08-图8 How Long Does It Take
08-图8 How Long Does It Take (25分)
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 NN (\le 100≤100), the number of activity check points (hence it is assumed that the check points are numbered from 0 to N-1N−1), and MM, the number of activities. Then MM 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
题目分析：
这是一个拓扑排序的变形，重点在于这个要求
For each test case, if the scheduling is possible, print in a line its earliest completion time; or simply output “Impossible”.
要对老师给的TopSort函数做一个简单的处理，让它达成这个要求。
做一个全局变量Earliest[]，用来计算到这个节点所花费的时间，然后不断地更新它，如果有多条路径到达，选择花费时间最长的；
被测试点误导了一次，其实就算是多个起点多个终点，也要选择Earliest[]中最长的，这才是整个项目的完成时间。
#include */
WeightType Weight; /* 权重 */
};
typedef PtrToENode Edge;
/* 邻接点的定义 */
typedef struct AdjVNode *PtrToAdjVNode;
struct AdjVNode{
Vertex AdjV; /* 邻接点下标 */
WeightType Weight; /* 边权重 */
PtrToAdjVNode Next; /* 指向下一个邻接点的指针 */
};
/* 顶点表头结点的定义 */
typedef struct Vnode{
PtrToAdjVNode FirstEdge;/* 边表头指针 */
} AdjList[MaxVertexNum]; /* AdjList是邻接表类型 */
/* 图结点的定义 */
typedef struct GNode *PtrToGNode;
struct GNode{
int Nv; /* 顶点数 */
int Ne; /* 边数 */
AdjList G; /* 邻接表 */
};
typedef PtrToGNode LGraph; /* 以邻接表方式存储的图类型 */
typedef int Position;
typedef int ElementType;
struct QNode {
ElementType *Data; /* 存储元素的数组 */
Position Front, Rear; /* 队列的头、尾指针 */
int MaxSize; /* 队列最大容量 */
};
typedef struct QNode *Queue;
LGraph CreateGraph( int VertexNum );
void InsertEdge( LGraph Graph, Edge E );
LGraph BuildGraph();
bool TopSort( LGraph Graph, Vertex TopOrder[] );
Queue CreateQueue( int MaxSize );
bool IsFull( Queue Q );
bool AddQ( Queue Q, ElementType X );
bool IsEmpty( Queue Q );
ElementType DeleteQ( Queue Q );
//全局变量
int Earliest[MaxVertexNum] = {0};//用来计算每个事项的完成时间
int main()
{
//freopen("in1.txt","r",stdin);
//freopen("in2.txt","r",stdin);
LGraph Graph;
bool flag;
Vertex TopOrder[MaxVertexNum] = {0};
Graph = BuildGraph();//建表
flag = TopSort( Graph, TopOrder);//拓扑排序
if(flag == false)
{
printf("Impossible");
}
else if(flag = true)
{
int max = Earliest[0];
for(int i=0; iNv; i++)//一条路径花费时间最大的就是结果
{
if(maxprintf("%d",max);// 输出
}
return 0;
}
LGraph CreateGraph( int VertexNum )
{ /* 初始化一个有VertexNum个顶点但没有边的图 */
Vertex V;
LGraph Graph;
Graph = (LGraph)malloc( sizeof(struct GNode) ); /* 建立图 */
Graph->Nv = VertexNum;
Graph->Ne = 0;
/* 初始化邻接表头指针 */
/* 注意：这里默认顶点编号从0开始，到(Graph->Nv - 1) */
for (V=0; VNv; V++)
Graph->G[V].FirstEdge = NULL;
return Graph;
}
void InsertEdge( LGraph Graph, Edge E )
{
PtrToAdjVNode NewNode;
/* 插入边 */
/* 为V2建立新的邻接点 */
NewNode = (PtrToAdjVNode)malloc(sizeof(struct AdjVNode));
NewNode->AdjV = E->V2;
NewNode->Weight = E->Weight;
/* 将V2插入V1的表头 */
NewNode->Next = Graph->G[E->V1].FirstEdge;
Graph->G[E->V1].FirstEdge = NewNode;
}
LGraph BuildGraph()
{
LGraph Graph;
Edge E;
Vertex V;
int Nv, i;
scanf("%d", &Nv); /* 读入顶点个数 */
Graph = CreateGraph(Nv); /* 初始化有Nv个顶点但没有边的图 */
scanf("%d", &(Graph->Ne)); /* 读入边数 */
if ( Graph->Ne != 0 ) { /* 如果有边 */
E = (Edge)malloc( sizeof(struct ENode) ); /* 建立边结点 */
/* 读入边，格式为"起点 终点 权重"，插入邻接矩阵 */
for (i=0; iNe; i++) {
scanf("%d %d %d", &E->V1, &E->V2, &E->Weight);
/* 注意：如果权重不是整型，Weight的读入格式要改 */
InsertEdge( Graph, E );
}
}
return Graph;
}
/* 邻接表存储 - 拓扑排序算法 */
bool TopSort( LGraph Graph, Vertex TopOrder[] )
{ /* 对Graph进行拓扑排序, TopOrder[]顺序存储排序后的顶点下标 */
int Indegree[MaxVertexNum], cnt;
Vertex V;
PtrToAdjVNode W;
Queue Q = CreateQueue( Graph->Nv );
/* 初始化Indegree[] */
for (V=0; VNv; V++)
Indegree[V] = 0;
/* 遍历图，得到Indegree[] */
for (V=0; VNv; V++)
for (W=Graph->G[V].FirstEdge; W; W=W->Next)
Indegree[W->AdjV]++; /* 对有向边AdjV>累计终点的入度 */
/* 将所有入度为0的顶点入列 */
for (V=0; VNv; V++)
if ( Indegree[V]==0 )
{
AddQ(Q, V);
Earliest[V] = 0;//所有入度为0的顶点所花费时间均为0
}
/* 下面进入拓扑排序 */
cnt = 0;
while( !IsEmpty(Q) ){
V = DeleteQ(Q); /* 弹出一个入度为0的顶点 */
TopOrder[cnt++] = V; /* 将之存为结果序列的下一个元素 */
/* 对V的每个邻接点W->AdjV */
for ( W=Graph->G[V].FirstEdge; W; W=W->Next )
if ( --Indegree[W->AdjV] == 0 )/* 若删除V使得W->AdjV入度为0 */
{
AddQ(Q, W->AdjV); /* 则该顶点入列 */
Earliest[W->AdjV] = Earliest[V] + W->Weight;
if( ( ( Earliest[V] + W->Weight ) > Earliest[W->AdjV] ) && Earliest[W->AdjV] )
{ //有多条路径到达，选择花费时间最长的
Earliest[W->AdjV] = Earliest[V] + W->Weight;
}
}
} /* while结束*/
if ( cnt != Graph->Nv )
return false; /* 说明图中有回路, 返回不成功标志 */
else
return true;
}
//队列相关
Queue CreateQueue( int MaxSize )
{
Queue Q = (Queue)malloc(sizeof(struct QNode));
Q->Data = (ElementType *)malloc(MaxSize * sizeof(ElementType));
Q->Front = Q->Rear = 0;
Q->MaxSize = MaxSize;
return Q;
}
bool IsFull( Queue Q )
{
return ((Q->Rear+1)%Q->MaxSize == Q->Front);
}
bool AddQ( Queue Q, ElementType X )
{
if ( IsFull(Q) ) {
printf("队列满");
return false;
}
else {
Q->Rear = (Q->Rear+1)%Q->MaxSize;
Q->Data[Q->Rear] = X;
return true;
}
}
bool IsEmpty( Queue Q )
{
return (Q->Front == Q->Rear);
}
ElementType DeleteQ( Queue Q )
{
if ( IsEmpty(Q) ) {
printf("队列空");
return ERROR;
}
else {
Q->Front =(Q->Front+1)%Q->MaxSize;
return Q->Data[Q->Front];
}
}