[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
", 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[8] = {0, 0, -1, 1, 1, 1, -1, -1};
const int dy[8] = {-1, 1, 0, 0, 1, -1, 1, -1 };
const int maxn = 120000;
const int md = 1000000007;
const int inf = 1e9 + 7;
const LL inf_L = 1e18 + 7;
const double pi = acos(-1.0);
const double eps = 1e-6;
 
template<class T>T gcd(T a, T b){return b==0?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[6][maxn];
     int *sa, *x, *y, *c, *rnk, *height;
    SuffixArray() { sa = arr[0]; x = arr[1]; y = arr[2]; c = arr[3]; rnk = arr[4]; height = arr[5]; }
    void resize(int nn) {  n = nn; mem0(arr[0]); }
    void build_sa(int s[], int m) { // m is biger than the max value of char
        rep_up0(i, m) c[i] = 0;
        rep_up0(i, n) c[x[i] = s[i]]++;
        rep_up1(i, m - 1) c[i] += c[i - 1];
        rep_down0(i, n) sa[--c[x[i]]] = i;
        for (int k = 1; k <= n; k <<= 1) {
            int p = 0;
            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] = 0;
            rep_up0(i, n) c[x[y[i]]]++;
            rep_up0(i, m) c[i] += c[i - 1];
            rep_down0(i, n) sa[--c[x[y[i]]]] = y[i];
            swap(x, y);
            p = 1; x[sa[0]] = 0;
            for (int i = 1; i < n; i++) {
                x[sa[i]] = y[sa[i - 1]] == y[sa[i]] && y[sa[i - 1] + k] == y[sa[i] + k]? p - 1 : p++;
            }
            if (p >= n) break;
            m = p;
        }
    }
    void build_height(int s[]) {
        mem0(height);
        int k = 0;
        rep_up0(i, n) rnk[sa[i]] = i;
        rep_up0(i, n) {
            if (k) k--;
            int j = sa[rnk[i] - 1];
            while (s[i + k] == s[j + k]) k++;
            height[rnk[i]] = k;
        }
    }
    int solve(int n) {
        int ans = 0;
        for (int i = 2; i <= n; i ++) {
            if (height[i] > height[i - 1]) ans += height[i] - height[i - 1];
        }
        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) + 1;
        rep_up0(i, len) ss[i] = s[i];
        sa.resize(len);
        sa.build_sa(ss, 128);
        sa.build_height(ss);
        cout << sa.solve(len - 1) << endl;
    }
    return 0;
}

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。