08-图8 How Long Does It Take
一、题目
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 (≤), 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
二、思路
规规矩矩的拓扑排序
三、参考代码
![](https://images.cnblogs.com/OutliningIndicators/ContractedBlock.gif)
#include <stdlib.h> #include <cstdio> #include <queue> #define MaxVertexNum 102 #define INFINITY 65536 using namespace std; typedef int Vertex; typedef int WeightType; typedef int DataType; int Indegree[MaxVertexNum]; typedef struct ENode *Edge; struct ENode{ Vertex V1, V2; WeightType Weight; }; typedef struct AdjVNode *PtrToAdjVNode; struct AdjVNode{ Vertex AdjV; WeightType Weight; PtrToAdjVNode Next; }; typedef struct Vnode{ PtrToAdjVNode FirstEdge; DataType Data; } AdjList[MaxVertexNum]; /* AdjListÊÇÁÚ½Ó±íÀàÐÍ */ typedef struct GNode *LGraph; struct GNode{ int Nv; int Ne; AdjList G; }; LGraph CreateGraph( int VertexNum ); void InsertEdge( LGraph Graph, Edge E ); LGraph BuildGraph(); bool topSort(LGraph Graph); void find_max(LGraph Graph); int main() { LGraph Graph = BuildGraph(); if( !topSort(Graph) ) printf("Impossible\n"); else { find_max(Graph); } } LGraph CreateGraph( int VertexNum ) { Vertex V; LGraph Graph; Graph = (LGraph)malloc( sizeof(struct GNode) ); Graph->Nv = VertexNum; Graph->Ne = 0; for (V=0; V<Graph->Nv; V++) Graph->G[V].FirstEdge = NULL; return Graph; } void InsertEdge( LGraph Graph, Edge E ) { PtrToAdjVNode newNode = new AdjVNode; newNode->Weight = E->Weight; newNode->AdjV = E->V2; newNode->Next = Graph->G[E->V1].FirstEdge; Graph->G[E->V1].FirstEdge = newNode; } LGraph BuildGraph() { LGraph Graph; int Nv; Edge E; Vertex V; scanf("%d", &Nv); Graph = CreateGraph(Nv); scanf("%d", &(Graph->Ne)); if(Graph->Ne) { E = new ENode; for(int i=0; i<Graph->Ne; i++) { scanf("%d %d %d", &(E->V1), &(E->V2), &(E->Weight)); InsertEdge(Graph, E); } } for(V=0; V<Graph->Nv; V++) { Graph->G[V].Data = 0; } return Graph; } bool topSort(LGraph Graph) { int cnt; Vertex V; queue<Vertex> Q; cnt = 0; for( V=0; V<Graph->Nv; V++) Indegree[V] = 0; for( V = 0; V < Graph->Nv; V++) { for(PtrToAdjVNode W = Graph->G[V].FirstEdge; W; W=W->Next) { Indegree[W->AdjV]++; Graph->G[W->AdjV].Data = 0; } } for(V=0; V<Graph->Nv; V++) if(Indegree[V] == 0) Q.push(V); while(!Q.empty()) { V = Q.front(); Q.pop(); cnt++; for(PtrToAdjVNode W = Graph->G[V].FirstEdge; W; W=W->Next) { if(--Indegree[W->AdjV] == 0) Q.push(W->AdjV); if(Graph->G[W->AdjV].Data < W->Weight + Graph->G[V].Data) Graph->G[W->AdjV].Data = W->Weight + Graph->G[V].Data; } } if(cnt != Graph->Nv) return false; return true; } void find_max(LGraph Graph) { Vertex V; int compTime; compTime = Graph->G[0].Data; for(V = 1; V < Graph->Nv; V++) { if(Graph->G[V].Data > compTime) compTime = Graph->G[V].Data; } printf("%d\n", compTime); }