115. Distinct Subsequences 不同的子序列

@TOC

# 题目描述

Given a string `S` and a string `T`, count the number of distinct subsequences of `S` which equals `T`.

A subsequence of a string is a new string which is formed from the original string by deleting some (can be none) of the characters without disturbing the relative positions of the remaining characters. (ie, `"ACE"` is a subsequence of `"ABCDE"` while `"AEC"` is not).

Example 1:

``````Input: S = "rabbbit", T = "rabbit"
Output: 3
Explanation:

As shown below, there are 3 ways you can generate "rabbit" from S.
(The caret symbol ^ means the chosen letters)

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.
(The caret symbol ^ means the chosen letters)

babgbag
^^ ^
babgbag
^^    ^
babgbag
^    ^^
babgbag
^  ^^
babgbag
^^^
``````

# 解题方法

# 动态规划

``````class Solution:
def numDistinct(self, s, t):
"""
:type s: str
:type t: str
:rtype: int
"""
M, N = len(s), len(t)
dp = [[0] * (M + 1) for _ in range(N + 1)]
for j in range(M + 1):
dp[0][j] = 1
for i in range(1, N + 1):
for j in range(1, M + 1):
if s[j - 1] == t[i - 1]:
dp[i][j] = dp[i - 1][j - 1] + dp[i][j - 1]
else:
dp[i][j] = dp[i][j - 1]
return dp[-1][-1]
``````

# 日期

2018 年 11 月 19 日 —— 周一又开始了