leetcode刷题笔记十正则表达式 Scala版本

问题描述：

Given an input string (s) and a pattern (p), implement regular expression matching with support for '.' and '*'.

'.' Matches any single character.
'*' Matches zero or more of the preceding element.

The matching should cover the entire input string (not partial).

Note:

s could be empty and contains only lowercase letters a-z.
p could be empty and contains only lowercase letters a-z, and characters like . or *.

Example 1:

Input:
s = "aa"
p = "a"
Output: false
Explanation: "a" does not match the entire string "aa".

Example 2:

Input:
s = "aa"
p = "a*"
Output: true
Explanation: '*' means zero or more of the preceding element, 'a'. Therefore, by repeating 'a' once, it becomes "aa".

Example 3:

Input:
s = "ab"
p = ".*"
Output: true
Explanation: ".*" means "zero or more (*) of any character (.)".

Example 4:

Input:
s = "aab"
p = "c*a*b"
Output: true
Explanation: c can be repeated 0 times, a can be repeated 1 time. Therefore, it matches "aab".

Example 5:

Input:
s = "mississippi"
p = "mis*is*p*."
Output: false

简要思路分析：

首先对正则表达式进行分析，对于s串，其对应小写字母a-z；对于p串，其对应小写字母a-z，.或者*。因为对于样式，每个字符有三种可能，我们对三种可能进行分析。

s[i] : 字符串s第i个字符的位置 p[j]:样式串p第j个字符的位置

match[i]:为第i个状态的正则匹配情况

（1）p[j] 为一个字母

设 s="aa" p="ab"

s[0] == p[0] ==> match[0] = T

s[1] != p[1] ==> match[1] = (match[0] && (s[1] == p[1])) => F

（2）p[j] = '.',这里'.'代表'.' 匹配任意单个字符

设s="aa", p="a."

由于 '.'可以匹配任意单个字符，当p[j]='.',我们不需要考虑对应的s串的字符是什么。

s[0] == p[0] ==> match[0] = T

s[1] != p[1] 但 p[1] ='.' ==> match[1] = (match[0] && (p[1] == '.')) => T

(3) p[j] = '*'， *匹配零个或多个前面的那一个元素

因为'*'存在两种情况，0次匹配或者多次匹配

就0次匹配而言，视其对于'*'号前一字符的影响也存在两种情况。

【1】0次匹配，且对前一字符消失

设s="a", p="ac" 这里p[2]='*',且'*'令前一个字符C消失，这里match[0][2] = match[0][0] j向前移动两位

【2】 0次匹配，不影响前一字符

设s="a",p="ac*" 或者 s = "a" , p=".*", 这里p[1]="*"

match[0][2] = match[0][0] ==> if ((s[0] == p[0]) || p[0] == '.')

【3】多次匹配，不影响前一字符

设s="aa",p="a*" ==> match[1][1] = match[1][0]

总结状态方程

match[i][j] = match[i-1][j-1] if p[j-1] != '*' && ((s[i-1] == p[j-1]) || p[j-1] == '.' )

match[i][j] = match[i][j-2] if p[j-1] == '*' && （s[i-1] != p[j-2]）

match[i][j] = match[i-1][j] || match[i][j-2] if p[j-1] == '*' && ((s[i-1] != p[j-2]) || p[j-2] == '.')

根据状态方程，可以通过回溯法或者动态规划实现

代码补充：

1.回溯法

object Solution {
    def isMatch(s: String, p: String): Boolean = {
      if (p.length <= 0 ) return s.length <= 0
      var imatch:Boolean = (s.length > 0 &&(s.charAt(0) == p.charAt(0) || p.charAt(0) == '.'))
      //println("imatch: " + imatch)
      if (p.length > 1 && p.charAt(1) == '*'){
        return isMatch(s, p.substring(2)) ||( imatch && isMatch(s.substring(1), p))
      }
      else{
        return imatch && (isMatch(s.substring(1),p.substring(1)))
      }

    }
}

2.动态规划

object Solution {
    def isMatch(s: String, p: String): Boolean = {
      var dp = Array.ofDim[Boolean](s.length+2, p.length+2)
      //var dp = Array.fill(s.length, p.length)(false)
      val sStr = ' ' + s
      val pStr = ' ' + p
      if (pStr.length <= 0) return sStr.length<=0
      dp(0)(0) = true

      for (i <- 1 to sStr.length){
        for(j <- 1 to pStr.length){
          //println("----------------------------")
          //println("i: "+i)
          //println("j: "+j)
          //println("p(j-1): " + pStr.charAt(j-1))
          //println("s(i-1): " + sStr.charAt(i-1))

          if (pStr.charAt(j-1) != '*'){
            if (pStr.charAt(j-1) == sStr.charAt(i-1) || pStr.charAt(j-1) == '.'){dp(i)(j) = dp(i-1)(j-1)}
            else {dp(i)(j)=false}
            //println("!*")
            //println("dp(i-1)(j-1): "+dp(i-1)(j-1))
          }
          else{
            if (pStr.charAt(j-2) == sStr.charAt(i-1) || pStr.charAt(j-2) == '.') dp(i)(j) = dp(i)(j-2) || dp(i-1)(j)
            else dp(i)(j) = dp(i)(j-2)
            //dp(i)(j) = dp(i)(j-2)||dp(i-1)(j)
            //println("*")
            //println("dp(i)(j-2): "+dp(i)(j-2))
            //println("dp(i-1)(j): "+dp(i-1)(j))
          }
          //println("dp(i)(j): " + dp(i)(j))
          //println("dp(i)(j): " + dp(i)(j))
        }
      }
      return dp(s.length+1)(p.length+1)
    }
}

leetcode刷题笔记十 正则表达式 Scala版本

leetcode刷题笔记十正则表达式 Scala版本