用c语言实现在一个木板上切割两个尺寸不同的产品,使木板的利用率最高并给出木板利用率由高到低排序的前三种切割方式
时间: 2024-03-25 09:39:56 浏览: 10
好的,这个问题可以使用贪心算法来解决,具体步骤如下:
1. 定义一个木板的结构体,包括木板的宽度和长度:
```c
typedef struct {
int width; // 宽度
int length; // 长度
} Board;
```
2. 定义一个产品的结构体,包括产品的宽度和长度:
```c
typedef struct {
int width; // 宽度
int length; // 长度
} Product;
```
3. 定义一个比较函数,用于按照利用率从高到低排序:
```c
int compare(const void* a, const void* b) {
double ua = *((double*)a);
double ub = *((double*)b);
if (ua < ub) return 1;
if (ua > ub) return -1;
return 0;
}
```
4. 定义一个函数,用来计算在一个木板上切割两个尺寸不同的产品,并返回木板的利用率。这个函数的实现可以使用贪心算法,每次选择剩余面积最大的位置来切割产品。
```c
double calculate_utilization_rate(Board board, Product p1, Product p2) {
int w1, l1, w2, l2;
double s1, s2, s_board, utilization_rate;
double areas[4];
w1 = p1.width;
l1 = p1.length;
w2 = p2.width;
l2 = p2.length;
areas[0] = board.width * board.length - w1 * l1 - w2 * l2;
areas[1] = board.width * (board.length - l1) - w2 * l2;
areas[2] = board.width * (board.length - l2) - w1 * l1;
areas[3] = (board.width - w1) * board.length - w2 * l2;
qsort(areas, 4, sizeof(double), compare);
s1 = w1 * l1;
s2 = w2 * l2;
s_board = board.width * board.length;
utilization_rate = (s1 + s2) / s_board;
for (int i = 0; i < 4; i++) {
double area = areas[i];
if (area >= s1 && area >= s2) {
utilization_rate += (s1 + s2) / s_board;
s_board = area;
break;
} else if (area >= s1) {
utilization_rate += s1 / s_board;
s_board = area;
s2 = 0;
} else if (area >= s2) {
utilization_rate += s2 / s_board;
s_board = area;
s1 = 0;
} else {
utilization_rate += area / s_board;
s_board = area;
s1 = 0;
s2 = 0;
}
}
return utilization_rate;
}
```
5. 接下来,我们可以编写一个主函数,用来测试我们的算法,并输出利用率前三名的切割方式。
```c
int main() {
Board board = {10, 10};
Product p1 = {3, 5};
Product p2 = {2, 4};
double rates[6];
int indices[6];
rates[0] = calculate_utilization_rate(board, p1, p2);
indices[0] = 0;
rates[1] = calculate_utilization_rate(board, p2, p1);
indices[1] = 1;
rates[2] = calculate_utilization_rate(board, p1, p2);
indices[2] = 2;
rates[3] = calculate_utilization_rate(board, p2, p1);
indices[3] = 3;
rates[4] = calculate_utilization_rate(board, p1, p2);
indices[4] = 4;
rates[5] = calculate_utilization_rate(board, p2, p1);
indices[5] = 5;
qsort(rates, 6, sizeof(double), compare);
printf("Top 3 utilization rates:\n");
for (int i = 0; i < 3; i++) {
int index = indices[rates[i]];
printf("%d. Cut p%d at (%d, %d) and p%d at (%d, %d)\n", i+1, index/2+1, (index%2)?p2.width:0, (index%2)?p1.length:0, 3-index/2, (index%2)?0:p1.width, (index%2)?p1.length:p2.length);
}
return 0;
}
```
注意,这里的输出格式是针对本题的,实际上具体的输出格式需要根据具体情况进行修改。