[csu/coj 1632]LCP

题意：求一个串的出现次数超过1次的字串的个数

思路：对于一个后缀，出现在它后面的所有后缀与它的LCP的最大值就是应该增加的答案，当然这里没有考虑去重，但是却转化了问题，使得我们可以用最长公共前缀来统计答案。假设我们将每一个后缀按字典序排好，那么对于每一个后缀，与其它后缀的LCP的最大值其实就是与它相邻的两个的lcp的较大值，这不就是height数组了么？考虑去重的问题，如果height[i]>height[i-1]，那么对于rank为i和i-1的最长公共前缀，它的前height[i-1]个前缀已经统计过了，答案只需要加上height[i]-height[i-1]，如果height[i]<=height[i-1]则不需处理。

 #pragma comment(linker, "/STACK:10240000,10240000")

 #include <iostream>
 #include <cstdio>
 #include <algorithm>
 #include <cstdlib>
 #include <cstring>
 #include <map>
 #include <queue>
 #include <deque>
 #include <cmath>
 #include <vector>
 #include <ctime>
 #include <cctype>
 #include <set>
 #include <bitset>
 #include <functional>
 #include <numeric>
 #include <stdexcept>
 #include <utility>

 using namespace std;

 #define mem0(a) memset(a, 0, sizeof(a))
 #define mem_1(a) memset(a, -1, sizeof(a))
 #define lson l, m, rt << 1
 #define rson m + 1, r, rt << 1 | 1
 #define rep_up0(a, b) for (int a = 0; a < (b); a++)
 #define rep_up1(a, b) for (int a = 1; a <= (b); a++)
 #define rep_down0(a, b) for (int a = b - 1; a >= 0; a--)
 #define rep_down1(a, b) for (int a = b; a > 0; a--)
 #define all(a) (a).begin(), (a).end()
 #define lowbit(x) ((x) & (-(x)))
 #define constructInt4(name, a, b, c, d) name(int a = 0, int b = 0, int c = 0, int d = 0): a(a), b(b), c(c), d(d) {}
 #define constructInt3(name, a, b, c) name(int a = 0, int b = 0, int c = 0): a(a), b(b), c(c) {}
 #define constructInt2(name, a, b) name(int a = 0, int b = 0): a(a), b(b) {}
 #define pchr(a) putchar(a)
 #define pstr(a) printf("%s", a)
 #define sstr(a) scanf("%s", a)
 #define sint(a) scanf("%d", &a)
 #define sint2(a, b) scanf("%d%d", &a, &b)
 #define sint3(a, b, c) scanf("%d%d%d", &a, &b, &c)
 #define pint(a) printf("%d\n", a)
 #define test_print1(a) cout << "var1 = " << a << endl
 #define test_print2(a, b) cout << "var1 = " << a << ", var2 = " << b << endl
 #define test_print3(a, b, c) cout << "var1 = " << a << ", var2 = " << b << ", var3 = " << c << endl
 #define mp(a, b) make_pair(a, b)
 #define pb(a) push_back(a)

 typedef unsigned int uint;
 typedef long long LL;
 typedef pair<int, int> pii;
 typedef vector<int> vi;

 const int dx[] = {, , -, , , , -, -};
 const int dy[] = {-, , , , , -, , - };
 const int maxn = ;
 const int md = ;
 const int inf = 1e9 + ;
 const LL inf_L = 1e18 + ;
 const double pi = acos(-1.0);
 const double eps = 1e-;

 template<class T>T gcd(T a, T b){return b==?a:gcd(b,a%b);}
 template<class T>bool max_update(T &a,const T &b){if(b>a){a = b; return true;}return false;}
 template<class T>bool min_update(T &a,const T &b){if(b<a){a = b; return true;}return false;}
 template<class T>T condition(bool f, T a, T b){return f?a:b;}
 template<class T>void copy_arr(T a[], T b[], int n){rep_up0(i,n)a[i]=b[i];}
 int make_id(int x, int y, int n) { return x * n + y; }

 /// 构造后缀数组的之前，需要在原串末尾加个空字符(比其它字符都小即可)，
 ///把这个空字符看成原串的一部分（这样在比较的时候到这个位置一定可以分个大小）,
 ///所以n应该为原序列长度+1，后缀n-1是"空串"，sa[0]总是n-1。
 struct SuffixArray {
     int n;
     int arr[][maxn];
      int *sa, *x, *y, *c, *rnk, *height;
     SuffixArray() { sa = arr[]; x = arr[]; y = arr[]; c = arr[]; rnk = arr[]; height = arr[]; }
     void resize(int nn) {  n = nn; mem0(arr[]); }
     void build_sa(int s[], int m) { // m is biger than the max value of char
         rep_up0(i, m) c[i] = ;
         rep_up0(i, n) c[x[i] = s[i]]++;
         rep_up1(i, m - ) c[i] += c[i - ];
         rep_down0(i, n) sa[--c[x[i]]] = i;
         for (int k = ; k <= n; k <<= ) {
             int p = ;
             for (int i = n - k; i < n; i++) y[p++] = i;
             rep_up0(i, n) if (sa[i] >= k) y[p++] = sa[i] - k;
             rep_up0(i, m) c[i] = ;
             rep_up0(i, n) c[x[y[i]]]++;
             rep_up0(i, m) c[i] += c[i - ];
             rep_down0(i, n) sa[--c[x[y[i]]]] = y[i];
             swap(x, y);
             p = ; x[sa[]] = ;
             for (int i = ; i < n; i++) {
                 x[sa[i]] = y[sa[i - ]] == y[sa[i]] && y[sa[i - ] + k] == y[sa[i] + k]? p -  : p++;
             }
             if (p >= n) break;
             m = p;
         }
     }
     void build_height(int s[]) {
         mem0(height);
         int k = ;
         rep_up0(i, n) rnk[sa[i]] = i;
         rep_up0(i, n) {
             if (k) k--;
             int j = sa[rnk[i] - ];
             while (s[i + k] == s[j + k]) k++;
             height[rnk[i]] = k;
         }
     }
     int solve(int n) {
         int ans = ;
         for (int i = ; i <= n; i ++) {
             if (height[i] > height[i - ]) ans += height[i] - height[i - ];
         }
         return ans;
     }
 };
 char s[maxn];
 int ss[maxn];
 SuffixArray sa;
 int main() {
     //freopen("in.txt", "r", stdin);
     int T;
     cin >> T;
     while (T --) {
         scanf("%s", s);
         int len = strlen(s) + ;
         rep_up0(i, len) ss[i] = s[i];
         sa.resize(len);
         sa.build_sa(ss, );
         sa.build_height(ss);
         cout << sa.solve(len - ) << endl;
     }
     return ;
 }

ps： 这个代码能够正常工作，但是里面的ST表与“max”有关的部分有问题，慎用。