LeetCode 30 days Challenge - Day 26
本系列將對LeetCode新推出的30天算法挑戰進行總結記錄,旨在記錄學習成果、方便未來查閱,同時望爲廣大網友提供幫助。
Longest Common Subsequence
Given two strings text1
and text2
, return the length of their longest common subsequence.
A subsequence of a string is a new string generated from the original string with some characters(can be none) deleted without changing the relative order of the remaining characters. (eg, “ace” is a subsequence of “abcde” while “aec” is not). A common subsequence of two strings is a subsequence that is common to both strings.
If there is no common subsequence, return 0.
Example 1:
Input: text1 = "abcde", text2 = "ace"
Output: 3
Explanation: The longest common subsequence is "ace" and its length is 3.
Example 2:
Input: text1 = "abc", text2 = "abc"
Output: 3
Explanation: The longest common subsequence is "abc" and its length is 3.
Example 3:
Input: text1 = "abc", text2 = "def"
Output: 0
Explanation: There is no such common subsequence, so the result is 0.
Constraints:
1 <= text1.length <= 1000
1 <= text2.length <= 1000
- The input strings consist of lowercase English characters only.
Solution
題目要求分析:給定兩個字符串,求其中最長公共子串的長度。
解法:
本題需要注意區分子序列、子串:subsequence是子序列,子序列中各元素不需要連續,substring是子串,子串中每個元素必須是連續的。
本題是經典的動態規劃題,維護一個二維動態規劃數組dp,其中:
i:1 - text1.length()
;j:1 - text2.length()
;dp[i][j]
:text1[0:i-1]子串以及text2[0:j-1]子串之間最長公共子串的長度。- 更新規則(對text1的每一個位置 - i-1,遍歷text2所有的位置 - j-1):
- 當
text1[i-1] == text2[j-1]
:dp[i][j] = dp[i-1][j-1] + 1;
- 否則:
dp[i][j] = max(dp[i-1][j], dp[i][j-1]);
- 當
最終結果即爲 dp[text1.length()][text2.length()]
。
int longestCommonSubsequence(string text1, string text2) {
vector<vector<int>> dp(text1.length()+1, vector<int>(text2.length()+1, 0));
for (int i = 1; i <= text1.length(); i++) {
for (int j = 1; j <= text2.length(); j++) {
if (text1[i-1] == text2[j-1]) dp[i][j] = dp[i-1][j-1] + 1;
else dp[i][j] = max(dp[i-1][j], dp[i][j-1]);
}
}
return dp[text1.length()][text2.length()];
}
傳送門:Longest Common Subsequence
2020/4 Karl