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115. Distinct Subsequences

Description

Given two strings s and t, return the number of distinct subsequences of s which equals t.

The test cases are generated so that the answer fits on a 32-bit signed integer.

 

Example 1:

Input: s = "rabbbit", t = "rabbit"
Output: 3
Explanation:
As shown below, there are 3 ways you can generate "rabbit" from s.
rabbbit
rabbbit
rabbbit

Example 2:

Input: s = "babgbag", t = "bag"
Output: 5
Explanation:
As shown below, there are 5 ways you can generate "bag" from s.
babgbag
babgbag
babgbag
babgbag
babgbag

 

Constraints:

  • 1 <= s.length, t.length <= 1000
  • s and t consist of English letters.

 

Solutions

Solution: Dynamic Programming

  • Time complexity: O(mn)
  • Space complexity: O(mn)

 

JavaScript

js
/**
 * @param {string} s
 * @param {string} t
 * @return {number}
 */
const numDistinct = function (s, t) {
  const memo = new Map();
  const dp = (a, b) => {
    if (b === t.length) return 1;
    if (a === s.length || s.length - a < t.length - b) return 0;
    const key = `${a},${b}`;

    if (memo.has(key)) return memo.get(key);
    let result = dp(a + 1, b);

    if (s[a] === t[b]) {
      result += dp(a + 1, b + 1);
    }
    memo.set(key, result);
    return result;
  };

  return dp(0, 0);
};

Released under the MIT license