POJ 3903 Stock Exchange LIS

Posted 2020-10-02 EricJeffrey

题目链接：http://poj.org/problem?id=3903

题目大意：LIS的nlog(n)写法。

解题思路：dp[i]:=长度为i的最长递增子序列的末尾元素最小值。那么由于dp[i]形成了一个有序的序列，所以可以采用二分的办法。

dp[j] = a[i] 　　dp[j] <= a[j] < dp[j + 1]

代码：

 1 const int inf = 0x3f3f3f3f;
 2 const int maxn = 1e5 + 5;
 3 int a[maxn], n;
 4 int dp[maxn];
 5 
 6 void solve(){
 7     memset(dp, 0x3f, sizeof(dp));
 8     for(int i = 1; i <= n; i++){
 9         *lower_bound(dp + 1, dp + 1 + n, a[i]) = a[i];
10     }
11     int ans = lower_bound(dp + 1, dp + 1 + n, inf) - dp - 1;
12     printf("%d\n", ans);
13 }
14 int main(){
15     while(scanf("%d", &n) != EOF){
16         for(int i = 1; i <= n; i++) scanf("%d", &a[i]);
17         solve();
18     }
19 }

题目：

Stock Exchange

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 7115		Accepted: 2474

Description

The world financial crisis is quite a subject. Some people are more relaxed while others are quite anxious. John is one of them. He is very concerned about the evolution of the stock exchange. He follows stock prices every day looking for rising trends. Given a sequence of numbers p1, p2,...,pn representing stock prices, a rising trend is a subsequence pi1 < pi2 < ... < pik, with i1 < i2 < ... < ik. John’s problem is to find very quickly the longest rising trend.

Input

Each data set in the file stands for a particular set of stock prices. A data set starts with the length L (L ≤ 100000) of the sequence of numbers, followed by the numbers (a number fits a long integer). 
White spaces can occur freely in the input. The input data are correct and terminate with an end of file.

Output

The program prints the length of the longest rising trend. 
For each set of data the program prints the result to the standard output from the beginning of a line.

Sample Input

6 
5 2 1 4 5 3 
3  
1 1 1 
4 
4 3 2 1

Sample Output

3 
1 
1

Hint

There are three data sets. In the first case, the length L of the sequence is 6. The sequence is 5, 2, 1, 4, 5, 3. The result for the data set is the length of the longest rising trend: 3.