; i <= m; i++) dp[i][0] = 1;
for (int i = 1; i <= m; i++) {
for (int j = 1; j <= n; j++) {
dp[i][j] = dp[i-1][j];
if (s[i-1] == t[j-1]) dp[i][j] += dp[i-1][j-1];
}
}
return (int)dp[m][n];
}public int numDistinct(String s, String t) {
int m = s.length(), n = t.length();
if (n > m) return 0;
long[][] dp = new long[m + 1][n + 1];
for (int i = 0; i <= m; i++) dp[i][0] = 1;
for (int i = 1; i <= m; i++) {
for (int j = 1; j <= n; j++) {
dp[i][j] = dp[i-1][j];
if (s.charAt(i-1) == t.charAt(j-1)) dp[i][j] += dp[i-1][j-1];
}
}
return (int) dp[m][n];
}Complexity
- Time: O(m * n)
- Space: O(m * n)
Explanation
When chars match at position i,j: either we use s[i-1] for t[j-1] (count = dp[i-1][j-1]) or we skip s[i-1] (count = dp[i-1][j]). Otherwise just skip.
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