leetcode 712. Minimum ASCII Delete Sum for Two Strings ( Python )

描述

Given two strings s1, s2, find the lowest ASCII sum of deleted characters to make two strings equal.

Example 1:

Input: s1 = "sea", s2 = "eat"
Output: 231
Explanation: Deleting "s" from "sea" adds the ASCII value of "s" (115) to the sum.
Deleting "t" from "eat" adds 116 to the sum.
At the end, both strings are equal, and 115 + 116 = 231 is the minimum sum possible to achieve this.
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Example 2:

Input: s1 = "delete", s2 = "leet"
Output: 403
Explanation: Deleting "dee" from "delete" to turn the string into "let",
adds 100[d]+101[e]+101[e] to the sum.  Deleting "e" from "leet" adds 101[e] to the sum.
At the end, both strings are equal to "let", and the answer is 100+101+101+101 = 403.
If instead we turned both strings into "lee" or "eet", we would get answers of 433 or 417, which are higher.
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Note:

0 < s1.length, s2.length <= 1000.
All elements of each string will have an ASCII value in [97, 122].
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解析

根據題意，能夠看出這種求最優的問題能夠用 DP 算法來解決，其實直接使用 LCS 的 ASCII 之和做爲狀態就好了。設 dp[i][j] 爲 s1 前 i 個字符與 s2 前 j 個字符獲得的 LCS 的 ASCII 和。

轉移方程是：
對於 s1[0…i−1] 和 s2[0…j−1] 的 LCS 的 ASCII 的和應該是這樣的：
1. 若 s1[i−1]==s2[j−1] ，則 dp[i][j] = dp[i - 1][j - 1] + ord(s1[i - 1])
2. 若不相等，則 s1[i−1], s2[j−1] 選擇刪除一個，dp[i][j] = max(dp[i - 1][j], dp[i][j - 1])
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時間複雜度爲 O(N^2)，空間複雜度爲 O(N^2)。

解答

class Solution(object):
def minimumDeleteSum(self, s1, s2):
    """
    :type s1: str
    :type s2: str
    :rtype: int
    """
    l1, l2 = len(s1), len(s2)
    dp = [[0] * (l2 + 1) for _ in range(l1 + 1)]
    for i in range(1, l1 + 1):
        for j in range(1, l2 + 1):
            if s1[i - 1] == s2[j - 1]:
                dp[i][j] = dp[i - 1][j - 1] + ord(s1[i - 1])
            else:
                dp[i][j] = max(dp[i - 1][j], dp[i][j - 1])
    result = sum(map(ord, s1 + s2)) - dp[-1][-1] * 2
    return result
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運行結果

Runtime: 596 ms, faster than 73.80% of Python online submissions for Minimum ASCII Delete Sum for Two Strings.
Memory Usage: 12.6 MB, less than 94.12% of Python online submissions for Minimum ASCII Delete Sum for Two Strings.
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