POJ 3160 Father Christmas flymouse 强连通分量+缩点+DP

这道题的大意就是,给出一个有向图,每个点有一个点权,点权可能是正也可能为负,一个人从某点出发,沿着一些路,访问结点,或者仅仅是路过这个结点,而不去访问,最后求他能访问到的最大的点权和。

我们注意到,他对某个结点是可以选择访问或者不访问的,那么只用访问那些点权为正数的点了。

首先,求强连通分量,缩点,然后新点的点权就是原强连通分量中,所有正点权之和。

之后就要进行DP求解,我在本题中使用了Kosaraju算法,其好处就是,最后缩点后,恰好形成拓扑序列,而DP就要从拓扑序靠后的点往前进行DP,这样才能从叶子结点往根部进行DP,从而得到正确答案


/*
ID: sdj22251
PROG: subset
LANG: C++
*/
#include <iostream>
#include <vector>
#include <list>
#include <map>
#include <set>
#include <deque>
#include <queue>
#include <stack>
#include <bitset>
#include <algorithm>
#include <functional>
#include <numeric>
#include <utility>
#include <sstream>
#include <iomanip>
#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <cctype>
#include <string>
#include <cstring>
#include <cmath>
#include <ctime>
#define LOCA
#define MAXN 5005
#define INF 100000000
#define eps 1e-7
using namespace std;
struct Edge
{
    int v, next;
}edge[10 * MAXN], revedge[10 * MAXN], newedge[MAXN];
int head[MAXN], revhead[MAXN], e, visited[MAXN], newhead[MAXN];
int order[MAXN], cnt, id[MAXN], val[MAXN], newval[MAXN];
int uu[5 * MAXN], vv[5 * MAXN], out[MAXN], dp[MAXN];
int n, m;
int ans;
void init()
{
    e = 0;
    memset(head, -1, sizeof(head));
    memset(revhead, -1, sizeof(revhead));
    memset(newhead, -1, sizeof(newhead));
    memset(out, 0 , sizeof(out));
    memset(newval, 0, sizeof(newval));
    memset(dp, 0, sizeof(dp));
}
void insert(const int &x, const int &y)
{
    edge[e].v = y;
    edge[e].next = head[x];
    head[x] = e;
    revedge[e].v = x;
    revedge[e].next = revhead[y];
    revhead[y] = e;
    e++;
}
void newinsert(const int &x, const int &y)
{
    newedge[e].v = y;
    newedge[e].next = newhead[x];
    newhead[x] = e++;
}
void readdata()
{
    for(int i = 1; i <= n; i++)
        scanf("%d", &val[i]);
    for(int i = 0; i < m; i++)
    {
        scanf("%d%d", &uu[i], &vv[i]);
        uu[i]++;
        vv[i]++;
        insert(uu[i], vv[i]);
    }
}
void dfs(int u)
{
    visited[u] = 1;
    for(int i = head[u]; i != -1; i = edge[i].next)
    {
        int v = edge[i].v;
        if(!visited[v])
            dfs(v);
    }
    order[cnt++] = u;
}
void dfs_rev(int u)
{
    visited[u] = 1;
    id[u] = cnt;
    if(val[u] > 0) newval[cnt] += val[u];
    for(int i = revhead[u]; i != -1; i = revedge[i].next)
    {
        int v = revedge[i].v;
        if(!visited[v])
            dfs_rev(v);
    }
}
void Kosaraju()
{
    init();
    readdata();
    memset(visited, 0, sizeof(visited));
    cnt = 0;
    for(int i = 1; i <= n; i++)
    {
        if(!visited[i])
            dfs(i);
    }
    memset(visited, 0, sizeof(visited));
    cnt = 0;
    for(int i = n - 1; i >= 0; i--)
    {
        if(!visited[order[i]])
        {
            cnt++;
            dfs_rev(order[i]);
        }
    }
    e = 0;
    for(int i = 0; i < m; i++)
    {
        int u = id[uu[i]];
        int v = id[vv[i]];
        if(u != v) newinsert(u, v);
    }
    ans = 0;
    for(int u = cnt; u >= 1; u--)
    {
        int tmp = 0;
        dp[u] = newval[u];
        for(int i = newhead[u]; i != -1; i = newedge[i].next)
        {
            int v = newedge[i].v;
            tmp = max(tmp, dp[v]);
        }
        dp[u] += tmp;
        ans = max(ans, dp[u]);
    }
}
int main()
{
    while(scanf("%d%d", &n, &m) != EOF)
    {
        Kosaraju();
        printf("%d\n", ans);
    }
    return 0;
}


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