[NWPU][2014][TRN][6]动态规划第一讲——简单线性dp_A题
来源:互联网 发布:手机版淘宝店入驻申请 编辑:程序博客网 时间:2024/06/05 23:42
题目:
Description
A military contractor for the Department of Defense has just completed a series of preliminary tests for a new defensive missile called the CATCHER which is capable of intercepting multiple incoming offensive missiles. The CATCHER is supposed to be a remarkable defensive missile. It can move forward, laterally, and downward at very fast speeds, and it can intercept an offensive missile without being damaged. But it does have one major flaw. Although it can be fired to reach any initial elevation, it has no power to move higher than the last missile that it has intercepted.
The tests which the contractor completed were computer simulations of battlefield and hostile attack conditions. Since they were only preliminary, the simulations tested only the CATCHER's vertical movement capability. In each simulation, the CATCHER was fired at a sequence of offensive missiles which were incoming at fixed time intervals. The only information available to the CATCHER for each incoming missile was its height at the point it could be intercepted and where it appeared in the sequence of missiles. Each incoming missile for a test run is represented in the sequence only once.
The result of each test is reported as the sequence of incoming missiles and the total number of those missiles that are intercepted by the CATCHER in that test.
The General Accounting Office wants to be sure that the simulation test results submitted by the military contractor are attainable, given the constraints of the CATCHER. You must write a program that takes input data representing the pattern of incoming missiles for several different tests and outputs the maximum numbers of missiles that the CATCHER can intercept for those tests. For any incoming missile in a test, the CATCHER is able to intercept it if and only if it satisfies one of these two conditions:
The incoming missile is the first missile to be intercepted in this test.
-or-
The missile was fired after the last missile that was intercepted and it is not higher than the last missile which was intercepted.
The tests which the contractor completed were computer simulations of battlefield and hostile attack conditions. Since they were only preliminary, the simulations tested only the CATCHER's vertical movement capability. In each simulation, the CATCHER was fired at a sequence of offensive missiles which were incoming at fixed time intervals. The only information available to the CATCHER for each incoming missile was its height at the point it could be intercepted and where it appeared in the sequence of missiles. Each incoming missile for a test run is represented in the sequence only once.
The result of each test is reported as the sequence of incoming missiles and the total number of those missiles that are intercepted by the CATCHER in that test.
The General Accounting Office wants to be sure that the simulation test results submitted by the military contractor are attainable, given the constraints of the CATCHER. You must write a program that takes input data representing the pattern of incoming missiles for several different tests and outputs the maximum numbers of missiles that the CATCHER can intercept for those tests. For any incoming missile in a test, the CATCHER is able to intercept it if and only if it satisfies one of these two conditions:
The incoming missile is the first missile to be intercepted in this test.
-or-
The missile was fired after the last missile that was intercepted and it is not higher than the last missile which was intercepted.
Input
The input data for any test consists of a sequence of one or more non-negative integers, all of which are less than or equal to 32,767, representing the heights of the incoming missiles (the test pattern). The last number in each sequence is -1, which signifies the end of data for that particular test and is not considered to represent a missile height. The end of data for the entire input is the number -1 as the first value in a test; it is not considered to be a separate test.
Output
Output for each test consists of a test number (Test #1, Test #2, etc.) and the maximum number of incoming missiles that the CATCHER could possibly intercept for the test. That maximum number appears after an identifying message. There must be at least one blank line between output for successive data sets.
Note: The number of missiles for any given test is not limited. If your solution is based on an inefficient algorithm, it may not execute in the allotted time.
Note: The number of missiles for any given test is not limited. If your solution is based on an inefficient algorithm, it may not execute in the allotted time.
Sample Input
38920715530029917015865-1233421-1-1
Sample Output
Test #1: maximum possible interceptions: 6Test #2: maximum possible interceptions: 2
题解:
这道题就是求最长不上升子序列的个数,很明显的动态规划dp类问题,拿到后二话不说,直接考虑涉及到的状态表示及状态转移方程,注意,有些题是求子序列的和,而这里是求子序列的个数,根据这个得出,用个一维的数组f[ ]表示状态,状态转移方程也好确定。
状态:f[i]表示能拦截前i个导弹最大的个数;
状态转移方程:f[i]=max{f[j]+1} (f[j]<=f[i]&&a[j]>=a[i]&&j<i),初值设为1;
方法:可以从前到后递推,也可以从后到前用记忆化搜索,个人习惯用递推;
代码:
#include<cstdio>using namespace std;int main(){ int n,m,dat[10005],f[10005],i,j,k=0,cnt=0,max; while(~scanf("%d",&n)&&n!=-1) { dat[0]=n; i=1; max=1; while(~scanf("%d",&m)&&m!=-1) dat[i++]=m; f[0]=1; for(j=1;j<=i-1;j++) { f[j]=1; for(k=0;k<j;k++) if(dat[k]>dat[j]&&f[k]+1>f[j]) f[j]=f[k]+1; //递推实现 if(f[j]>max) max=f[j]; //寻找最大值 } cnt++; printf("Test #%d:\n maximum possible interceptions: %d\n\n",cnt,max); } return 0;}
0 0
- [NWPU][2014][TRN][6]动态规划第一讲——简单线性dp_A题
- [NWPU][2014][TRN][6]动态规划第一讲——简单线性dp_B题
- [NWPU][2014][TRN][6]动态规划第一讲——简单线性dp_C题
- [NWPU][2014][TRN][6]动态规划第一讲——简单线性dp-D题
- [NWPU][2014][TRN][13]线段树第一讲 A - 基础 POJ 2352
- [NWPU][2014][TRN][13]线段树第一讲 B - 基础 POJ 3264
- [NWPU][2014][TRN][3]搜索 总结
- 7.12 [NWPU][2014][TRN][4]搜索 C - 广搜 基础
- [NWPU][2014][TRN][5]二分和贪心 HDU 4296
- [NWPU][2014][TRN][16]图论拓扑排序 H - 基础
- 简单线性动态规划 —— 编辑距离
- NOIP算法总结——关于简单 线性动态规划
- 7.12 [NWPU][2014][TRN][3]搜索 POJ 1562 H - 深搜/广搜 基础
- 7-12 [NWPU][2014][TRN][3]搜索 D - 广搜 基础 POJ 1915
- [NWPU][2014][TRN][5]二分和贪心 M - 贪心 基础 POJ 2709
- [NWPU][2014][TRN][12]并查集D - A Bug's Life POJ 2492
- [NWPU][2014][TRN][16]图论拓扑排序 E - 基础 HDU 1285
- [NWPU][2014][TRN][17]最小生成树 B - 基础 POJ 2421
- android十款UI框架
- 设计模式
- 《Linux》天影linux系列笔记一——linux常用命令详解:file
- linux安装谷歌浏览器
- BEGINNING SHAREPOINT® 2013 DEVELOPMENT 第3章节--SharePoint 2013 开发人员工具 用SPD开发SharePoint应用程序
- [NWPU][2014][TRN][6]动态规划第一讲——简单线性dp_A题
- Cocos2d-x PluginX (一)使用手册
- Linux 固件子系统----如何更新固件
- 【翻译自mos文章】当并行事务恢复进程在运行时,禁用并行事务恢复的方法
- 《Linux》天影linux系列笔记一——linux常用命令详解:which
- android 自动化测试之MonkeyRunner学习(二)
- Ubuntu常用快捷键
- 语音编解码器
- KMP的原理和代码实现(详细注释|参考多个博客总结|可作为模板)