poj 1743 Musical Theme(后缀数组)

本文介绍了如何使用后缀数组和前缀匹配算法解决POJ1743MusicalTheme问题,通过构建后缀数组并进行高度计算,实现了对序列的高效处理和匹配,最终找到了解决问题的最优解。

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题目链接:poj 1743 Musical Theme

代码

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

using namespace std;
const int maxn = 2 * 1e4 + 5;

struct Suffix_Arr {
    int n, s[maxn];
    int SA[maxn], rank[maxn], height[maxn];
    int tmp_one[maxn], tmp_two[maxn], c[205];

    void init (int* t, int k);
    void build(int m);
    void getHeight();

    bool judge(int m);
    int solve();
}AC;

int N, A[maxn];

int main () {
    while (scanf("%d", &N) == 1 && N) {
        for (int i = 0; i < N; i++) scanf("%d", &A[i]);
        for (int i = 0; i < N-1; i++) A[i] = A[i+1] - A[i] + 89;
        AC.init(A, N-1);
        printf("%d\n", AC.solve());
    }
    return 0;
}

bool Suffix_Arr::judge(int m) {
    int p = 1;

    while (p < n) {
        while (p < n && height[p] < m) p++;
        if (p >= n) break;
        int l = SA[p-1];
        int r = SA[p-1];

        while (p < n && height[p] >= m) {
            l = min(l, SA[p]);
            r = max(r, SA[p]);
            p++;
        }
        if (r - l >= m) return true;
    }
    return false;
}

int Suffix_Arr::solve() {
    build(200);
    getHeight();

    int l = 0, r = n / 2;
    for (int i = 0; i < 100; i++) {
        int mid = (l + r) >> 1;
        if (judge(mid)) l = mid;
        else r = mid;
    }
    if (l < 4) return 0;
    return l + 1;
}

void Suffix_Arr::init(int* t, int k) {
    n = 0;
    for (int i = 0; i < k; i++)
        s[n++] = t[i];
    s[n++] = 0;
}

void Suffix_Arr::getHeight() {
    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 (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;
    }
}
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