PKU 3700 Missile Defence System

Description

To play against the threats of malicious countries nearby, Country R has updated their missile defence system. The new type system can bring down a series of missiles as long as they are coming in ascending order by altitude or descending order by altitude.

Given the heights of a sequence of coming missiles, the general wants to know how many sets of the new type systems are needed to bring down all of them.

Input

The input consists of several test cases. The first line of each test case contains an integer n(1 ≤ n ≤ 50). The next line contains n different integers indicating the heights.

Output

For each test case output a single line containing the number of systems needed.

Sample Input

5
3 5 2 4 1
0
Sample Output

2

贪心+dfs

dfs很清楚，关键是贪心的部分。基本思想是

对于每一个元素，要么用增序来包含他，要么用降序来包含他。（dfs）

当用增序时，用一个比他小的，且最后一个最大（下界）的序列来包含他。(贪心)降序同理。

 

//#include "stdafx.h" //============================================================================ // Name : acmcpp.cpp // Author : Yubo Chow // Version : // Copyright : Your copyright notice // Description : Hello World in C++, Ansi-style //============================================================================ #include <iostream> #include <stdlib.h> #include <stdio.h> #include <queue> #include <math.h> #include <algorithm> #include <set> #include <limits.h> #include <float.h> #include <bitset> #include <cmath> #include <vector> #include <map> #include <list> #include <string.h> using namespace std; int N; int num[55]; int ret; int a[55], d[55]; int na, nd; int *lower_bound(int x) { if (na == 0) { return 0; } int low = 0; int high = na - 1; while (low < high) { int middle = (low + high) >> 1; if (a[middle] < x) { high = middle; } else { low = middle + 1; } } if (a[low] < x) { return &a[low]; } else { return 0; } } int *upper_bound(int x) { if (nd == 0) { return 0; } int low = 0; int high = nd - 1; while (low < high) { int middle = (low + high) >> 1; if (d[middle] > x) { high = middle; } else { low = middle + 1; } } if (d[low] > x) { return &d[low]; } else { return 0; } } void dfs(int i) { if (na + nd >= ret) { return; } if (i == N) { ret = na + nd; return; } int *p = lower_bound(num[i]); if (p) { int b = *p; *p = num[i]; dfs(i + 1); *p = b; } else { a[na++] = num[i]; dfs(i + 1); na--; } p = upper_bound(num[i]); if (p) { int b = *p; *p = num[i]; dfs(i + 1); *p = b; } else { d[nd++] = num[i]; dfs(i + 1); nd--; } } int main() { #ifndef ONLINE_JUDGE freopen("case.txt", "r", stdin); #endif while (scanf("%d", &N) == 1 && N) { for (int i = 0; i < N; ++i) { scanf("%d", &num[i]); } ret = (int) sqrt(double(N)) + 1; na = nd = 0; dfs(0); printf("%d/n", ret); } return 0; }