CF 427D 后缀数组

Posted 2020-06-18 Live In A Dream

大意是寻找两个字符串中最短的公共子串，要求子串在两个串中都是唯一的。

造一个S#T的串，做后缀数组，从小到大枚举子串长度在height数组中扫描，如果某一个组中来自两个串的数量分别为1，就找到了答案。

 1 #include <iostream>
 2 #include <vector>
 3 #include <algorithm>
 4 #include <string>
 5 #include <string.h>
 6 #include <stdio.h>
 7 #include <math.h>
 8 #include <stdlib.h>
 9 #include <queue>
10 #include <stack>
11 #include <map>
12 #include <set>
13 #include <ctime>
14 #include <numeric>
15 #include <cassert>
16 
17 using namespace std;
18 
19 const int N=10005;;
20 
21 char s[N];
22 
23 struct SuffixArray {
24     int wa[N], wb[N], cnt[N], wv[N];
25     int rk[N], height[N];
26     int sa[N];
27     bool cmp(int r[], int a, int b, int l) {
28         return r[a] == r[b] && r[a+l] == r[b+l];
29     }
30     void calcSA(char r[], int n, int m) {
31         int i, j, p, *x = wa, *y = wb;
32         for (i = 0; i < m; ++i) cnt[i] = 0;
33         for (i = 0; i < n; ++i) cnt[x[i]=r[i]]++;
34         for (i = 1; i < m; ++i) cnt[i] += cnt[i-1];
35         for (i = n-1; i >= 0; --i) sa[--cnt[x[i]]] = i;
36         for (j = 1, p = 1; p < n; j *= 2, m = p) {
37             for (p = 0, i = n - j; i < n; ++i) y[p++] = i;
38             for (i = 0; i < n; ++i) if (sa[i] >= j) y[p++] = sa[i] - j;
39             for (i = 0; i < n; ++i) wv[i] = x[y[i]];
40             for (i = 0; i < m; ++i) cnt[i] = 0;
41             for (i = 0; i < n; ++i) cnt[wv[i]]++;
42             for (i = 1; i < m; ++i) cnt[i] += cnt[i-1];
43             for (i = n-1; i >= 0; --i) sa[--cnt[wv[i]]] = y[i];
44             for (swap(x, y), p = 1, x[sa[0]] = 0, i = 1; i < n; ++i)
45                 x[sa[i]] = cmp(y, sa[i-1], sa[i], j) ? p-1 : p++;
46         }
47     }
48     void calcHeight(char r[], int n) {
49         int i, j, k = 0;
50         for (i = 0; i <= n; ++i) rk[sa[i]] = i;
51         for (i = 0; i < n; height[rk[i++]] = k)
52             for (k?k--:0, j = sa[rk[i]-1]; r[i+k] == r[j+k]; k++);
53     }
54     bool solve(int k,int n,int div) {
55         int ca=0,cb=0;
56         for (int i=1;i<=n;i++) {
57             if (height[i]<k) {
58                 if (ca==1&&cb==1)
59                     return true;
60                 ca=0;cb=0;
61                 if (sa[i]<div) ca++;
62                 else if (sa[i]>div) cb++;
63                 continue;
64             }
65             if (sa[i]<div) ca++;
66             else if (sa[i]>div) cb++;
67         }
68         return ca==1&&cb==1;
69     }
70 }suf;
71 
72 char a[N],b[N];
73 
74 int main(){
75     scanf("%s %s",a,b);
76     int n=strlen(a),m=strlen(b);
77     strcpy(s,a);
78     s[n]=‘#‘;
79     strcpy(s+n+1,b);
80     int tot=n+m+1;
81     suf.calcSA(s,tot+1,128);
82     suf.calcHeight(s,tot);
83     int ret=-1;
84     for (int i=1;i<=n;i++) {
85         if (suf.solve(i,tot,n)) {
86             ret=i;
87             break;
88         }
89     }
90     printf("%d\n",ret);
91     return 0;
92 }

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