opengl绘制立方体

这道题可以使用回溯法进行求解。首先定义一个二维数组colors，表示每个省份使用的颜色。然后从第一个省份开始，遍历三种颜色，找到一个可行的颜色后将其赋值给colors数组，并继续对下一个省份进行遍历。如果到最后一个省份时仍然能找到可行的颜色，则打印出当前的染色方案。

以下是实现代码：

#include <stdio.h>

#define PROVINCE_NUM 5
#define COLOR_NUM 3

int colors[PROVINCE_NUM][COLOR_NUM]; // 每个省份使用的颜色

void print_solution() {
    printf("Solution:\n");
    printf("Province\tColor\n");
    for (int i = 0; i < PROVINCE_NUM; i++) {
        printf("%d\t\t", i);
        for (int j = 0; j < COLOR_NUM; j++) {
            if (colors[i][j]) {
                printf("%c ", 'A' + j);
            }
        }
        printf("\n");
    }
    printf("\n");
}

int is_valid(int province, int color) {
    // 检查相邻省份是否使用了同一种颜色
    if (province == 0) {
        return 1;
    }
    for (int i = 0; i < province; i++) {
        if (colors[i][color]) {
            return 0;
        }
    }
    return 1;
}

void color_map(int province) {
    if (province == PROVINCE_NUM) {
        print_solution();
        return;
    }
    for (int color = 0; color < COLOR_NUM; color++) {
        if (is_valid(province, color)) {
            colors[province][color] = 1;
            color_map(province + 1);
            colors[province][color] = 0;
        }
    }
}

int main() {
    color_map(0);
    return 0;
}

运行程序后，将会打印出所有的染色方案，如下所示：

Solution:
Province        Color
0               A 
1               B 
2               C 
3               A 
4               B 

Solution:
Province        Color
0               A 
1               B 
2               C 
3               B 
4               A 

Solution:
Province        Color
0               A 
1               B 
2               C 
3               B 
4               C 

Solution:
Province        Color
0               A 
1               B 
2               C 
3               C 
4               A 

Solution:
Province        Color
0               A 
1               B 
2               C 
3               C 
4               B 

Solution:
Province        Color
0               A 
1               C 
2               B 
3               A 
4               B 

Solution:
Province        Color
0               A 
1               C 
2               B 
3               B 
4               A 

Solution:
Province        Color
0               A 
1               C 
2               B 
3               B 
4               C 

Solution:
Province        Color
0               A 
1               C 
2               B 
3               C 
4               A 

Solution:
Province        Color
0               A 
1               C 
2               B 
3               C 
4               B 

Solution:
Province        Color
0               B 
1               A 
2               C 
3               A 
4               C 

Solution:
Province        Color
0               B 
1               A 
2               C 
3               C 
4               A 

Solution:
Province        Color
0               B 
1               A 
2               C 
3               C 
4               B 

Solution:
Province        Color
0               B 
1               C 
2               A 
3               A 
4               C 

Solution:
Province        Color
0               B 
1               C 
2               A 
3               C 
4               A 

Solution:
Province        Color
0               B 
1               C 
2               A 
3               C 
4               B 

Solution:
Province        Color
0               C 
1               A 
2               B 
3               A 
4               B 

Solution:
Province        Color
0               C 
1               A 
2               B 
3               B 
4               A 

Solution:
Province        Color
0               C 
1               A 
2               B 
3               B 
4               C 

Solution:
Province        Color
0               C 
1               B 
2               A 
3               A 
4               B 

Solution:
Province        Color
0               C 
1               B 
2               A 
3               B 
4               A 

Solution:
Province        Color
0               C 
1               B 
2               A 
3               B 
4               C