uva 10829 - L-Gap Substrings(后缀数组)

题目链接：uva 10829 - L-Gap Substrings

题目大意：给定一个字符串，问有多少字符串满足UVU的形式，要求U非空，V的长度为g。

解题思路；对字符串的正序和逆序构建后缀数组，然后枚举U的长度l，每次以长度l分区间，在l和l+d+g所在的两个区间上确定U的最大长度。

#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <algorithm>

using namespace std;

typedef long long ll;
const int maxn = 100005;

struct Suffix_Arr {
    int n, len, s[maxn];
    int SA[maxn], rank[maxn], height[maxn];
    int tmp_one[maxn], tmp_two[maxn], c[30];

    int d[maxn][20];

    void init(char* str);
    void build_arr(int m);
    void get_height();

    void rmq_init();
    int rmq_query(int l, int r);
    ll solve(int m);

    void put();
}AC;

char str[maxn];

int main () {
    int cas, n;
    scanf("%d", &cas);
    for (int i = 1; i <= cas; i++) {
        scanf("%d%s", &n, str);
        AC.init(str);
        printf("Case %d: %lld\n", i, AC.solve(n));
    }
    return 0;
}

void Suffix_Arr::put () {
    for (int i = 0; i < n; i++)
        printf("%d ", SA[i]);
    printf("\n");

    for (int i = 0; i < n; i++)
        printf("%d ", height[i]);
    printf("\n");
}

ll Suffix_Arr::solve(int m) {
    build_arr(28);
    get_height();

    rmq_init();

    ll ret = 0;
    for (int l = 1; l < len / 2; l++) {
        for (int i = 0; i < len; i += l) {
            int j = i + l + m, sum = 0;

            if (j < len)
                sum += min(rmq_query(rank[i], rank[j]), l);
            if (i)
                sum += min(rmq_query(rank[n-i-1], rank[n-j-1]), l-1);
            ret += max(0, sum - l + 1);
        }
    }
    return ret;
}

int Suffix_Arr::rmq_query(int l, int r) {

    if (l > r) swap(l, r);
    l++;

    int k = 0;
    while ((1<<(k+1)) <= r - l + 1) k++;
    return min(d[l][k], d[r - (1<<k) + 1][k]);
}

void Suffix_Arr::rmq_init() {
    for (int i = 0; i < n; i++) d[i][0] = height[i];

    for (int k = 1; (1<<k) <= n; k++) {
        for (int i = 0; i + (1<<k) - 1 < n; i++)
            d[i][k] = min(d[i][k-1], d[i+(1<<(k-1))][k-1]);
    }
}

void Suffix_Arr::init(char* str) {
    n = 0;
    len = strlen(str);
    for (int i = 0; i < len; i++)
        s[n++] = str[i] - 'a' + 1;
    s[n++] = 27;
    for (int i = len - 1; i >= 0; i--)
        s[n++] = str[i] - 'a' + 1;
    s[n++] = 0;
}

void Suffix_Arr::get_height() {
    for (int i = 0; i < n; i++)
        rank[SA[i]] = i;

    int mv = height[0] = 0;
    for (int i = 0; i < n - 1; i++) {
        if (mv) mv--;

        int j = SA[rank[i] - 1];
        while (s[i+mv] == s[j+mv])
            mv++;
        height[rank[i]] = mv;
    }
}

void Suffix_Arr::build_arr(int m) {
    int *x = tmp_one, *y = tmp_two;

    for (int i = 0; i < m; i++) c[i] = 0;
    for (int i = 0; i < n; i++) c[x[i] = s[i]]++;
    for (int i = 1; i < m; i++) c[i] += c[i-1];
    for (int i = n-1; i >= 0; i--) SA[--c[x[i]]] = i;

    for (int k = 1; k <= n; k <<= 1) {

        int mv = 0;
        for (int i = n - k; i < n; i++) y[mv++] = i;
        for (int i = 0; i < n; i++) if (SA[i] >= k)
            y[mv++] = SA[i] - k;

        for (int i = 0; i < m; i++) c[i] = 0;
        for (int i = 0; i < n; i++) c[x[y[i]]]++;
        for (int i = 1; i < m; i++) c[i] += c[i-1];
        for (int i = n-1; i >= 0; i--) SA[--c[x[y[i]]]] = y[i];

        swap(x, y);
        mv = 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] ? mv - 1 : mv++);

        if (mv >= n)
            break;
        m = mv;
    }
}