【HDU 1051】Wooden Sticks(最长上升子序列)

Wooden Sticks

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 24742    Accepted Submission(s): 9967

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

 

先按照L从大到小进行排序，然后直接DP求最长上升子序列即可.

答案即为最长上升子序列的长度+1

#include<iostream>
#include<algorithm>
#include<string.h>
using namespace std;
#define MAXN 10050
struct stick
{
	int l,w;
 }s[MAXN];
 bool cmp(stick a,stick b)
 {
 	if(a.l==b.l) return a.w>=b.w;
	 return a.l>b.l; 
 }
 int dp[MAXN];
 int main()
 {
 	int t,n;
 	cin>>t;
 	while(t--)
 	{
 		cin>>n;
 		for(int i=0;i<n;i++)
 		{
 			cin>>s[i].l>>s[i].w;
		}
		memset(dp,0,sizeof(dp));
		sort(s,s+n,cmp);
		for(int i=n-1;i>=0;i--)
		{
			for(int j=i+1;j<n;j++)
			{
				if(s[j].w>s[i].w&&dp[i]<dp[j]+1)
				{
					dp[i]=dp[j]+1;
				}
			}
		}
		int maxx=0;
		for(int i=0;i<n;i++)
		{
			if(dp[i]>maxx)
			{
				maxx=dp[i];
			}
		}
		cout<<maxx+1<<endl;
	 }
	 return 0;
 }