【作業存檔】Dijkstra算法的練習

作爲一個無腦莽撞的少年，完成這次（超簡單的）作業歷經波折。

目標是用函數實現，找到圖中每個點到源所有的加權最短路徑，記錄下總長度（邊的權值和）和條數。如果不相連，總長度爲-1和條數0

dist記錄總長度，count記錄找到了幾條這樣的路徑。

用Dijkstra算法可以直接實現非常簡單，但是我太心急和浮躁，沒有徹底弄清楚D算法就直接上手，導致繞了遠路。

不過，也學到了很重要的東西：

1.寫代碼前一定要搞清楚算法，

2.學習數據結構不能聽聽課就好，課下要花功夫鑽研。

3.發現自己的算法改起來很困難的時候，直接推翻換一個思路。

4.寫同一個代碼超過兩個小時就去做點別的事情，回來可以直接推翻重寫。

【知識點複習】：用矩陣表示有向圖，行代表出發的結點，列代表進入的節點

【錯誤總結】：

如果要用Queue來實現Dijkstra算法，需要用最小堆纔可以（（（非常麻煩所以在數據量很小的時候就用數組儲存吧

用兩次D算法（參考網上代碼，後來發現可以合併成一次）和用一次D算法中有很多細節錯誤（if語句括號沒括全），但最重要的問題是，缺少Graph->G[V][W]!= INFINITY

然而題目並沒有說過這種事情（（

下面放上最後的代碼

void ShortestDist(MGraph Graph, int dist[], int count[], Vertex S){
    bool isVisit[MaxVertexNum];
    int i, minDis,V, W, tmpDis;
    
    for (i = 0; i < Graph->Nv; i++){
        dist[i] = -1;
        
        count[i] = 0;
        isVisit[i] = false;
    }
    dist[S] = 0;
    count[S] = 1;
    
    while (1){
        minDis = INFINITY;
        
        for (i = 0; i < Graph->Nv; i++){
            if (!isVisit[i] && dist[i] < minDis && dist[i] != -1){
                V = i;
                minDis = dist[V];
            }
        }
        if (minDis == INFINITY) break;
        isVisit[V] = true;
        
        for (W = 0; W < Graph->Nv; W++){
            tmpDis = dist[V] + Graph->G[V][W];
            if(isVisit[W] == false && Graph->G[V][W] >= 0 && Graph->G[V][W] != INFINITY){
                if( (dist[V] + Graph->G[V][W] < dist[W]||dist[W] == -1)){
                    dist[W] = tmpDis;
                    count[W] = count[V];
                }
                else if (dist[V] + Graph->G[V][W] == dist[W]){
                    count[W] += count[V];
                    
                }
            }
        }
    }
    
    
    
}

下面爲題目

4-1 Shortest Path [3]   (25分)

Write a program to not only find the weighted shortest distances, but also count the number of different minimum paths from any vertex to a given source vertex in a digraph. It is guaranteed that all the weights are positive.

Format of functions:

void ShortestDist( MGraph Graph, int dist[], int count[], Vertex S );

where MGraph is defined as the following:

typedef struct GNode *PtrToGNode;
struct GNode{
    int Nv;
    int Ne;
    WeightType G[MaxVertexNum][MaxVertexNum];
};
typedef PtrToGNode MGraph;

The shortest distance from V to the source S is supposed to be stored in dist[V]. If V cannot be reached from S, store -1 instead. The number of different minimum paths from V to the source S is supposed to be stored in count[V] and count[S]=1.

Sample program of judge:

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

typedef enum {false, true} bool;
#define INFINITY 1000000
#define MaxVertexNum 10  /* maximum number of vertices */
typedef int Vertex;      /* vertices are numbered from 0 to MaxVertexNum-1 */
typedef int WeightType;

typedef struct GNode *PtrToGNode;
struct GNode{
    int Nv;
    int Ne;
    WeightType G[MaxVertexNum][MaxVertexNum];
};
typedef PtrToGNode MGraph;

MGraph ReadG(); /* details omitted */

void ShortestDist( MGraph Graph, int dist[], int count[], Vertex S );

int main()
{
    int dist[MaxVertexNum], count[MaxVertexNum];
    Vertex S, V;
    MGraph G = ReadG();

    scanf("%d", &S);
    ShortestDist( G, dist, count, S );

    for ( V=0; V<G->Nv; V++ )
        printf("%d ", dist[V]);
    printf("\n");
    for ( V=0; V<G->Nv; V++ )
        printf("%d ", count[V]);
    printf("\n");

    return 0;
}

/* Your function will be put here */

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

8 11
0 4 5
0 7 10
1 7 30
3 0 40
3 1 20
3 2 100
3 7 70
4 7 5
6 2 1
7 5 3
7 2 50
3

Sample Output:

40 20 100 0 45 53 -1 50 
1 1 4 1 1 3 0 3