BZOJ 2427 [HAOI2010]软件安装 | 这道树形背包裸题严谨地证明了我的菜

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BZOJ 2427

题解

Tarjan把环缩成点，然后跑树形背包即可。

我用的树形背包是DFS序上搞的那种。

要注意dp数组初始化成-INF！

要注意dp顺推的时候也不要忘记看数组是否越界！

长太息以掩涕兮，

哀bug之难De...

#include <cstdio>
#include <cmath>
#include <cstring>
#include <algorithm>
#include <cstdlib>
#include <ctime>
using namespace std;
typedef long long ll;
#define enter putchar('\n')
#define space putchar(' ')
template <class T>
void read(T &x){
    char c;
    bool op = 0;
    while(c = getchar(), c > '9' || c < '0')
        if(c == '-') op = 1;
    x = c - '0';
    while(c = getchar(), c >= '0' && c <= '9')
        x = x * 10 + c - '0';
    if(op) x = -x;
}
template <class T>
void write(T x){
    if(x < 0) putchar('-'), x = -x;
    if(x >= 10) write(x / 10);
    putchar('0' + x % 10);
}

const int N = 105, M = 505, _INF = 0xc0c0c0c0;
int n, m, ans, _c[N], _w[N], c[N], w[N], fa[N], _adj[N], _nxt[N];
int dfn[N], low[N], idx, stk[N], top, bel[N], scc, cnt[N];
int adj[N], nxt[N], dp[N][M], sze[N], seq[N], tot;
bool ins[N];
void tarjan(int u){
    dfn[u] = low[u] = ++idx;
    stk[++top] = u, ins[u] = 1;
    for(int v = _adj[u]; v; v = _nxt[v])
        if(!dfn[v])
            tarjan(v), low[u] = min(low[u], low[v]);
        else if(ins[v])
            low[u] = min(low[u], dfn[v]);
    if(low[u] == dfn[u]){
        ++scc;
        int v = 0;
        while(v != u){
            ins[v = stk[top--]] = 0;
            bel[v] = scc, cnt[scc]++;
            c[scc] += _c[v], w[scc] += _w[v];
        }
    }
}
void rebuild(){
    static bool vis[N] = {0};
    for(int i = 1; i <= n; i++)
        if(cnt[bel[i]] > 1 && !vis[bel[i]])
            nxt[bel[i]] = adj[0], adj[0] = bel[i], vis[bel[i]] = 1;
        else if(cnt[bel[i]] == 1)
            nxt[bel[i]] = adj[bel[fa[i]]], adj[bel[fa[i]]] = bel[i];
}
void dfs(int u){
    seq[++tot] = u, sze[u] = 1;
    for(int v = adj[u]; v; v = nxt[v])
        dfs(v), sze[u] += sze[v];
}
int main(){
    read(n), read(m);
    for(int i = 1; i <= n; i++) read(_c[i]);
    for(int i = 1; i <= n; i++) read(_w[i]);
    for(int i = 1; i <= n; i++)
        read(fa[i]), _nxt[i] = _adj[fa[i]], _adj[fa[i]] = i;
    for(int i = 1; i <= n; i++)
        if(!dfn[i]) tarjan(i);
    rebuild();
    dfs(0);
    memset(dp, _INF, sizeof(dp));
    dp[1][0] = 0;
    for(int i = 1; i <= tot; i++){
        for(int j = 0; j <= m; j++){
            dp[i + sze[seq[i]]][j] = max(dp[i + sze[seq[i]]][j], dp[i][j]);
            if(j + c[seq[i]] <= m)
                dp[i + 1][j + c[seq[i]]] = max(dp[i + 1][j + c[seq[i]]], dp[i][j] + w[seq[i]]);
        }
    }
    for(int j = 0; j <= m; j++)
        ans = max(ans, dp[tot + 1][j]);
    write(ans), enter;
    return 0;
}