第10题 正则表达式匹配(动态规划)
题目描述:
'.' Matches any single character. '*' Matches zero or more of the preceding element. The matching should cover the entire input string (not partial). The function prototype should be: bool isMatch(const char *s, const char *p) Some examples: isMatch("aa","a") → false isMatch("aa","aa") → true isMatch("aaa","aa") → false isMatch("aa", "a*") → true isMatch("aa", ".*") → true isMatch("ab", ".*") → true isMatch("aab", "c*a*b") → true
使用字符串p来表示字符串s,看是否匹配。比如“c*a*b“可以匹配”aab“,此时第一个*表示有0个c,第二个*表示有1个a。
思路:
1, If p.charAt(j) == s.charAt(i) : dp[i][j] = dp[i-1][j-1]; 2, If p.charAt(j) == '.' : dp[i][j] = dp[i-1][j-1]; 3, If p.charAt(j) == '*': here are two sub conditions: 1 if p.charAt(j-1) != s.charAt(i) : dp[i][j] = dp[i][j-2] //in this case, a* only counts as empty 2 if p.charAt(i-1) == s.charAt(i) or p.charAt(i-1) == '.': dp[i][j] = dp[i-1][j] //in this case, a* counts as multiple a or dp[i][j] = dp[i][j-1] // in this case, a* counts as single a or dp[i][j] = dp[i][j-2] // in this case, a* counts as empty
比如:s="aaab" , p="c*a*b"
c | * | a | * | b | |
a | 1 | 0 | 1 | 0 | 1 |
a | 0 | 0 | 0 | 0 | 0 |
a | 0 | 0 | 0 | 0 | 0 |
b | 0 | 0 | 0 | 0 |
代码:
package T010; public class RegularExpressionMatching { public static void main(String[] args) { System.out.println(isMatch("aab","c*a*b")); } public static boolean isMatch(String s, String p) { if (s == null || p == null) { return false; } boolean[][] dp = new boolean[s.length()+1][p.length()+1]; dp[0][0] = true; for (int i = 0; i < p.length(); i++) { if (p.charAt(i) == '*' && dp[0][i-1]) { dp[0][i+1] = true; } } printArray(dp); for (int i = 0 ; i < s.length(); i++) { for (int j = 0; j < p.length(); j++) { if (p.charAt(j) == '.' || p.charAt(j) == s.charAt(i)) { dp[i+1][j+1] = dp[i][j]; } if (p.charAt(j) == '*') { if (p.charAt(j-1) != s.charAt(i) && p.charAt(j-1) != '.') { dp[i+1][j+1] = dp[i+1][j-1]; } else { dp[i+1][j+1] = (dp[i+1][j] || dp[i][j+1] || dp[i+1][j-1]); } } } } // printArray(dp); return dp[s.length()][p.length()]; } /* * isMatch("aa","a") → false * isMatch("aa","aa") → true * isMatch("aaa","aa") → false * isMatch("aa", "a*") → true * isMatch("aa", ".*") → true * isMatch("ab", ".*") → true * isMatch("aab", "c*a*b") → true */ public static void printArray(boolean [] arr){ System.out.print("printArray:"); for(int i=0;i<arr.length;i++){ System.out.print(arr[i]+" "); } System.out.println(""); } public static void printArray(boolean[][] V){ System.out.println("printArray:"); int rows = V.length; int cols = V[0].length; for(int i=0;i<rows;i++){ for(int j=0;j<cols;j++){ System.out.print(V[i][j]+" "); } System.out.println(""); } System.out.println(""); } }
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