LeetCode刷题笔录Edit Distance
2014-04-30 12:34
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Given two words word1 and word2, find the minimum number of steps required to convert word1 to word2. (each operation is counted as 1 step.)
You have the following 3 operations permitted on a word:
a) Insert a character
b) Delete a character
c) Replace a character
标准Dynamic Programming。思路如下:
两个String看成两个char数组,分别是x[m]以及y
。对于x[1]...x[i]和y[1]...y[j]的edit distance为A[i][j]。那么有如下recursion:
A[i][j]=A[i-1][j-1] if x[i] = y[j];
A[i][j]=min(A[i-1][j], A[i][j-1], A[i-1][j-1])+1 if x[i] != y[j]
其中第二种x[i]!=y[j]的min中的三个元素分别代表insert, delete和replace三种情况,要看哪种最小。
Base case是A[0][j]=j, A[i][0] = i。
code如下:
You have the following 3 operations permitted on a word:
a) Insert a character
b) Delete a character
c) Replace a character
标准Dynamic Programming。思路如下:
两个String看成两个char数组,分别是x[m]以及y
。对于x[1]...x[i]和y[1]...y[j]的edit distance为A[i][j]。那么有如下recursion:
A[i][j]=A[i-1][j-1] if x[i] = y[j];
A[i][j]=min(A[i-1][j], A[i][j-1], A[i-1][j-1])+1 if x[i] != y[j]
其中第二种x[i]!=y[j]的min中的三个元素分别代表insert, delete和replace三种情况,要看哪种最小。
Base case是A[0][j]=j, A[i][0] = i。
code如下:
public class Solution { public int minDistance(String word1, String word2) { int m = word1.length(); int n = word2.length(); if(m == 0) return n; if(n == 0) return m; int A[][] = new int[m + 1][n + 1]; for(int i = 0; i <= m; i++) A[i][0] = i; for(int j = 0; j <= n; j++) A[0][j] = j; for(int i = 1; i <= m; i++){ for(int j = 1; j <= n; j++){ if(word1.charAt(i - 1) == word2.charAt(j - 1)){ A[i][j] = A[i - 1][j - 1]; } else{ A[i][j] = Math.min(A[i - 1][j], Math.min(A[i][j - 1], A[i - 1][j - 1])) + 1; } } } return A[m] ; } }
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