Leetcode 1143 最长公共子序列
Posted 牛有肉
tags:
篇首语:本文由小常识网(cha138.com)小编为大家整理,主要介绍了Leetcode 1143 最长公共子序列相关的知识,希望对你有一定的参考价值。
当一个问题用递推不好描述时,将目光从整体放到局部,用递归描述对于每个元素我们需要做什么。
问题:text 从 point1 、text2 从 point2 开始的最长公共子序列为 n ,具有递归结构,并存在大量重复子问题。
分治:
public final int longestCommonSubsequence(String text1, String text2) { return longestCommonSubsequence(text1, 0, text2, 0, new int[text1.length()][text2.length()]); } public final int longestCommonSubsequence(String text1, int point1, String text2, int point2, int[][] cache) { if ((point1 == text1.length()) || (point2 == text2.length())) { return 0; } if (cache[point1][point2] != 0) { return cache[point1][point2]; } int re = 0; if (text1.charAt(point1) == text2.charAt(point2)) { re = longestCommonSubsequence(text1, point1 + 1, text2, point2 + 1, cache) + 1; } else { int re0 = longestCommonSubsequence(text1, point1, text2, point2 + 1, cache); int re1 = longestCommonSubsequence(text1, point1 + 1, text2, point2 + 1, cache); int re2 = longestCommonSubsequence(text1, point1 + 1, text2, point2, cache); re = Math.max(re0, re1); re = Math.max(re, re2); } cache[point1][point2] = re; return re; }
DP:
public final int longestCommonSubsequenceDP(String text1, String text2) { int length1 = text1.length(); int length2 = text2.length(); int[][] dp = new int[length1][length2]; if (length1 == 0 || length2 == 0) { return 0; } dp[length1 - 1][length2 - 1] = text1.charAt(length1 - 1) == text2.charAt(length2 - 1) ? 1 : 0; for (int i = length2 - 2; i >= 0; i--) { dp[length1 - 1][i] = text1.charAt(length1 - 1) == text2.charAt(i) || dp[length1 - 1][i + 1] == 1 ? 1 : 0; } for (int i = length1 - 2; i >= 0; i--) { dp[i][length2 - 1] = text1.charAt(i) == text2.charAt(length2 - 1) || dp[i + 1][length2 - 1] == 1 ? 1 : 0; } for (int i = length1 - 2; i >= 0; i--) { for (int j = length2 - 2; j >= 0; j--) { if (text1.charAt(i) == text2.charAt(j)) { dp[i][j] = dp[i + 1][j + 1] + 1; } else { dp[i][j] = Math.max(dp[i][j + 1], dp[i + 1][j + 1]); dp[i][j] = Math.max(dp[i][j], dp[i + 1][j]); } } } return dp[0][0]; }
以上是关于Leetcode 1143 最长公共子序列的主要内容,如果未能解决你的问题,请参考以下文章
LeetCode1143. 最长公共子序列/300. 最长递增子序列//1713. 得到子序列的最少操作次数(好题!!!!!)