DP_Wooden Sticks

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 ( 9 , 4 ) , ( 2 , 5 ) , ( 1 , 2 ) , ( 5 , 3 ) , and ( 4 , 1 ) , then the minimum setup time should be 2 minutes since there is a sequence of pairs ( 4 , 1 ) , ( 5 , 3 ) , ( 9 , 4 ) , ( 1 , 2 ) , ( 2 , 5 ) .

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 2n 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

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题意：求同时满足木棒的长宽都构成不下降子序列的最少组数。

思路：1、将木棒按照长（或宽）进行升序排序。
　　　2、建立递推数组dp[]，表示操作当前木棒时所需要的设定次数。
　　　3、dp[]的递推公式：　　若前面存在一个木棒的宽度大于当前木棒的宽度的时，当前木棒所需要进行的设置数一定会大于这个木棒所需要的设置数。
　　　　　　　　　　　当前木棒的dp[]=max{dp[前面宽度大于当前木棒宽度的木棒所对应的下标]}+1
　　　4、遍历数组dp[]，最大的dp即为题目所求最少需要的设定次数.
注意：排序完成后的木棒默认只设定一次（即假设排序完成后的序列为一个不下降序列）dp[]值初始化为1
　　　排序时在长度相同的情况下应优先按照宽度再次进行排序。

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 #include<cstdio>
 #include<algorithm>
 using namespace std;
 int dp[];
 struct Node{
     int h,w;
 }p[];
 bool cmp( Node a, Node b){
     if( a.h!=b.h )
         return a.h<b.h ? true:false;
     return a.w<b.w ? true:false;
 }
 int main()
 {
     int t,n;
     int maxn;

     scanf("%d",&t);
     while( t-- ){
         maxn=;
         scanf("%d",&n);
         for( int i=; i<n; i++)
             scanf("%d%d",&p[i].h,&p[i].w);
         sort( p, p+n, cmp);
         for( int j=; j<n; j++)
             dp[j]=;
         for( int i=; i<n; i++){
             for( int j=; j<i; j++){
                 if( p[j].w>p[i].w ){
                     dp[i]=max(dp[i],dp[j]+);
                 }
             }
         }
         for( int i=; i<n; i++)
             if( dp[i]>maxn )
                 maxn=dp[i];
         printf("%d\n",maxn);
     }

     return ;
 }

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感谢SLH的耐心讲解