HDU-1051 Wooden Sticks

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本文探讨了如何通过排序和遍历策略来解决木棍加工的最小调整时间问题，旨在寻找最优的木棍加工顺序，以减少加工过程中的机器调整时间。

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题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=1051

Wooden Sticks

Time Limit:1000MS Memory Limit:32768KB 64bit IO Format:%I64d & %I64u

Submit Status

Description

There is a pile of n wooden sticks. The length and weight of each stick are known in advance. The sticks are to be processed by a woodworking machine in one by one fashion. It needs some time, called setup time, for the machine to prepare processing a stick. The setup times are associated with cleaning operations and changing tools and shapes in the machine. The setup times of the woodworking machine are given as follows:

(a) The setup time for the first wooden stick is 1 minute.
(b) Right after processing a stick of length l and weight w , the machine will need no setup time for a stick of length l' and weight w' if l<=l' and w<=w'. Otherwise, it will need 1 minute for setup.

You are to find the minimum setup time to process a given pile of n wooden sticks. For example, if you have five sticks whose pairs of length and weight are (4,9), (5,2), (2,1), (3,5), and (1,4), then the minimum setup time should be 2 minutes since there is a sequence of pairs (1,4), (3,5), (4,9), (2,1), (5,2).

Input

The input consists of T test cases. The number of test cases (T) is given in the first line of the input file. Each test case consists of two lines: The first line has an integer n , 1<=n<=5000, that represents the number of wooden sticks in the test case, and the second line contains n 2 positive integers l1, w1, l2, w2, ..., ln, wn, each of magnitude at most 10000 , where li and wi are the length and weight of the i th wooden stick, respectively. The 2n integers are delimited by one or more spaces.

Output

The output should contain the minimum setup time in minutes, one per line.

Sample Input

4 9

5 2

2 1

3 5

1 4

2 2

1 1

2 2

1 3

2 2

3 1

Sample Output

题意：

给定n根木棍，以及每根木棍的长度l和重量w。现在要对它们进行加工，机器调整时间为1分钟，如果加工完一根长l重w的木棍后，下一根长l′重w'′的木棍满足l≤l'l≤l′且w≤w'，那么机器就可以继续加工而不需要进入调整时间。否则的话，又需要1分钟的调整时间才能继续加工。求总共最小需要的调整时间。

解题思路：

先进行排序，若长度不等，则将长度按从小到大的顺序排，若长度相等，则按重量从小到大的顺序排序，之后从第一根木棍开始，一次找符合条件的，找到之后以此重量接着找符合条件的，以此类推，注意最后一组有没有计算进去。

代码：

#include <stdio.h>
#include <string.h>
#include <algorithm>
using namespace std;
struct wooden
{
	int l;
	int w;
}q[10010];

bool cmp(wooden a,wooden b)
{
	if(a.l==b.l)
		return a.w<b.w;
	return a.l<b.l;
}

int main()
{
	int t,n,i,j,count,w0;
	int vis[10010];
	scanf("%d",&t);
	while(t--)
	{
		count=0;
		scanf("%d",&n);
		for(i=0;i<n;i++)
			scanf("%d%d",&q[i].l,&q[i].w);
		sort(q,q+n,cmp);
		/*for(i=0;i<n;i++)
			printf("%d %d\n",q[i].l,q[i].w);*/
		memset(vis,0,sizeof(vis));
		for(i=0;i<n-1;i++)
		{
			if(vis[i]==1)
				continue;
			count++; 
			vis[i]=1;
			w0=q[i].w;
			for(j=i+1;j<n;j++)
			{
				if(vis[j]==0&&q[j].w>=w0)
				{
					vis[j]=1;
					w0=q[j].w;
				}
			}
		}
		if(vis[n-1]==0)
			count++;
		printf("%d\n",count);
	}
	return 0;
}