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  • BZOJ 1652: [Usaco2006 Feb]Treats for the Cows


    题目


    1652: [Usaco2006 Feb]Treats for the Cows

    Time Limit: 5 Sec  Memory Limit: 64 MB
    Submit: 234  Solved: 185
    [Submit][Status]

    Description

    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.

    约翰经常给产奶量高的奶牛发特殊津贴,于是很快奶牛们拥有了大笔不知该怎么花的钱.为此,约翰购置了N(1≤N≤2000)份美味的零食来卖给奶牛们.每天约翰售出一份零食.当然约翰希望这些零食全部售出后能得到最大的收益.这些零食有以下这些有趣的特性:

    •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.
      Vi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.

    Input

    * Line 1: A single integer,

    N * Lines 2..N+1: Line i+1 contains the value of treat v(i)

    Output

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

    Sample Input

    5
    1
    3
    1
    5
    2

    Five treats. On the first day FJ can sell either treat #1 (value 1) or
    treat #5 (value 2).

    Sample Output

    43

    OUTPUT DETAILS:

    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


    这道题用区间DP,f[i][j]表示最后i-j+1天卖i~j的商品的最大收益。转移见代码。


    代码

     1 /*Author:WNJXYK*/
     2 #include<cstdio>
     3 using namespace std;
     4 
     5 #define LL long long
     6 #define Inf 2147483647
     7 #define InfL 10000000000LL
     8 
     9 inline int abs(int x){if (x<0) return -x;return x;}
    10 inline int abs(LL x){if (x<0) return -x;return x;}
    11 inline void swap(int &x,int &y){int tmp=x;x=y;y=tmp;}
    12 inline void swap(LL &x,LL &y){LL tmp=x;x=y;y=tmp;}
    13 inline int remin(int a,int b){if (a<b) return a;return b;}
    14 inline int remax(int a,int b){if (a>b) return a;return b;}
    15 inline LL remin(LL a,LL b){if (a<b) return a;return b;}
    16 inline LL remax(LL a,LL b){if (a>b) return a;return b;}
    17 inline void read(int &x){x=0;int f=1;char ch=getchar();while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}x=x*f;}
    18 inline void read(LL &x){x=0;LL f=1;char ch=getchar();while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}x=x*f;}
    19 inline void read(int &x,int &y){read(x);read(y);}
    20 inline void read(LL &x,LL &y){read(x);read(y);}
    21 inline void read(int &x,int &y,int &z){read(x,y);read(z);}
    22 inline void read(int &x,int &y,int &n,int &m){read(x,y);read(n,m);}
    23 inline void read(LL &x,LL &y,LL &z){read(x,y);read(z);}
    24 inline void read(LL &x,LL &y,LL &n,LL &m){read(x,y);read(n,m);}
    25 
    26 const int Maxn=2000;
    27 int n,v[Maxn+10];
    28 int f[Maxn+5][Maxn+5];
    29 int main(){
    30     read(n);
    31     for (int i=1;i<=n;i++) read(v[i]);
    32     for (int i=1;i<=n;i++)
    33         f[i][i]=v[i]*n;
    34     for (int k=1;k<n;k++){
    35         for (int i=1;i<=n-k;i++){
    36             int j=i+k;
    37             f[i][j]=remax(v[i]*(n-k)+f[i+1][j],v[j]*(n-k)+f[i][j-1]);
    38         }
    39     }
    40     printf("%d
    ",f[1][n]);
    41     return 0;
    42 }
    View Code


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  • 原文地址:https://www.cnblogs.com/WNJXYK/p/4065601.html
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