Input Format

In the first line of input, there is a single number N. In the next N lines input the value of a[i].

Constraints

1 ≤ N ≤ 10⁶

1 ≤ a[i] ≤ 10⁵

Output Format

In a single line, output the length of the longest increasing sub-sequence.

Sample Input

5
2
7
4
3
8

Sample Output

3

Explanation

{2,7,8} is the longest increasing sub-sequence, hence the answer is 3 (the length of this sub-sequence).

#include<cstdio>
#include<algorithm>
using namespace std;
const int MAX_N=1e6+10, oo=1e6;
int A[MAX_N], f[MAX_N];
//二分法: binary_search(y, f())
//设有一个单调（不要求严格单调）的函数f()
//可以在O(log N)的时间内求解以下问题：
//给定y,求满足f(x)<=y/f(x)>=y的最大/最小的x
//

int binary_search(int y, int l, int r){ //y is the keyint mid;while(r-l>1){ //r is illegalmid=(l+r)>>1;if(f[mid]<y){l=mid;}else r=mid;}return l;
}int main(){//freopen("in", "r", stdin);int N, ans=0;scanf("%d", &N);for(int i=1; i<=N; i++) scanf("%d", A+i);f[0]=0;for(int i=1; i<=N; i++) f[i]=oo;for(int i=1; i<=N; i++){int tmp=binary_search(A[i], 0, ans+1)+1;ans=max(ans, tmp);f[tmp]=min(f[tmp], A[i]);}printf("%d\n", ans);return 0;
}

#include<bits/stdc++.h>
using namespace std;
const int MAX_M=1e5+5, MAX_N=1e6+5;
int ma[MAX_M<<2];
void insert(int id, int L, int R, int pos, int v){if(L==R){ma[id]=v;}else{int mid=(L+R)>>1;if(pos<=mid){insert(id<<1, L, mid, pos, v);}else{insert(id<<1|1, mid+1, R, pos, v);}ma[id]=max(ma[id<<1], ma[id<<1|1]);}
}
int query(int id, int L, int R, int l, int r){if(l<=L && R<=r) return ma[id];int mid=(L+R)>>1;int res=0;if(l<=mid){res=max(res, query(id<<1, L, mid, l, r));}if(r>mid){res=max(res, query(id<<1|1, mid+1, R, l, r));}return res;
}
int a[MAX_N];
int main(){//freopen("in", "r", stdin);int N;//single case, leave out initializationscanf("%d", &N);int rb;for(int i=0; i<N; i++) scanf("%d", a+i), rb=max(rb, a[i]);int ans=0;for(int i=0; i<N; i++){int tmp=query(1, 0, rb, 0, a[i]-1)+1;ans=max(ans, tmp);insert(1, 0, rb, a[i], tmp);    //over-head
    }printf("%d\n", ans);return 0;
}

insert(1, 0, rb, a[i], tmp); 

#include<bits/stdc++.h>
using namespace std;
const int MAX_N=1e6+5, MAX_M=1e5+5;
int bit[MAX_M], M;
int a[MAX_N];
int query(int i){int res=0;while(i){res=max(res, bit[i]);i-=i&-i;}return res;
}
void modify(int i, int v){while(i<=M){if(bit[i]>=v) return;bit[i]=v;i+=i&-i;}
}
int main(){//freopen("in", "r", stdin);int N;scanf("%d", &N);M=0;for(int i=0; i<N; i++)  scanf("%d", a+i), M=max(M, a[i]);int ans=0;int tmp;for(int i=0; i<N; i++){tmp=query(a[i]-1)+1;modify(a[i], tmp);ans=max(ans, tmp);}printf("%d\n", ans);return 0;
}