Is Topological Order pta 6-29

先讲思路，答案是第一段代码，题目在最后；

插个图方便理解：

这道题属于拓扑排序的运用，可以用拓扑排序的思路做，but，我的代码用了更简洁的思路：遍历Seq的每一个元素 Seq[ i ] 并确定其在 图Graph 中对应的下标 v ,collected[v]=1(收集v)；  p=Graph->G[v].FirstEdge，遍历（p=p->Next）同时判断p包括p之后的每一个Next是否有collected[p->AdjV]==1，若有则说明v指向的点中有已收集的，比如：5 2 1 3 6；i=2时v对应图中1（此时5和2都已经被收集），1指向2和3，而2已被收集，说明不是拓扑排序，return false；

答案代码如下：

//直接把seq带进去   seq[i]标记收集，
//i对应的每一个点走到，如果遍历i指向的点时遇到已经收集的点就return false 
bool IsTopSeq( LGraph Graph, Vertex Seq[] ){
	PtrToAdjVNode p;
	int collected[MaxVertexNum],i,v;
//标记已收集的边,注意这道题的不能定义在函数外面，因为题目一个main里调了好几次 
	for(i=0;i<MaxVertexNum;i++){
		collected[i]=0;
	}
	for(int i=0;i<Graph->Nv;i++){
		int v=Seq[i]-1;
		collected[v]=1;
		p=Graph->G[v].FirstEdge;//注意v-1 
		while(p){
			if(collected[p->AdjV]) return false;
			p=p->Next;
		}
	} 
	return true;
}

题目：

Write a program to test if a give sequence Seq is a topological order of a given graph Graph.

Format of functions:

bool IsTopSeq( LGraph Graph, Vertex Seq[] );

where LGraph is defined as the following:

typedef struct AdjVNode *PtrToAdjVNode; struct AdjVNode{ Vertex AdjV; PtrToAdjVNode Next; }; typedef struct Vnode{ PtrToAdjVNode FirstEdge; } AdjList[MaxVertexNum]; typedef struct GNode *PtrToGNode; struct GNode{ int Nv; int Ne; AdjList G; }; typedef PtrToGNode LGraph;

The function IsTopSeq must return true if Seq does correspond to a topological order; otherwise return false.

Note: Although the vertices are numbered from 1 to MaxVertexNum, they are indexed from 0 in the LGraph structure.

Sample program of judge:

#include <stdio.h>
#include <stdlib.h>

typedef enum {false, true} bool;
#define MaxVertexNum 10  /* maximum number of vertices */
typedef int Vertex;      /* vertices are numbered from 1 to MaxVertexNum */

typedef struct AdjVNode *PtrToAdjVNode; 
struct AdjVNode{
    Vertex AdjV;
    PtrToAdjVNode Next;
};

typedef struct Vnode{
    PtrToAdjVNode FirstEdge;
} AdjList[MaxVertexNum];

typedef struct GNode *PtrToGNode;
struct GNode{  
    int Nv;
    int Ne;
    AdjList G;
};
typedef PtrToGNode LGraph;

LGraph ReadG(); /* details omitted */

bool IsTopSeq( LGraph Graph, Vertex Seq[] );

int main()
{
    int i, j, N;
    Vertex Seq[MaxVertexNum];
    LGraph G = ReadG();
    scanf("%d", &N);
    for (i=0; i<N; i++) {
        for (j=0; j<G->Nv; j++)
            scanf("%d", &Seq[j]);
        if ( IsTopSeq(G, Seq)==true ) printf("yes\n");
        else printf("no\n");
    }

    return 0;
}

/* Your function will be put here */

Sample Input (for the graph shown in the figure):

6 8
1 2
1 3
5 2
5 4
2 3
2 6
3 4
6 4
5
1 5 2 3 6 4
5 1 2 6 3 4
5 1 2 3 6 4
5 2 1 6 3 4
1 2 3 4 5 6

Sample Output:

yes
yes
yes
no
no