POJ1952(最长下降子序列+去重)
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BUY LOW, BUY LOWER
Time Limit: 1000MS Memory Limit: 30000KTotal Submissions: 9623 Accepted: 3366
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:
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:
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:
"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 12Price 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 10Price 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.
* 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.
* 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
1268 69 54 64 68 64 70 67 78 6298 87
Sample Output
4 2
这题是最长上升子序列LIS的拓展版,增加了这几个要求:
1.最长上升改为最长下降
2.计算该长度的序列个数
3.计算序列个数时不能重复
1和2都比较好处理,原有模板代码稍作修改即可,关键是3的处理。dp[i]为以a[i]结尾序列的LIS长度,可增设一个数组c[i],来存储以i为下标的dp[i序列长度的个数。
AC代码:
#include <stdio.h>#define max(a,b) a>b?a:bint main(){ int n,a[5005],dp[5005],c[5005],max1,i,j,num; while(scanf("%d",&n)!=EOF) { for(i=1;i<=n;i++) scanf("%d",&a[i]); for(i=1;i<=n;i++) { dp[i]=1; c[i]=1; } for(i=1;i<=n;i++) { for(j=i-1;j>0;j--) { if(a[j]>a[i]) { if(dp[i]<dp[j]+1) { dp[i]=dp[j]+1; c[i]=c[j]; } else if(dp[i]==dp[j]+1) c[i]+=c[j]; } else if(a[i]==a[j]) //去重 { if(dp[i]==1) c[i]=0; break; } } } max1=-1; num=0; for(i=1;i<=n;i++) max1=max(max1,dp[i]); for(i=1;i<=n;i++) if(max1==dp[i]) num+=c[i]; printf("%d %d\n",max1,num); } return 0;}
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