zoj 1455 Schedule Problem 差分约束

        设d[i]为 第i个工作开始的时间,根据题意有:

        FAS a b: d[a] + time[a] >= d[b]

        FAF a b: d[a] + time[a] >= d[b] + time[b]

        SAF a b: d[a] >= d[b] + time[b]

        SAS a b: d[a] >= d[b]

       还有: d[i] >= 0 即 d[i] – d[0] >= 0

       以0为源点开始搜索,0是超源点

 

#include <iostream>

#include <queue>

#include <cstring>

#include <cstdio>

using namespace std;



const int MAX = 100000;

const int N = 10000;

const int INF = 1000000000;



struct Node

{

	int v;

	int cost;

	int next;

};



Node node[MAX];

int cnt[N];

int adj[N];

bool in_q[N];

int d[N], times[N];

int n;

int size;



void add_edge(int u, int v, int cost)

{

	node[size].v = v;

	node[size].cost = cost;

	node[size].next = adj[u];

	adj[u] = size++;

}



bool spfa()

{

	queue<int> Q;



	memset(cnt, 0, sizeof(cnt));

	memset(in_q, false, sizeof(in_q));

	for (int i = 0; i <= n; i++)

		d[i] = -INF;



	d[0] = 0;

	Q.push(0);

	in_q[0] = true;

	int u, v, w;



	while (!Q.empty())

	{

		u = Q.front();

		Q.pop();

		in_q[u] = false;



		for (int i = adj[u]; i != -1; i = node[i].next)

		{

			v = node[i].v;

			w = node[i].cost;



			if (d[v] < d[u] + w)

			{

				d[v] = d[u] + w;

				if (!in_q[v])

				{

					in_q[v] = true;

					Q.push(v);



					if (++cnt[v] > n) return false;

				}

			}

		}

	}



	return true;

}



int main()

{

	char c[20];

	int a, b;

	int cases = 1;



	while (scanf("%d", &n) != EOF)

	{

		if (n == 0) break;

		

		

		size = 0;

		for (int i = 0; i <= n; i++)

			adj[i] = -1;



		for (int i = 1; i <= n; i++)

			scanf("%d", &times[i]);



		while (1)

		{

			getchar();

			scanf("%s", c);

			if (strcmp(c, "#") == 0)

				break;

			else if (strcmp(c, "FAS") == 0)

			{

				scanf("%d%d", &a, &b);

				add_edge(b,a, -times[a]);

			}

			else if (strcmp(c, "FAF") == 0)

			{

				scanf("%d%d", &a, &b);

				add_edge(b,a, times[b]-times[a]);

			}

			else if (strcmp(c, "SAF") == 0)

			{

				scanf("%d%d", &a, &b);

				add_edge(b, a, times[b]);

			}

			else if (strcmp(c, "SAS") == 0)

			{

				scanf("%d%d", &a, &b);

				add_edge(b, a, 0);

			}

		}



		for (int i = 1; i <= n; i++)

			add_edge(0, i, 0);

		printf("Case %d:\n", cases++);



		if (spfa())

		{		

			for (int i = 1; i <= n; i++)

				printf("%d %d\n", i, d[i]);

		}

		else	

			printf("impossible\n");

		

		printf("\n");

		

	}

	return 0;

}

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