From 5e2fb41dc8a70e9ca66323b605aa04635a3b9c1f Mon Sep 17 00:00:00 2001 From: CyC2018 Date: Fri, 30 Oct 2026 20:18:00 +0800 Subject: [PATCH] =?UTF-8?q?Update=2019.=20=E6=AD=A3=E5=88=99=E8=A1=A8?= =?UTF-8?q?=E8=BE=BE=E5=BC=8F=E5=8C=B9=E9=85=8D.md?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit 补充动态规划解法说明及状态转移配图,调整代码实现并精简 '*' 匹配的处理逻辑,补充复杂度分析。 --- notes/19. 正则表达式匹配.md | 46 +++++++++++++++++++------------- notes/pics/offer19-regex-dp.png | Bin 0 -> 163886 bytes 2 files changed, 28 insertions(+), 18 deletions(-) create mode 100644 notes/pics/offer19-regex-dp.png diff --git a/notes/19. 正则表达式匹配.md b/notes/19. 正则表达式匹配.md index cb722e96..06aa4563 100644 --- a/notes/19. 正则表达式匹配.md +++ b/notes/19. 正则表达式匹配.md @@ -10,31 +10,41 @@ ## 解题思路 -应该注意到,'.' 是用来当做一个任意字符,而 '\*' 是用来重复前面的字符。这两个的作用不同,不能把 '.' 的作用和 '\*' 进行类比,从而把它当成重复前面字符一次。 +'\*' 不能单独看,它和前面的字符构成一个整体 "x\*",表示 x 出现 0 次或多次;'.' 只匹配一个任意字符,不会重复。 + +用动态规划求解。dp[i][j] 表示 s 的前 i 个字符能否匹配 p 的前 j 个字符,按 p 的第 j 个字符分情况: + +- p[j-1] 是普通字符或 '.':它必须和 s[i-1] 匹配,并且前面的部分也要匹配,dp[i][j] = dp[i-1][j-1]; +- p[j-1] 是 '\*',记前一个字符为 x:让 "x\*" 匹配 0 次,相当于删掉这两个字符,dp[i][j] = dp[i][j-2];如果 x 能匹配 s[i-1](相等或 x 为 '.'),还可以让 "x\*" 吃掉 s[i-1],而 "x\*" 本身保留下来继续匹配前面的字符,dp[i][j] = dp[i-1][j]。两种情况有一种成立即可。 + +初始时 dp[0][0] = true;空串只能被 "a\*b\*" 这类每个字符都带 '\*' 的模式匹配,因此 p[j-1] 为 '\*' 时 dp[0][j] = dp[0][j-2]。 + +以 s = "abbc"、p = "c\*ab\*." 为例,dp 表和得到结果的一条路径如下: + +

```java public boolean articleMatch(String s, String p) { - int m = s.length(), n = p.length(); boolean[][] dp = new boolean[m + 1][n + 1]; - dp[0][0] = true; - for (int i = 1; i <= n; i++) - if (p.charAt(i - 1) == '*') - dp[0][i] = dp[0][i - 2]; - - for (int i = 1; i <= m; i++) - for (int j = 1; j <= n; j++) - if (s.charAt(i - 1) == p.charAt(j - 1) || p.charAt(j - 1) == '.') + for (int j = 2; j <= n; j++) + if (p.charAt(j - 1) == '*') + dp[0][j] = dp[0][j - 2]; + for (int i = 1; i <= m; i++) { + for (int j = 1; j <= n; j++) { + char sc = s.charAt(i - 1), pc = p.charAt(j - 1); + if (pc == sc || pc == '.') { dp[i][j] = dp[i - 1][j - 1]; - else if (p.charAt(j - 1) == '*') - if (p.charAt(j - 2) == s.charAt(i - 1) || p.charAt(j - 2) == '.') { - dp[i][j] |= dp[i][j - 1]; // a* counts as single a - dp[i][j] |= dp[i - 1][j]; // a* counts as multiple a - dp[i][j] |= dp[i][j - 2]; // a* counts as empty - } else - dp[i][j] = dp[i][j - 2]; // a* only counts as empty - + } else if (pc == '*') { + char x = p.charAt(j - 2); + dp[i][j] = dp[i][j - 2] // x* 匹配 0 次 + || ((x == sc || x == '.') && dp[i - 1][j]); // x* 再匹配一个 sc + } + } + } return dp[m][n]; } ``` + +时间和空间复杂度都是 O(MN)。 diff --git a/notes/pics/offer19-regex-dp.png b/notes/pics/offer19-regex-dp.png new file mode 100644 index 0000000000000000000000000000000000000000..1a8a0408dae0842faff7dc51ba3250ea775d07ad GIT binary patch literal 163886 zcmXtA1yogAw7npm(w$Nw3J4;gbV`@BbeFUeQqqlpgdi;-ASEEu9g-p?(jldEN&R)- z|Njif&>?W{IeV{|bFR6GP*ah^$DzhSAQ1RZzKM*x;mP=+9RaAr0(WYw*1ry@+`>;LJholdE<7L z_tVrkSZJPdCbyX^IOJz%XICKB-G$4v?I<&-RLh*_mB7x}V%f_(nihP&{yK!zW7H5jiY zScuh+6(uB0siJlAMj3Nte0oh=dSC9{z0hR58Qx_UD4spJg^r3+WxP)=Qb0<|aJO@p ziI`eAbI61T3k`KMLtRZx?dD0WDdph+JebQi3o-Ug+St|+UI$i)WHVpks7*ZQmb>sF zk6(MX1v`uBc2sxXP;s*z06`Av3V69 z7Is}D%`6cY6BHD*l!yLPmOpg8#B`dEQt{8y`-~U7ypl@7ALML;6M}+r8>Py$&8e#4 zB_pIyf3Cl`!8ofK)a6#rQ1#nP4GKcF!Jt&&3k}QH;UG2p`r4Ed7SdiFHbPY2#956q zIajAAmTX^$r#NU$Yec?4Wq#c#2s*Q^lBc(b8gGN<56$ 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