【最短路】 HDOJ 3873 Invade the Mars

最新推荐文章于 2020-02-13 20:04:06 发布

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本文探讨了Dijkstra算法的一种变形，用于解决在特定图中寻找到达每个节点的最短路径与通过其卫星节点的最大时间的问题。通过维护入度并关注单向边，实现了高效求解。

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dijstra的变形，对于每一个点，到达这个点的时间就是原图上到达该点的最短路和到达他的卫星中的最大值。。。维护一下入度就行了。。。。注意题目中的边是单向的。。。。

#include <iostream>
#include <queue> 
#include <stack> 
#include <map> 
#include <set> 
#include <bitset> 
#include <cstdio> 
#include <algorithm> 
#include <cstring> 
#include <climits>
#include <cstdlib>
#include <cmath>
#include <time.h>
#define maxn 3005
#define maxm 20000005
#define eps 1e-10
#define mod 1000000007
#define INF 1e17
#define lowbit(x) (x&(-x))
#define mp make_pair
#define ls o<<1
#define rs o<<1 | 1
#define lson o<<1, L, mid 
#define rson o<<1 | 1, mid+1, R 
typedef long long LL;
typedef unsigned long long ULL;
//typedef int LL;
using namespace std;

struct Edge
{
	int v;
	LL c;
	Edge *next;
}pool[maxm], *edges, *H[maxn], *h[maxn];

struct node
{
	int u;
	LL d;
	bool operator < (const node& b) const {
		return d > b.d;
	}
}now, tmp;

priority_queue<node> q;
LL dist[maxn], most[maxn];
int vis[maxn], in[maxn];
int n, m;

void addedges(int u, int v)
{
	edges->v = v;
	edges->next = h[u];
	h[u] = edges++;
}

void Addedges(int u, int v, LL c)
{
	edges->v = v;
	edges->c = c;
	edges->next = H[u];
	H[u] = edges++;
}

void init(void)
{
	edges = pool;
	memset(h, 0, sizeof h);
	memset(H, 0, sizeof H);
	memset(in, 0, sizeof in);
	memset(vis, 0, sizeof vis);
	memset(most, 0, sizeof most);
}

void read(void)
{
	int a, b;
	LL c;
	scanf("%d%d", &n, &m);
	while(m--) {
		scanf("%d%d%I64d", &a, &b, &c);
		Addedges(a, b, c);
	}
	for(int i = 1; i <= n; i++) {
		scanf("%d", &m);
		while(m--) {
			scanf("%d", &a);
			addedges(a, i);
			in[i]++;
		}
	}
}

LL dijstra(int s)
{
	for(int i = 0; i <= n; i++) dist[i] = INF;
	tmp.u = s, tmp.d = 0, dist[s] = 0;
	q.push(tmp);
	while(!q.empty()) {
		now = q.top(), q.pop();
		int u = now.u, d = now.d;
		if(vis[u]) continue;
		vis[u] = 1;
		for(Edge *e = H[u]; e; e = e->next) {
			if(dist[e->v] > dist[u] + e->c) {
				dist[e->v] = dist[u] + e->c;
				if(!in[e->v]) {
					dist[e->v] = max(dist[e->v], most[e->v]);
					tmp.u = e->v, tmp.d = dist[e->v];
					q.push(tmp);
				}
			}
		}
		for(Edge *e = h[u]; e; e = e->next) {
			most[e->v] = max(dist[u], most[e->v]);
			in[e->v]--;
			if(!in[e->v] && dist[e->v] != INF) {
				dist[e->v] = max(dist[e->v], most[e->v]);
				tmp.u = e->v, tmp.d = dist[e->v];
				q.push(tmp);
			}
		}
	}
	return dist[n];
}

void work(void)
{
	printf("%I64d\n", dijstra(1));
}

int main(void)
{
	int _;
	while(scanf("%d", &_)!=EOF) {
		while(_--) {
			init();
			read();
			work();
		}
	}

	return 0;
}