Luogu P2743 [USACO5.1]乐曲主题Musical Themes

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人生第一道后缀数组的题目。首先要对输入的串进行差分处理，差分后长度为（\(n - 1\)）的相同子段就是原串中长度为\(n\)的相同（可变调）子段。求出来\(height\)以后，二分一个最大不相交重复子段长度，在\(can\_use\)里面维护长度为\(k\)的段划分，判断不相交只要用\(sa\)的差值算一下长度就好。

\(p.s.\)细节真的很多。

#include <bits/stdc++.h>
using namespace std;

const int N = 5010;

int n, m = 255, s[N], sa[N], rk[N], tp[N], _rk[N], bin[N], height[N];

void base_sort () {
    for (int i = 0; i <= m; ++i) bin[i] = 0;
    for (int i = 1; i <= n; ++i) bin[rk[tp[i]]]++;
    for (int i = 1; i <= m; ++i) bin[i] += bin[i - 1];
    for (int i = n; i >= 1; --i) sa[bin[rk[tp[i]]]--] = tp[i];
}

void suffix_sort () {
    for (int i = 1; i <= n; ++i) {
        rk[i] = s[i];
        tp[i] = i;
    }
    base_sort ();
    for (int w = 1; w <= n; w <<= 1) {
        int cnt = 0;
        for (int i = n - w + 1; i <= n; ++i) {
            tp[++cnt] = i;
        }
        for (int i = 1; i <= n; ++i) {
            if (sa[i] > w) {
                tp[++cnt] = sa[i] - w;
            }
        }
        base_sort ();
        memcpy (_rk, rk, sizeof (rk));
        rk[sa[1]] = cnt = 1;
        for (int i = 2; i <= n; ++i) {
            rk[sa[i]] = _rk[sa[i]] == _rk[sa[i - 1]] && _rk[sa[i] + w] == _rk[sa[i - 1] + w] ? cnt : ++cnt;
        }
        if (cnt == n) break;
        m = cnt;
    }
}

void get_height () {
    int k = 0;
    for (int i = 1; i <= n; ++i) {
        if (k != 0) k = k - 1;
        int j = sa[rk[i] - 1];
        while (s[i + k] == s[j + k]) {
            k = k + 1;
        }
        height[rk[i]] = k;
    }
}

const int INF = 0x3f3f3f3f;

bool can_use (int k) {
    //是否有长度>=k的不交叉子串
    int max_sa = sa[1], min_sa = sa[1];
    for (int i = 2; i <= n; ++i) {
        if (height[i] >= (k - 1)) {
            //即原串中旋律长度 >= k
            max_sa = max (max_sa, sa[i]);
            min_sa = min (min_sa, sa[i]);
            if (max_sa - min_sa >= k) {
                return true;
            }
        } else {
            max_sa = sa[i];
            min_sa = sa[i];
        }
    }
    return false;
}

int main () {
    cin >> n;
    for (int i = 1; i <= n; ++i) {
        cin >> s[i];
    }
    for (int i = n; i >= 1; --i) {
        s[i] = s[i] - s[i - 1] + 90;
        //把s差分,出现n-1个相同项说明最长为n
    }
    // printf ("str Test   :  "); for (int i = 1; i <= n; ++i) printf ("%3d ", s[i]); putchar ('\n');
    suffix_sort ();
    get_height ();
    // printf ("height Test : "); for (int i = 1; i <= n; ++i) printf ("%3d ", height[i]); printf ("\n");
    int l = 0, r = n;
    while (l < r) {
        // printf ("l = %d, r = %d\n", l, r);
        int mid = (l + r + 1) >> 1;
        if (can_use (mid)) {
            //存在长度 >= mid的不交叉子串
            l = mid;
        } else {
            r = mid - 1;
        }
    }
    if (l < 5) printf ("0\n");
    else printf ("%d\n", l);
}

Luogu P2743 [USACO5.1]乐曲主题Musical Themes

原文：https://www.cnblogs.com/maomao9173/p/10433030.html