poj 1952 BUY LOW, BUY LOWER(求最长下降子序列个数)

BUY LOW, BUY LOWER

Time Limit: 1000MS		Memory Limit: 30000K
Total Submissions: 7475		Accepted: 2608

Description

The advice to "buy low" is half the formula to success in the bovine stock market.To be considered a great investor you must also follow this problems' advice:

                    "Buy low; buy lower"

Each time you buy a stock, you must purchase it at a lower price than the previous time you bought it. The more times you buy at a lower price than before, the better! Your goal is to see how many times you can continue purchasing at ever lower prices.

You will be given the daily selling prices of a stock (positive 16-bit integers) over a period of time. You can choose to buy stock on any of the days. Each time you choose to buy, the price must be strictly lower than the previous time you bought stock. Write a program which identifies which days you should buy stock in order to maximize the number of times you buy.

Here is a list of stock prices:

 Day   1  2  3  4  5  6  7  8  9 10 11 12

Price 68 69 54 64 68 64 70 67 78 62 98 87

The best investor (by this problem, anyway) can buy at most four times if each purchase is lower then the previous purchase. One four day sequence (there might be others) of acceptable buys is:

Day    2  5  6 10

Price 69 68 64 62

Input

* Line 1: N (1 <= N <= 5000), the number of days for which stock prices are given

* Lines 2..etc: A series of N space-separated integers, ten per line except the final line which might have fewer integers.

Output

Two integers on a single line:
* The length of the longest sequence of decreasing prices
* The number of sequences that have this length (guaranteed to fit in 31 bits)

In counting the number of solutions, two potential solutions are considered the same (and would only count as one solution) if they repeat the same string of decreasing prices, that is, if they "look the same" when the successive prices are compared. Thus, two different sequence of "buy" days could produce the same string of decreasing prices and be counted as only a single solution.

Sample Input

12
68 69 54 64 68 64 70 67 78 62
98 87

Sample Output

4 2

题意：求最长下降子序列，且要求最长下降子序列的出现次数。

思路： 这里用o(n^2)的方法求最长下降子序列的长度，设dp[i]表示以a[i]结尾的子序列的最长长度。求出现次数，可以设cnt[i]表示以a[i]结尾的最长下降子序列的出现次数。

AC代码：

#include <cstring>
#include <string>
#include <cstdio>
#include <algorithm>
#include <queue>
#include <cmath>
#include <vector>
#include <cstdlib>
#include <iostream>

using namespace std;


int main()
{
    int dp[5005],cnt[5005];
    int a[5005];
    int n;
    scanf("%d",&n);
    for(int i=0; i<n; i++)
        scanf("%d",&a[i]);
    for(int i=0; i<n; i++)
    {
        dp[i]=1;
        cnt[i]=1;
    }
    for(int i=0; i<n; i++)
        for(int j=i-1; j>=0; j--)
        {
            if(a[j]>a[i])
            {
                if(dp[j]+1>dp[i])        //将a[i]加到序列中，序列长度变长，序列是唯一的
                {
                    dp[i]=dp[j]+1;
                    cnt[i]=cnt[j];
                }
                else if(dp[j]+1==dp[i])   //序列不同但是长度相同的序列，即a[i]同时在这两个序列中
                 cnt[i]+=cnt[j];
            }
            else if(a[j]==a[i])
            {
                if(dp[i]==1) cnt[i]=0;    //如果a[j]==a[i]&&dp[i]==1，则这个数是不需要的，赋值为0，避免下一个小于它的a[i]的cnt[i]+1
                break;
            }
        }
    int max=0,k=0;
    for(int i=0;i<n;i++)
    if(dp[i]>max) max=dp[i];

    for(int i=0;i<n;i++)
    if(dp[i]==max) k+=cnt[i];

    cout<<max<<" "<<k<<endl;
    return 0;
}