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P3900 [湖南集训] 图森

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P3900 [湖南集训] 图森

题面

题目链接

解法

代码极其恶心，所以简单写下思路。

基本思路是$dp$和建图。首先将所有串正向和反向串起来，这样$dp[i]$就表示当前回文串的其中一边拓展到了端点，另一边拓展到$i$的位置。往后转移只要枚举在其中一边加上哪个小串，用后缀数组$O(1)$找到能拓展几位。将这个$dp$的转移建图，如果不是DAG则显然有无限长度，输出Infinity。否则在上面做DAG最长路即可。时间复杂度$O(n^2L)$。

接下来是特殊处理。首先是初始状态，需要找出每个小串的前缀回文串和后缀回文串。这个用SA似乎可以暴力做。其次是图的边集$E$的大小，应当于时间复杂度同阶，显然不可能存下来，所以需要在每次做DAG时求一边边集，这样就保证空间复杂度不会太高。

除此之外，你还需要计算每个小串中包含的最长回文串。。。不然只有$90pts$（别问我怎么知道的）。所以再写个manacher吧。

下面放出我shit一样的代码

AC代码

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/**
 * @file:           P3900.cpp
 * @author:         yaoxi-std
 * @url:            https://www.luogu.com.cn/problem/P3900
*/
// #pragma GCC optimize ("O2")
// #pragma GCC optimize ("Ofast", "inline", "-ffast-math")
// #pragma GCC target ("avx,sse2,sse3,sse4,mmx")
#include <bits/stdc++.h>
using namespace std;
#define int long long
#define resetIO(x) \
    freopen(#x ".in", "r", stdin), freopen(#x ".out", "w", stdout)
#define debug(fmt, ...) \
    fprintf(stderr, "[%s:%d] " fmt "\n", __FILE__, __LINE__, ##__VA_ARGS__)
template <class _Tp>
inline _Tp& read(_Tp& x) {
    bool sign = false;
    char ch = getchar();
    long double tmp = 1;
    for (; !isdigit(ch); ch = getchar())
        sign |= (ch == '-');
    for (x = 0; isdigit(ch); ch = getchar())
        x = x * 10 + (ch ^ 48);
    if (ch == '.')
        for (ch = getchar(); isdigit(ch); ch = getchar())
            tmp /= 10.0, x += tmp * (ch ^ 48);
    return sign ? (x = -x) : x;
}
template <class _Tp>
inline void write(_Tp x) {
    if (x < 0)
        putchar('-'), x = -x;
    if (x > 9)
        write(x / 10);
    putchar((x % 10) ^ 48);
}
const int MAXN = 120;
const int MAXM = 1e6 + 10;
const int LOGM = 20;
const int INF = 0x3f3f3f3f3f3f3f3f;
struct SuffixArray {
    int n, sa[MAXM], rk[MAXM], tp[MAXM], he[MAXM];
    void radix_sort(int m) {
        static int buc[MAXM];
        for (int i = 0; i <= m; ++i)
            buc[i] = 0;
        for (int i = 1; i <= n; ++i)
            buc[rk[i]]++;
        for (int i = 1; i <= m; ++i)
            buc[i] += buc[i - 1];
        for (int i = n; i >= 1; --i)
            sa[buc[rk[tp[i]]]--] = tp[i];
    }
    void init(int n, char* s) {
        this->n = n;
        int m = 200;
        for (int i = 1; i <= n; ++i)
            rk[i] = s[i] + 1, tp[i] = i;
        radix_sort(m);
        for (int w = 1, p = 0; p < n; m = p, w <<= 1) {
            p = 0;
            for (int i = 1; i <= w; ++i)
                tp[++p] = n - w + i;
            for (int i = 1; i <= n; ++i)
                if (sa[i] > w)
                    tp[++p] = sa[i] - w;
            radix_sort(m);
            copy(rk + 1, rk + n + 1, tp + 1);
            rk[sa[1]] = p = 1;
            for (int i = 2; i <= n; ++i) {
                if (tp[sa[i - 1]] == tp[sa[i]] && tp[sa[i - 1] + w] == tp[sa[i] + w])
                    rk[sa[i]] = p;
                else
                    rk[sa[i]] = ++p;
            }
        }
        for (int i = 1, k = 0; i <= n; ++i) {
            if (k)
                k--;
            while (s[i + k] == s[sa[rk[i] - 1] + k])
                k++;
            he[rk[i]] = k;
        }
    }
} sa;
int n, m, tot, cnt, ans;
int fr[MAXN], bk[MAXN], ln[MAXN];
int lg2[MAXM], st[MAXM][LOGM];
int id[MAXM], dis[MAXM], deg[MAXM];
char buf[MAXM], str[MAXM];
vector<int> palfr[MAXN], palbk[MAXN];
int getlcp(int x, int y) {
    int l = sa.rk[x], r = sa.rk[y];
    if (l > r)
        swap(l, r);
    if (l == r)
        return INF;
    int k = lg2[r - l];
    return min(st[l + 1][k], st[r - (1 << k) + 1][k]);
}
void findedges(int i, function<void(int, int, int)> addedge) {
    if (i == 0) {
        for (int j = 1; j <= n; ++j) {
            for (auto l : palfr[j])
                addedge(i, fr[j] + l, l);
            for (auto l : palbk[j])
                addedge(i, bk[j] + l, l);
        }
        return;
    }
    if (i > m || str[i] == '$')
        return;
    int t = upper_bound(fr + 1, fr + n + 1, i) - fr - 1;
    if (i < bk[t]) {
        int len = ln[t] - (i - fr[t]);
        for (int j = 1; j <= n; ++j) {
            int lcp = min({len, ln[j], getlcp(i, bk[j])});
            if (lcp == len && lcp == ln[j]) {
                addedge(i, 0, lcp * 2);
            } else if (lcp == len) {
                addedge(i, bk[j] + lcp, lcp * 2);
            } else if (lcp == ln[j]) {
                addedge(i, i + lcp, lcp * 2);
            } else {
                addedge(i, m + 1, lcp * 2);
            }
        }
    } else {
        int len = ln[t] - (i - bk[t]);
        for (int j = 1; j <= n; ++j) {
            int lcp = min({len, ln[j], getlcp(i, fr[j])});
            if (lcp == len && lcp == ln[j]) {
                addedge(i, 0, lcp * 2);
            } else if (lcp == len) {
                addedge(i, fr[j] + lcp, lcp * 2);
            } else if (lcp == ln[j]) {
                addedge(i, i + lcp, lcp * 2);
            } else {
                addedge(i, m + 1, lcp * 2);
            }
        }
    }
}
int manacher(char* s, int tlen) {
    static int d[MAXM];
    static char t[MAXM];
    int len = 0;
    for (int i = 1; i <= tlen; ++i)
        t[++len] = '#', t[++len] = s[i];
    t[++len] = '#', t[++len] = '$';
    int mx = 0, id = 0, ans = 0;
    for (int i = 1; i <= len; ++i) {
        d[i] = mx > i ? min(d[id * 2 - i], mx - i) : 1;
        while (t[i + d[i]] == t[i - d[i]])
            ++d[i];
        if (i + d[i] > mx)
            mx = i + d[i], id = i;
        ans = max(ans, d[i] - 1);
    }
    return ans;
}
signed main() {
    read(n), m = 1;
    for (int i = 1; i <= n; ++i) {
        scanf("%s", buf);
        int t = ln[i] = strlen(buf);
        copy(buf, buf + t, str + m);
        fr[i] = m, str[m + t] = '$', m += t + 1;
        reverse(buf, buf + t);
        copy(buf, buf + t, str + m);
        bk[i] = m, str[m + t] = '$', m += t + 1;
    }
    str[m] = '$';
    sa.init(m, str);
    for (int i = 2; i <= m; ++i)
        lg2[i] = (i & (i - 1)) ? lg2[i - 1] : lg2[i - 1] + 1;
    for (int i = 1; i <= m; ++i)
        st[i][0] = sa.he[i];
    for (int j = 1; j < LOGM; ++j) {
        for (int i = 1; i + (1 << j) - 1 <= m; ++i) {
            st[i][j] = min(st[i][j - 1], st[i + (1 << (j - 1))][j - 1]);
        }
    }
    for (int i = 1; i <= n; ++i) {
        palfr[i].push_back(0);
        palfr[i].push_back(1);
        for (int j = 1; j + j <= ln[i]; ++j) {
            int p1 = fr[i] + j, p2 = bk[i] + (ln[i] - j);
            if (getlcp(p1, p2) >= j)
                palfr[i].push_back(j + j);
            if (j + j < ln[i]) {
                p1 = fr[i] + j + 1, p2 = bk[i] + (ln[i] - j);
                if (getlcp(p1, p2) >= j)
                    palfr[i].push_back(j + j + 1);
            }
        }
        palbk[i].push_back(0);
        palbk[i].push_back(1);
        for (int j = 1; j + j <= ln[i]; ++j) {
            int p1 = bk[i] + j, p2 = fr[i] + (ln[i] - j);
            if (getlcp(p1, p2) >= j)
                palbk[i].push_back(j + j);
            if (j + j < ln[i]) {
                p1 = bk[i] + j + 1, p2 = fr[i] + (ln[i] - j);
                if (getlcp(p1, p2) >= j)
                    palbk[i].push_back(j + j + 1);
            }
        }
    }
    for (int i = 0; i <= m; ++i) {
        findedges(i, [&](int u, int v, int w) -> void {
            ++deg[v];
        });
    }
    queue<int> que;
    for (int i = 0; i <= m + 1; ++i)
        if (!deg[i])
            que.push(i);
    while (!que.empty()) {
        int i = que.front();
        id[++cnt] = i, que.pop();
        findedges(i, [&](int u, int v, int w) -> void {
            if (--deg[v] == 0)
                que.push(v);
        });
    }
    for (int i = 0; i <= m + 1; ++i)
        if (deg[i])
            return puts("Infinity"), 0;
    memset(dis, -0x3f, sizeof(dis));
    dis[0] = 0;
    for (int i = 1; i <= cnt; ++i) {
        int x = id[i];
        findedges(x, [&](int u, int v, int w) -> void {
            dis[v] = max(dis[v], dis[u] + w);
        });
    }
    ans = dis[m + 1];
    for (int i = 1; i <= n; ++i)
        ans = max(ans, manacher(str + fr[i] - 1, ln[i]));
    write(ans), putchar('\n');
    return 0;
}