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
Source
题目类型：最长下降子序列
算法分析：详细参考http://www.hankcs.com/program/cpp/poj-1065-wooden-sticks.html和http://blog.csdn.net/vmurder/article/details/40818831和http://www.cnblogs.com/fstang/archive/2013/03/31/2991255.html
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/************************************************** filename :c.cpp author :maksyuki created time :2017/2/11 8:53:13 last modified :2017/2/11 9:03:28 file location :C:\Users\abcd\Desktop\TheEternalPoet ***************************************************/ #pragma comment(linker, "/STACK:102400000,102400000") #include <set> #include <bitset> #include <list> #include <map> #include <stack> #include <queue> #include <deque> #include <string> #include <vector> #include <ios> #include <iostream> #include <fstream> #include <sstream> #include <iomanip> #include <algorithm> #include <utility> #include <complex> #include <numeric> #include <functional> #include <cmath> #include <ctime> #include <climits> #include <cstdarg> #include <cstdio> #include <cstdlib> #include <cstring> #include <cctype> #include <cassert> using namespace std; #define CFF freopen ("in", "r", stdin) #define CPPFF ifstream cin ("in") #define DB(ccc) cout << #ccc << " = " << ccc << endl #define PB push_back #define MP(A, B) make_pair(A, B) typedef long long LL; typedef unsigned long long ULL; typedef double DB; typedef pair <int, int> PII; typedef pair <int, bool> PIB; const int INF = 0x7F7F7F7F; const int MOD = 1e9 + 7; const double EPS = 1e-10; const double PI = 2 * acos (0.0); const int maxn = 1e5 + 6666; struct point { int l, w; }; bool cmp(const point &a, const point &b) { return a.l < b.l; } point a[5000+666]; int dp[5000+666]; int main() { //CFF; //CPPFF; int t; scanf("%d", &t); while(t--) { int n; scanf("%d", &n); for(int i = 1; i <= n; i++) scanf("%d%d", &a[i].l, &a[i].w); sort(a + 1, a + 1 + n, cmp); for(int i = 1; i <= n; i++) dp[i] = 1; for(int i = 1; i <= n; i++) for(int j = 1; j < i; j++) if(a[i].w < a[j].w) dp[i] = max(dp[i], dp[j] + 1); int res = -INF; for(int i = 1; i <= n; i++) res = max(res, dp[i]); printf("%d\n", res); } return 0; } |
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