codeforce --- 340D

D. Bubble Sort Graph

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

Iahub recently has learned Bubble Sort, an algorithm that is used to sort a permutation with n elements a1, a2, ..., an in ascending order. He is bored of this so simple algorithm, so he invents his own graph. The graph (let's call it G) initially has n vertices and 0 edges. During Bubble Sort execution, edges appear as described in the following algorithm (pseudocode).

procedure bubbleSortGraph()
    build a graph G with n vertices and 0 edges
    repeat
        swapped = false
        for i = 1 to n - 1 inclusive do:
            if a[i] > a[i + 1] then
                add an undirected edge in G between a[i] and a[i + 1]
                swap( a[i], a[i + 1] )
                swapped = true
            end if
        end for
    until not swapped 
    /* repeat the algorithm as long as swapped value is true. */ 
end procedure

For a graph, an independent set is a set of vertices in a graph, no two of which are adjacent (so there are no edges between vertices of an independent set). A maximum independent set is an independent set which has maximum cardinality. Given the permutation, find the size of the maximum independent set of graph G, if we use such permutation as the premutation a in procedure bubbleSortGraph.

Input

The first line of the input contains an integer n (2 ≤ n ≤ 105). The next line contains n distinct integers a1, a2, ..., an (1 ≤ ai ≤ n).

Output

Output a single integer — the answer to the problem.

Sample test(s)

input

3
3 1 2

output

2

思路：用len[i]记录长度为i时的上升子序列对应的最小的那个数，每次插入一个数就更新len数组，使用二分查找进行修改操作，时间复杂度为O(nlogn)，最后i的值就是上升子序列的最大长度。

#include<iostream>
#include<cstring>
#include<cstdio>
using namespace std;
int a[100005];
int Binary(int temp, int len)
{
    int l = 1, r = len, mid;
    while(l <= r)
    {
        mid = (l + r) >> 1;
        if(temp > a[mid])
            l = mid + 1;
        else
            r = mid - 1;
    }
    return l;   
}

int main(int argc, char const *argv[]) 
{
    int n, len, k, temp, idx;
    /* freopen("in.c", "r", stdin); */
    while(~scanf("%d", &n))
    {
        len = 0;
        memset(a, 0, sizeof(a));
        for(int i = 1;i <= n;i ++)
        {
            scanf("%d", &temp);
            if(temp > a[len])
                a[++len] = temp;
            else
            {
                idx = Binary(temp, len);
                a[idx] = temp;
            }
        }
        printf("%d
", len);
    }
    return 0;
}