HDU 1051 Wooden Sticks

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:

• The setup time for the first wooden stick is 1 minute.
• 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 2n positive integers l₁, w₁, l₂, w₂, ..., l_n, w_n, each of magnitude at most 10000, where l_i and w_i 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

题目的意思
木棒有长度l和重量w两个属性。
给定一些木棒，设木棒s'排在木棒s后面，若 l <=l' and w <=w' 则setup time不用作任何处理，否则+1
不同的排序有不同的setup time,要求输出最小的setup time
实质就是求最小有几个递增序列

思路：
对所有木棒先按照l递增排序，若l一样再按照w递增排序。
如(1,3) (2,4) (3,1) (3,2) (4,3) (5,5)
此时我们可以看到，l的排序已经符合要求，现在求的就是所有的w组成的序列中最少有几个递增序列。
（其实没有所谓的最少，因为按照这样排序后递增序列的数目已经确定了）
所以现在题目转化为【给定序列，求递增子序列的个数】
类似拦截导弹 http://acm.nyist.net/JudgeOnline/problem.php?pid=79

初始化dis[]数组记录子序列个数。
遍历序列中每个元素i，i依次和它前面的元素j比较。
若wi大于前面的元素的wj，说明此时包含j在内的序列的递增性质被破坏了，
更新dis[i]:dis[j]+1（dis[i]表示i属于第几个递增子序列），所以若i破坏了j的递增性质，则i应当属于第dis[j]+1个递增序列。
如(1,3) (2,4) (3,1) (3,2) (4,3) (5,5)
遍历完毕后dis[] = {1,1,2,2,2,1}
此时输出dis[]最大那个就是答案啦~

#include<iostream>
#include<algorithm>
using namespace std;
struct Node
{
    int l,w;
};

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

int main()
{
    int m;
    
    cin >> m;
    
    while (m--)
    {
        int n;
        
        cin >> n;
        
        Node s[n];
        
        int dis[n];
        
        for (int i = 0; i < n; ++i)
        {
            cin >> s[i].l >> s[i].w;
        }
        
        sort(s, s+n, cmp);
        
        for (int i = 0; i < n; ++i)
            dis[i] = 1;
            
        for (int i = 0; i < n; ++i)
        {
            for (int j = 0; j < i; ++j)
            {
                if (s[i].w < s[j].w && dis[i] < dis[j]+1)
                    dis[i] = dis[j]+1;
            }
        }
        
        cout << *max_element(dis, dis+n) << endl;
    }
}