• P2858 [USACO06FEB]奶牛零食Treats for the Cows[区间dp]
• P2867 [USACO06NOV]大广场Big Square[dp]
• P2851 [USACO06DEC]最少的硬币The Fewest Coins[dp]
• P1879 [USACO06NOV]玉米田Corn Fields[状压dp]
• P1005 [NOIp2007]矩阵取数游戏[dp,高精度]
• P2513 [HAOI2009]逆序对数列[dp+前缀和]

## P2858 [USACO06FEB]奶牛零食Treats for the Cows[dp]

### 题目描述

FJ has purchased N (1 <= N <= 2000) yummy treats for the cows who get money for giving vast amounts of milk. FJ sells one treat per day and wants to maximize the money he receives over a given period time.

The treats are interesting for many reasons:The treats are numbered 1..N and stored sequentially in single file in a long box that is open at both ends. On any day, FJ can retrieve one treat from either end of his stash of treats.Like fine wines and delicious cheeses, the treats improve with age and command greater prices.The treats are not uniform: some are better and have higher intrinsic value. Treat i has value v(i) (1 <= v(i) <= 1000).Cows pay more for treats that have aged longer: a cow will pay v(i)*a for a treat of age a.Given the values v(i) of each of the treats lined up in order of the index i in their box, what is the greatest value FJ can receive for them if he orders their sale optimally?
The first treat is sold on day 1 and has age a=1. Each subsequent day increases the age by 1.

• 零食按照1．．N编号，它们被排成一列放在一个很长的盒子里．盒子的两端都有开口，约翰每天可以从盒子的任一端取出最外面的一个．
• 与美酒与好吃的奶酪相似，这些零食储存得越久就越好吃．当然，这样约翰就可以把它们卖出更高的价钱．
• 每份零食的初始价值不一定相同．约翰进货时，第i份零食的初始价值为Vi(1≤Vi≤1000)．
• 第i份零食如果在被买进后的第a天出售，则它的售价是vi×a．

$V_i$ 的是从盒子顶端往下的第i份零食的初始价值．约翰告诉了你所有零食的初始价值，并希望你能帮他计算一下，在这些零食全被卖出后，他最多能得到多少钱．

#### 输入输出格式

##### 输入格式：

Line 1: A single integer, N

Lines 2..N+1: Line i+1 contains the value of treat $V_i$

##### 输出格式：

Line 1: The maximum revenue FJ can achieve by selling the treats

5
1
3
1
5
2

43

#### 说明

Explanation of the sample:
Five treats. On the first day FJ can sell either treat #1 (value 1) or treat #5 (value 2).
FJ sells the treats (values 1, 3, 1, 5, 2) in the following order of indices: 1, 5, 2, 3, 4, making 1x1 + 2x2 + 3x3 + 4x1 + 5x5 = 43.

### 题解

$f[i][j]$ 表示取 $i~j$ 段能够得到最多的钱

$f[i][i]=n*a[i]$;

## P2851 [USACO06DEC]最少的硬币The Fewest Coins[dp]

### 题目描述

Farmer John has gone to town to buy some farm supplies. Being a very efficient man, he always pays for his goods in such a way that the smallest number of coins changes hands, i.e., the number of coins he uses to pay plus the number of coins he receives in change is minimized. Help him to determine what this minimum number is.
FJ wants to buy T ($1 ≤ T ≤ 10,000$) cents of supplies. The currency system has N (1 ≤ N ≤ 100) different coins, with values V1, V2, …, VN (1 ≤ Vi ≤ 120). Farmer John is carrying C1 coins of value V1, C2 coins of value V2, …., and CN coins of value VN (0 ≤ Ci ≤ 10,000). The shopkeeper has an unlimited supply of all the coins, and always makes change in the most efficient manner (although Farmer John must be sure to pay in a way that makes it possible to make the correct change).

#### 说明

30%的数据 $n\le12$

100%的数据 $n\le1000，k\le1000$

### 题解

$s[i][j]$表示$f[i][0]$~$f[i][j]$的和

A了,然后改数据,加极端数据.

## 其他

NOIp考过的(链到xsc博客去了(逃))