DP

M - Bounty hunter **Time Limit:**5000MS **Memory Limit:**65536KB 64bit IO Format:%lld & %llu Submit Status Description Bounty hunter is a hero who always moves along cities to earn money by his power. One day he decides to N cities one by one At the beginning ,Bounty hunter has X money and Y points of Attack force. At day 1, he will goes to city 1, then city 2 at day 2, city 3 at day 3, … At last ,he goes to city N at day N and leaves it at day N+1. In each city, he can increase his attack force by money and earn some money by accepting a task. In the city i, it costs him ai money to increase one point of attack force. And he can gets bi*yi money after finishing the task in city i while yi is his attack force after his increasing at city i.

果然dp還是弱項啊啊啊啊．． 不過比最開始的完全無從下手強了不少應該．．． 至少dp狀態表示相對了．．．．轉移方程沒想出來嗚嗚嗚 官方題解：设d(i, j)d(i,j)表示前ii个数，模pp为jj的方案数，则容易得到d(0, 0)=1, d(i, j)=d(i-1, j)+sum_{j=0}^{p-1} d(i-1, (j-a[i]) mod p)d(0,0)=1,d(i,j)=d(i−1,j)+∑j=0p−1d(i−1,(j−a[i]) mod p)，很多人没1a是因为没注意|a_i| le 10^9∣ai∣≤109

背包还是理解的不够透彻．． 因为每次都是用那个一维形式的． 这道题的做法类似01背包. 此外还可以有一个优化… 当n>m的时候．．．根绝抽屉原理．．一定为yes..

比赛的时候以为是贪心… 想了好久. 不过最后没敢写，因为没办法证明正确性，只是直觉== 最后剩下的时间给队友改另一道题了.. 果然明智… 蠢的人的直觉真心不靠谱..

dp 方程想错了。果然还是欠练啊。 如果我们不考虑坏点，那么从 (0,0) 到 (x,y) 的方案数是 c(x+y,x) 或者 c(x+y,y)。 因为有坏点的存在，我们可以逆向思维，先求出总数，然后减去那些由于坏点的影响不能走的方案数。

很容易看出来是dp 我们左右一起，一对一对放． 对于每一对，有三种方法，分别是两左，一左一右，两右． 初始区间长度为２n，每次放完后缩小区间长度 ，最后一定是放２个n，这个时候区间长度缩小为２，表明一种满足题意的情况．

比赛的时候想到了是dp搞… 不过dp废….. 可能更多的是心理上… 这道题并不怎么难想，但是以觉得是dp，就给了自己一种暗示…这题我搞不出来…

最大连续区间和是一个经典的问题。给定一个长度为 n 的序列 a[1],a[2]…a[n-1],a[n]，求一个连续的子序列 a[i],a[i+1]…a[j-1],a[j]，使得 a[i]+a[i+1]…a[j-1]+a[j]最大。

FatMouse’s Speed # Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others) Total Submission(s): 10172 Accepted Submission(s): 4521 Special Judge Problem Description FatMouse believes that the fatter a mouse is, the faster it runs. To disprove this, you want to take the data on a collection of mice and put as large a subset of this data as possible into a sequence so that the weights are increasing, but the speeds are decreasing.

Tickets # **Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others) Total Submission(s): 1408 Accepted Submission(s): 687 ** Problem Description Jesus, what a great movie! Thousands of people are rushing to the cinema. However, this is really a tuff time for Joe who sells the film tickets. He is wandering when could he go back home as early as possible. A good approach, reducing the total time of tickets selling, is let adjacent people buy tickets together. As the restriction of the Ticket Seller Machine, Joe can sell a single ticket or two adjacent tickets at a time. Since you are the great JESUS, you know exactly how much time needed for every person to buy a single ticket or two tickets for him/her. Could you so kind to tell poor Joe at what time could he go back home as early as possible? If so, I guess Joe would full of appreciation for your help.

免费馅饼 # **Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others) Total Submission(s): 29065 Accepted Submission(s): 9921 ** Problem Description 都说天上不会掉馅饼，但有一天gameboy正走在回家的小径上，忽然天上掉下大把大把的馅饼。说来gameboy的人品实在是太好了，这馅饼别处都不掉，就掉落在他身旁的10米范围内。馅饼如果掉在了地上当然就不能吃了，所以gameboy马上卸下身上的背包去接。但由于小径两侧都不能站人，所以他只能在小径上接。由于gameboy平时老呆在房间里玩游戏，虽然在游戏中是个身手敏捷的高手，但在现实中运动神经特别迟钝，每秒种只有在移动不超过一米的范围内接住坠落的馅饼。现在给这条小径如图标上坐标：

F - Piggy-Bank **Time Limit:**1000MS **Memory Limit:**32768KB 64bit IO Format:%I64d & %I64u Submit Status Description Before ACM can do anything, a budget must be prepared and the necessary financial support obtained. The main income for this action comes from Irreversibly Bound Money (IBM). The idea behind is simple. Whenever some ACM member has any small money, he takes all the coins and throws them into a piggy-bank. You know that this process is irreversible, the coins cannot be removed without breaking the pig. After a sufficiently long time, there should be enough cash in the piggy-bank to pay everything that needs to be paid.

E - Super Jumping! Jumping! Jumping! **Time Limit:**1000MS **Memory Limit:**32768KB 64bit IO Format:%I64d & %I64u Submit Status Description Nowadays, a kind of chess game called “Super Jumping! Jumping! Jumping!” is very popular in HDU. Maybe you are a good boy, and know little about this game, so I introduce it to you now. The game can be played by two or more than two players. It consists of a chessboard（棋盘）and some chessmen（棋子）, and all chessmen are marked by a positive integer or “start” or “end”. The player starts from start-point and must jumps into end-point finally. In the course of jumping, the player will visit the chessmen in the path, but everyone must jumps from one chessman to another absolutely bigger (you can assume start-point is a minimum and end-point is a maximum.). And all players cannot go backwards. One jumping can go from a chessman to next, also can go across many chessmen, and even you can straightly get to end-point from start-point. Of course you get zero point in this situation. A player is a winner if and only if he can get a bigger score according to his jumping solution. Note that your score comes from the sum of value on the chessmen in you jumping path. Your task is to output the maximum value according to the given chessmen list.

C - Monkey and Banana **Time Limit:**1000MS **Memory Limit:**32768KB 64bit IO Format:%I64d & %I64u Submit Status Description A group of researchers are designing an experiment to test the IQ of a monkey. They will hang a banana at the roof of a building, and at the mean time, provide the monkey with some blocks. If the monkey is clever enough, it shall be able to reach the banana by placing one block on the top another to build a tower and climb up to get its favorite food.

**Time Limit: 10000/5000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others) Total Submission(s): 26534 Accepted Submission(s): 9332 ** Problem Description Nowadays, we all know that Computer College is the biggest department in HDU. But, maybe you don’t know that Computer College had ever been split into Computer College and Software College in 2002. The splitting is absolutely a big event in HDU! At the same time, it is a trouble thing too. All facilities must go halves. First, all facilities are assessed, and two facilities are thought to be same if they have the same value. It is assumed that there is N (0<N<1000) kinds of facilities (different value, different kinds).

I NEED A OFFER! # **Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others) Total Submission(s): 18287 Accepted Submission(s): 7320 ** Problem Description Speakless很早就想出国，现在他已经考完了所有需要的考试，准备了所有要准备的材料，于是，便需要去申请学校了。要申请国外的任何大学，你都要交纳一定的申请费用，这可是很惊人的。Speakless没有多少钱，总共只攒了n万美元。他将在m个学校中选择若干的（当然要在他的经济承受范围内）。每个学校都有不同的申请费用a（万美元），并且Speakless估计了他得到这个学校offer的可能性b。不同学校之间是否得到offer不会互相影响。“I NEED A OFFER”，他大叫一声。帮帮这个可怜的人吧，帮助他计算一下，他可以收到至少一份offer的最大概率。（如果Speakless选择了多个学校，得到任意一个学校的offer都可以）。

饭卡 # **Time Limit: 5000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others) Total Submission(s): 14225 Accepted Submission(s): 4945 ** Problem Description 电子科大本部食堂的饭卡有一种很诡异的设计，即在购买之前判断余额。如果购买一个商品之前，卡上的剩余金额大于或等于5元，就一定可以购买成功（即使购买后卡上余额为负），否则无法购买（即使金额足够）。所以大家都希望尽量使卡上的余额最少。 某天，食堂中有n种菜出售，每种菜可购买一次。已知每种菜的价格以及卡上的余额，问最少可使卡上的余额为多少。

Description Matt has N friends. They are playing a game together. Each of Matt’s friends has a magic number. In the game, Matt selects some (could be zero) of his friends. If the xor (exclusive-or) sum of the selected friends’magic numbers is no less than M , Matt wins. Matt wants to know the number of ways to win. Input The first line contains only one integer T , which indicates the number of test cases.