洛谷 P1137 旅行计划 （拓扑排序+dp）

在DAG中，拓扑排序可以确定dp的顺序

把图的信息转化到一个拓扑序上

注意转移的时候要用边转移

这道题的dp是用刷表法

#include<bits/stdc++.h>
#define REP(i, a, b) for(register int i = (a); i < (b); i++)
#define _for(i, a, b) for(register int i = (a); i <= (b); i++)
using namespace std;

const int MAXN = 1e5 + ;
struct Edge{ int to, next; };
Edge e[MAXN << ];
int head[MAXN], d[MAXN];
int topo[MAXN], dp[MAXN];
int n, m, cnt, tot;

void AddEdge(int from, int to)
{
    e[tot] = Edge{to, head[from]};
    head[from] = tot++;
}

void read(int& x)
{
    int f = ; x = ; char ch = getchar();
    while(!isdigit(ch)) { if(ch == '-') f = -; ch = getchar(); }
    while(isdigit(ch)) { x = x *  + ch - ''; ch = getchar(); }
    x *= f;
}

void toposort()
{
    queue<int> q;
    _for(i, , n)
        if(!d[i])
            q.push(i);
    while(!q.empty())
    {
        int u = q.front(); q.pop();
        topo[++cnt] = u;
        for(int i = head[u]; ~i; i = e[i].next)
        {
            int v = e[i].to;
            if(--d[v] == ) q.push(v);
        }
    }
}

int main()
{
    memset(head, -, sizeof(head)); tot = ;
    read(n); read(m);

    _for(i, , m)
    {
        int u, v;
        read(u); read(v);
        AddEdge(u, v);
        d[v]++;
    }

    toposort();
    _for(i, , n) dp[i] = ;
    _for(i, , n)
    {
        int u = topo[i];
        for(int i = head[u]; ~i; i = e[i].next)
        {
            int v = e[i].to;
            dp[v] = max(dp[v], dp[u] + );
        }
    }
    _for(i, , n) printf("%d\n", dp[i]);

    return ;
}

还可以用记忆化搜索

#include<bits/stdc++.h>
#define REP(i, a, b) for(register int i = (a); i < (b); i++)
#define _for(i, a, b) for(register int i = (a); i <= (b); i++)
using namespace std;

const int MAXN = 1e5 + ;
struct Edge{ int to, next; };
Edge e[MAXN << ];
int head[MAXN], dp[MAXN];
int n, m, cnt, tot;

void AddEdge(int from, int to)
{
    e[tot] = Edge{to, head[from]};
    head[from] = tot++;
}

void read(int& x)
{
    int f = ; x = ; char ch = getchar();
    while(!isdigit(ch)) { if(ch == '-') f = -; ch = getchar(); }
    while(isdigit(ch)) { x = x *  + ch - ''; ch = getchar(); }
    x *= f;
}

int dfs(int u)
{
    if(dp[u] != -) return dp[u];
    dp[u] = ;
    for(int i = head[u]; ~i; i = e[i].next)
    {
        int v = e[i].to;
        dp[u] = max(dp[u], dfs(v) + );
    }
    return dp[u];
}

int main()
{
    memset(head, -, sizeof(head)); tot = ;
    read(n); read(m);

    _for(i, , m)
    {
        int u, v;
        read(u); read(v);
        AddEdge(v, u);
    }

    memset(dp, -, sizeof(dp));
    _for(i, , n) printf("%d\n", dfs(i));

    return ;
}