Wooden Sticks POJ - 1065 (DP)

蔚落 2022-02-25 11:56 192阅读 0赞

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

解题思路:

先根据第一根筷子的长度从左到右排序,然后求最长下降序列(最长上升序列反一下)

#include <iostream>
    #include <algorithm>
    #include <string.h>
    using namespace std;
    const int MAXN = 5010;
    int N,K;
    int stDp[MAXN]; 
    struct stick {
    	int x, y;  //首,尾
    }sticks[MAXN];
    bool scmp(stick a, stick b) {
    	if (a.x != b.x) {
    		return a.x < b.x;
    	}
    	else {
    		return a.y < b.y;
    	}
    }
    int main() {
    	cin >> N;
    	while (N--) {
    		cin >> K;
    		for (int i = 0; i < K; ++i) {
    			cin >> sticks[i].x >> sticks[i].y;
    		}
    		sort(sticks, sticks + K,scmp); //按照初始长度排序
    		memset(stDp, 0, sizeof(stDp));
    		for (int i = 0; i < K; ++i) {
    			stDp[i] = 1;  //记住一定要赋初值
    			for (int j = 0; j < i; ++j) {
    				if (sticks[i].y < sticks[j].y) {
    					stDp[i] = max(stDp[i], stDp[j] + 1);
    				}
    			}
    		}
    		cout <<*max_element(stDp, stDp + K) << endl;
    	}
    
    	system("PAUSE");
    	return 0;
    }