[Codeforces178F2]Representative Sampling

Problem

给定n个字符串Si，任意选出k个字符串Ai，使得其中任意两个字符串lcp之和最大。

Solution

建一棵trie树，枚举每一个节点对答案的贡献，树形dp，时间复杂度像是O(N^3)

由于每个点对只在自己LCA的时候枚举到贡献，所以是O(N^2)

Notice

这道题分析时间复杂度十分重要

Code

#include<cmath>
#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
using namespace std;
#define sqz main
#define ll long long
#define reg register int
#define rep(i, a, b) for (reg i = a; i <= b; i++)
#define per(i, a, b) for (reg i = a; i >= b; i--)
#define travel(i, u) for (reg i = head[u]; i; i = edge[i].next)
const int INF = 1e9, N = 2000, M = N * 500;
const double eps = 1e-6, phi = acos(-1);
ll mod(ll a, ll b) {if (a >= b || a < 0) a %= b; if (a < 0) a += b; return a;}
ll read(){ ll x = 0; int zf = 1; char ch; while (ch != '-' && (ch < '0' || ch > '9')) ch = getchar();
if (ch == '-') zf = -1, ch = getchar(); while (ch >= '0' && ch <= '9') x = x * 10 + ch - '0', ch = getchar(); return x * zf;}
void write(ll y) { if (y < 0) putchar('-'), y = -y; if (y > 9) write(y / 10); putchar(y % 10 + '0');}
int S = 0, num = 0, cnt[M + 5], deep[M + 5], head[M + 5], F[N * 2 + 5][N + 5], Size[M + 5], son[M][26];
char st[N + 5];
struct node
{
    int vet, next, val;
}edge[2 * M];
void add(int u, int v, int w)
{
    edge[++num].vet = v;
    edge[num].next = head[u];
    edge[num].val = w;
    head[u] = num;
}
void dfs(int u, int fa, int last)
{
    deep[u] = deep[fa] + 1;
    int tot = cnt[u];
    rep(i, 0, 25)
        if (son[u][i]) tot++;
    if (tot != 1 || cnt[u]) add(last, u, deep[u] - deep[last]);
    rep(i, 0, 25)
        if (son[u][i])
                if (tot == 1 && !cnt[u]) dfs(son[u][i], u, last);
                else dfs(son[u][i], u, u);
}
int dp(int u, int fa, int len)
{
    int now = ++S;
    Size[u] = cnt[u];
    per(i, cnt[u], 1) F[now][i] = i * (i - 1) / 2 * len;
    travel(i, u)
    {
        int v = edge[i].vet;
        if (v == u) continue;
        int pre = dp(v, u, edge[i].val);
        Size[u] += Size[v];
        per(j, Size[u], 1)
            rep(k, 1, min(j, Size[v]))
                F[now][j] = max(F[now][j], F[now][j - k] + F[pre][k] + len * (j - k) * k + len * k * (k - 1) / 2);
    }
    return now;
}
int sqz()
{
    memset(head, 0, sizeof head);
    int n = read(), m = read(), point = 0;
    rep(i, 1, n)
    {
        scanf("%s", st + 1);
        int len = strlen(st + 1), now = 0;
        rep(j, 1, len)
        {
            if (!son[now][st[j] - 'a']) son[now][st[j] - 'a'] = ++point;
            now = son[now][st[j] - 'a'];
        }
        cnt[now]++;
    }
    dfs(0, -1, 0);
    dp(0, -1, 0);
    printf("%d\n", F[1][m]);
    return 0;
}