数据结构-图

一、图的定义

二、邻接矩阵

三、边集数组

四、遍历

题目：

#include "stdio.h"
#include "time.h"


#define X 8
#define Y 8

 int chess[X][Y];

 int netxtxy(int *x, int *y, int count)
 {
     switch (count)
     {
        case 0:
            if (*x + 2 <= X - 1 && *y - 1 >= 0 && chess[*x + 2][*y - 1] == 0)
            {
                *x += 2;
                *y -= 1;
                return 1;
            }
            break;
        case 1:
            if (*x + 2 <= X - 1 && *y - 1 <= Y - 1  && chess[*x + 2][*y + 1] == 0)
            {
                *x += 2;
                *y += 1;
                return 1;
            }
            break;  
        case 2:
            if (*x + 1 <= X - 1 && *y - 2 >= 0  && chess[*x + 1][*y - 2] == 0)
            {
                *x += 1;
                *y -= 2;
                return 1;
            }
            break; 
        case 3:
            if (*x + 1 <= X - 1 && *y + 2 <= Y - 1  && chess[*x + 1][*y + 2] == 0)
            {
                *x += 1;
                *y += 2;
                return 1;
            }
            break;       
        case 4:
            if (*x - 1 >= 0 && *y - 2 >= 0  && chess[*x - 1][*y - 2] == 0)
            {
                *x -= 1;
                *y -= 2;
                return 1;
            }
            break;      
        case 5:
            if (*x - 1 >= 0 && *y + 2 <= Y - 1  && chess[*x - 1][*y + 2] == 0)
            {
                *x -= 1;
                *y += 2;
                return 1;
            }
            break;      
        case 6:
            if (*x - 2 >= 0 && *y - 1 >= 0  && chess[*x - 2][*y - 1] == 0)
            {
                *x -= 2;
                *y -= 1;
                return 1;
            }
            break;      
        case 7:
            if (*x - 2 >= 0 && *y + 1 <= Y - 1  && chess[*x - 2][*y + 1] == 0)
            {
                *x -= 2;
                *y += 1;
                return 1;
            }
            break;       
        default:
            break;
     }
     return 0;
 }

void print(void)
{
    int i, j;
    for (i = 0; i < X; i++)
    {
        for (j = 0; j < Y; j++)
        {
            printf("%2d\t", chess[i][j]);
        }
        printf("\n");
    }
    printf("\n");
}
// 深度优先遍历棋盘(x,y)为位置坐标，tag为标记变量,每走一步  tag+1
 int TravelChessBoard(int x, int y, int tag)
 {
     int x1 = x, y1 = y, flag = 0, count = 0;
     chess[x][y] = tag;
     if (X * Y == tag)
     {
         print();
         return 1;    // 打印棋盘
     }
     flag = netxtxy(&x1, &y1,count);
     while (0 == flag && count < 7)
     {
         count++;
         flag = netxtxy(&x1, &y1,count);
     }
     
     // 找到马的下一可走目标(x1, y1), 若果找到flag = 1;否则为0
     while (flag)
     {
         if(TravelChessBoard(x1, y1, tag + 1))
         {
             return 1;
         }
         // 继续找到马的下一步可走的坐标(x1, y1),若果找到flag = 1;否则为0
        x1 = x;
        y1 = y;
        count++;
        flag = netxtxy(&x1, &y1,count);
        while (0 == flag && count < 7)
        {
            count++;
            flag = netxtxy(&x1, &y1,count);
        }       
     }
     
     if(0 == flag)
     {
         chess[x][y] = 0;
     }
     return 0;
 }

 int main()
 {
     int i, j;
     clock_t start, finsh;
     start = clock();
     for ( i = 0; i < X; i++)
     {
         for ( j = 0; j < Y; j++)
         {
             chess[i][j] = 0;
         }
     }
    if (!TravelChessBoard(2, 0, 1))
    {
        printf("失败了！");
    }
    finsh = clock();
    printf("本次耗时：%f秒\n\n", (double)(finsh - start)/CLOCKS_PER_SEC);
    return 0;    
 }	

普里姆算法详细解释：

克鲁斯卡尔算法求最小生成树

五、最短路径

迪杰斯特拉算法

弗洛伊德算法