求最長遞減子序列和最長子序列的種數。難在求種數

不需要使用高精度或者int64

BUY LOW, BUY LOWER

Time Limit: 1000MS	Memory Limit: 30000K
Total Submissions: 5490	Accepted: 1848

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

#include <iostream>
#define N 5005
using namespace std;
int a[N];
int dp[N];
int times[N];
int main()
{
    int n;
    while(cin>>n)
    {
        for(int i=1;i<=n;i++)
        {
            cin>>a[i];
            dp[i]=times[i]=1;
        }
        for(int i=1;i<=n;i++)//求以a[i]為終止時子序列的長度
        {
            for(int j=i-1;j>0;j--)
            {
                if(a[i]<a[j])
                {
                    if(dp[i]<dp[j]+1)
                    {
                        dp[i]=dp[j]+1;
                        times[i]=times[j];
                    }
                    else if(dp[i]==dp[j]+1)
                    {
                        times[i]+=times[j];
                    }
                }
                if(a[i]==a[j])
                {
                    if(dp[i]==1)//防止重複
                    //dp[i]==1,a[i],a[j]前面接的一樣,只能算作一次
                    times[i]=0;
                    break;
                }
            }
        }
            int len=0,t=0;
            for(int i=1;i<=n;i++)
                if(dp[i]>len)
                len=dp[i];
            for(int i=1;i<=n;i++)
                if(dp[i]==len)//統計次數
                t+=times[i];
              cout<<len<<" "<<t<<endl;
    }
}