ACMSTEP 1.3.7 Wooden Sticks //排序 DP （LIS）

原題地址

Wooden Sticks

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others) Total Submission(s): 562 Accepted Submission(s): 226

Problem 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

3 
5 
4 9 5 2 2 1 3 5 1 4 
3 
2 2 1 1 2 2 
3 
1 3 2 2 3 1

Sample Output

2
1
3

我記得這道題我以前在JOJ上做過，我還記得 是LIS （最長上升子序列的題） 有小半年的時間了。

但是看到這個題 感覺又不像是 LIS的題。仔細思索了一下，應該是在結構體按照長度排序完（我的代碼中把weight寫成了height。。），然後相同情況下同樣從小到大排序重量，然後尋找有多少個遞增子序列，有一個就需要那個1分鐘。一次AC。

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <cstdlib>
#include <cctype>
#include <string>
#include <vector>
#include <queue>
#include <algorithm>

using namespace std;

struct sticks
{
	int len;
	int height;	
}st[5005];

int cmp1(const void*a, const void *b)
{
	if ((*(sticks *)a).len != (*(sticks *)b).len)
	{
		return (*(sticks *)a).len - (*(sticks *)b).len;
	}
	else return (*(sticks *)a).height - (*(sticks *)b).height;
}
int main()
{
//	freopen("c:\\in.txt","r",stdin);
	int cases, n, i, j;
	int used[5005];
	cin>>cases;
	while (cases--)
	{
		cin>>n;
		for (i=0; i<n; i++)
		{
			scanf ("%d %d",&st[i].len,&st[i].height);
		}
		qsort (st, n, sizeof(st[0]),cmp1);
		
/*
		for (i=0; i<n; i++)
		{
			cout<<st[i].len<<" "<<st[i].height<<endl;
		}
*/
		
		int countn = 0, current;
		memset (used, 0, sizeof(used));
		for (i=0; i<n; i++)
		{
			if (used[i]==0)
			{
				current = st[i].height;
				used[i] = 1;countn++;
				for (j=1; j<n; j++)
				{
					if (used[j]==0 && st[j].height >= current)
					{
						current = st[j].height;
	
						used[j]=1;
					}	
				}
			}
		}
		cout<<countn<<endl;
	}
	return 0;
}