PTA_2019春_088_How Long Does It Take

Given the relations of all the activities of a project, you are supposed to find the earliest completion time of the project.

Input Specification:

Each input file contains one test case. Each case starts with a line containing two positive integers N (≤100), the number of activity check points (hence it is assumed that the check points are numbered from 0 to N−1), and M, the number of activities. Then M lines follow, each gives the description of an activity. For the i-th activity, three non-negative numbers are given: S[i], E[i], and L[i], where S[i] is the index of the starting check point, E[i] of the ending check point, and L[i] the lasting time of the activity. The numbers in a line are separated by a space.

Output Specification:

For each test case, if the scheduling is possible, print in a line its earliest completion time; or simply output "Impossible".

Sample Input 1:

9 12
0 1 6
0 2 4
0 3 5
1 4 1
2 4 1
3 5 2
5 4 0
4 6 9
4 7 7
5 7 4
6 8 2
7 8 4

Sample Output 1:

18

Sample Input 2:

4 5
0 1 1
0 2 2
2 1 3
1 3 4
3 2 5

Sample Output 2:

Impossible

/* How Long Does It Take*/
/*判断是否为拓扑排序，即是否存在回路*/
/*邻接表，有向图*/
/*Earliest[0]= 0
  Earliest[w] = max{Earliest[v]+weight<v,W>}*/
/*最后输出最大的Eariest即为最短时间*/
#include<stdio.h>
#include<stdlib.h>
/*边的定义*/
typedef struct Enode* Edge;
struct Enode {
	int V1, V2;
	int weight;
};
/*邻接点的定义*/

typedef struct Adjvnode* prttoadjvnode;
struct Adjvnode {
	int adjv;
	int weight;
	prttoadjvnode next;
};
/*顶点定义*/
typedef struct Vnode {
	prttoadjvnode firstedge;
}adjlist[102];
/*图节点定义*/

struct Gnode {
	int Nv;/*顶点数*/
	int Ne;/*边数*/
	adjlist G; /*邻接表*/
};
typedef struct Gnode* Lgraph;
/*队列定义*/
typedef struct Qnode* ptrtoQnode;
struct Qnode {
	int* Data;/*data数组，*/
	int front, rear;/*队列头尾指针*/
	int maxsize;/*容量*/
};
typedef ptrtoQnode Queue;

int AddQ(Queue Q, int x);
Queue CreateQueue(int maxsize);
int isempty(Queue Q);
int DeleteQ(Queue Q);

Lgraph buildgraph(int N, int M);
void insertedge(Lgraph graph, Edge E);
Lgraph creatgraph(int size);

int Topsort(Lgraph graph);

int main() {
	int N,M;
	scanf("%d %d", &N, &M);
	Lgraph graph = buildgraph(N, M);
	int flag = Topsort(graph);
	if (flag == -1) printf("Impossible");
	else printf("%d", flag);
	return 0;
}
Lgraph creatgraph(int size) {
	Lgraph graph = (Lgraph)malloc(sizeof(struct Gnode));
	graph->Nv = size;
	graph->Ne = 0;
	for (int i = 0; i < size; i++) {
		graph->G[i].firstedge = NULL;
	}
	return graph;
}
void insertedge(Lgraph graph, Edge E) {  /*有向图*/
	/*v1,v2*/
	prttoadjvnode newnode = (prttoadjvnode)malloc(sizeof(struct Adjvnode));
	newnode->adjv = E->V2;
	newnode->weight = E->weight;
	newnode->next = graph->G[E->V1].firstedge;
	graph->G[E->V1].firstedge = newnode;
}
Lgraph buildgraph(int N, int M) {
	Lgraph graph;
	graph = creatgraph(N);
	graph->Ne = M;
	if (graph->Ne != 0) {
		Edge E = (Edge)malloc(sizeof(struct Enode));
		for (int i = 0; i < graph->Ne; i++) {
			scanf("%d %d %d", &E->V1, &E->V2, &E->weight);
			insertedge(graph, E);
		}
	}
	return graph;
}
int Topsort(Lgraph graph) {
	int* indegree = (int*)malloc(graph->Nv * sizeof(int));
	int* earliest = (int*)malloc(graph->Nv * sizeof(int));

	int v;
	prttoadjvnode w,j;
	Queue Q = CreateQueue(graph->Nv);
	for (v = 0; v < graph->Nv; v++) {  /*初始化为0*/
		earliest[v] = 0;
	}
	for (v = 0; v < graph->Nv; v++) {  /*初始化为0*/
		indegree[v] = 0;
	}
	for (v = 0; v < graph->Nv; v++) {  /*遍历图获得入度*/
		for (w = graph->G[v].firstedge; w; w = w->next) {
			indegree[w->adjv]++;
		}
	}
	//printf("\n");
	for (v = 0; v < graph->Nv; v++) {  /*入度为0 的入队*/
		if (indegree[v] == 0) {
			AddQ(Q, v);
		}
	}
	int cnt = 0;
	
	while (isempty(Q) == 0) {
        int temp_weight = 0;
		v = DeleteQ(Q);
		cnt++;
		for (int i = 0; i < graph->Nv; i++) {    /*遍历图找到 指向V的邻接点*/
			for (j = graph->G[i].firstedge; j; j = j->next) {
				if (j->adjv == v) {   
					if (earliest[i] + j->weight > temp_weight) {
						temp_weight = earliest[i] + j->weight;
					}
				}
			}
		}
		earliest[v] = temp_weight;
		for (w = graph->G[v].firstedge; w; w = w->next) {/*对v的每个邻接点*/
			if (--indegree[w->adjv] == 0) {
				AddQ(Q, w->adjv);
			}

		}
	}/*while结束以后v指向最后一个顶点*/
//	printf("cnt is %d num is %d\n", cnt, graph->Nv);
	int min = 0;
	for (int i = 0; i < graph->Nv; i++) {
		if (earliest[i] > min) {
			min = earliest[i];
		}
	}
	if (cnt != graph->Nv) return -1;
	else return min;
}
Queue CreateQueue(int maxsize) {
	Queue Q = (Queue)malloc(sizeof(struct Qnode));
	Q->Data = (int*)malloc(maxsize * sizeof(int));
	Q->front = Q->rear = 0;
	Q->maxsize = maxsize;
	return Q;
}
int AddQ(Queue Q, int x) {
	Q->rear = (Q->rear + 1) % (Q->maxsize);     /*若1%1，则值为0*/
	Q->Data[Q->rear] = x;
	return 1;
}
int isempty(Queue Q) {
	return(Q->rear == Q->front);
}
int DeleteQ(Queue Q) {
	Q->front = (Q->front + 1) % Q->maxsize;
	return Q->Data[Q->front];
}