LIS(nlogn) POJ 3903 Stock Exchange

 1 /*
 2     最长递增子序列O(nlogn)算法： 
 3         设当前最长递增子序列为len，考虑元素a[i]; 
 4         若d[len]<a[i]，则len++，并将d[len]=a[i]; 
 5         否则,在d[1~len]中二分查找，找到第一个比它小的元素d[j]，并d[j]=a[i]。
 6 */
 7 #include <cstdio>
 8 #include <cstring>
 9 #include <iostream>
10 #include <algorithm>
11 #include <cmath>
12 #include <vector>
13 using namespace std;
14 
15 const int MAX_N = 100000 + 10;
16 const int INF = 999999999;
17 int a[MAX_N];
18 int d[MAX_N];
19 int n, m;
20 
21 int BinSearch(int key, int low, int high)
22 {
23     while(low <= high)
24     {
25         int mid = low +  (high - low) / 2;
26         if(key > d[mid])
27             low = mid + 1;
28         else
29             high = mid - 1;
30     }
31     return low;
32 }
33 
34 int LIS(void)        //O(nlogn) 二分查找优化
35 {
36     int len = 1;
37     int j;
38     d[1] = a[1];
39     
40     for (int i=2; i<=n; ++i)
41     {
42         if (d[len] < a[i])
43             d[++len] = a[i];
44         else
45         {
46             j = BinSearch (a[i], 1, len);
47             d[j] = a[i];
48         }
49     }
50     return len;
51 }
52 
53 int main(void)        //POJ 3903 Stock Exchange(LIS)
54 {
55     //freopen ("inE.txt", "r", stdin);
56 
57     while (scanf ("%d", &n) != EOF)
58     {
59         for (int i=1; i<=n; ++i)
60         {
61             scanf ("%d", &a[i]);
62         }
63         
64         printf ("%d\n", LIS ());
65     }
66     
67     return 0;
68 }
69 
70 
71 /*
72         int res = 0;
73         for (int i=1; i<=n; ++i)        //O(n^2) 超时
74         {
75             dp[i] = 1;
76             for (int j=1; j<i; ++j)
77             {
78                 if (a[i] < a[j] + 1)
79                 {
80                     dp[i] = dp[j] + 1;
81                 }
82             }
83             res = max (res, dp[i]);
84         }
85 */