hdu-3308 LCIS (线段树区间合并）

LCIS

Time Limit: 6000/2000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 8337    Accepted Submission(s): 3566

Problem Description

Given n integers.
You have two operations:
U A B: replace the Ath number by B. (index counting from 0)
Q A B: output the length of the longest consecutive increasing subsequence (LCIS) in [a, b].

Input

T in the first line, indicating the case number.
Each case starts with two integers n , m(0<n,m<=10⁵).
The next line has n integers(0<=val<=10⁵).
The next m lines each has an operation:
U A B(0<=A,n , 0<=B=10⁵)
OR
Q A B(0<=A<=B< n).

Output

For each Q, output the answer.

Sample Input

1
10 10
7 7 3 3 5 9 9 8 1 8
Q 6 6
U 3 4
Q 0 1
Q 0 5
Q 4 7
Q 3 5
Q 0 2
Q 4 6
U 6 10
Q 0 9

Sample Output

1
1
4
2
3
1
2
5

Author

shǎ崽

思路：

n个数字，q个操作，有两种操作：1.Q询问操作：在x,y区间内最长的连续递增子序列的长度。2，替换操作，把下标为x数替换为y.

这种询问，单点更新操作一般都是用线段树做。之前一直想成了最长递增子序列。。。完全没有思路，，其实他只要求最长的连续子串长度。。注意：是最长的连续的子串。

这样就是很裸的线段树区间合并了，

实现代码：

#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define lson l,m,rt<<1
#define rson m+1,r,rt<<1|1
#define mid int m = (l + r) >> 1
const int M = 2e5+;
int lsum[M<<],sum[M<<],rsum[M<<],num[M];
void pushup(int l,int r,int rt){
    int k = r - l + ;
    mid;
    lsum[rt] = lsum[rt<<]; rsum[rt] = rsum[rt<<|];
    sum[rt] = max(sum[rt<<],sum[rt<<|]);
    if(num[m] < num[m+]){
        if(lsum[rt] == (k - (k >> ))) lsum[rt] += lsum[rt<<|];
        if(rsum[rt] == (k>>)) rsum[rt] += rsum[rt<<];
        sum[rt] = max(sum[rt],lsum[rt<<|]+rsum[rt<<]);
    }
}
void build(int l,int r,int rt){
     if(l == r){
        sum[rt] = lsum[rt] = rsum[rt]  = ;
        return ;
     }
     mid;
     build(lson);
     build(rson);
     pushup(l,r,rt);
}
void update(int p,int c,int l,int r,int rt){
    if(l == r){
        num[l] = c;
        return ;
    }
    mid;
    if(p <= m) update(p,c,lson);
    if(p > m) update(p,c,rson);
    pushup(l,r,rt);
}
int query(int L,int R,int l,int r,int rt){
    if(L <= l&&R >= r) return sum[rt];
    int ret = ;
    mid;
    if(L <= m) ret = max(ret,query(L,R,lson));
    if(R > m) ret = max(ret,query(L,R,rson));
    if(num[m] < num[m+]){
        ret = max(ret,min(m - L + ,rsum[rt<<])+min(R-m,lsum[rt<<|]));
    }
    return ret;
}

int main(){
    int t,n,q,x,y;
    char c;
    scanf("%d",&t);
    while(t--){
        cin>>n>>q;
        for(int i = ; i <= n;i ++){
            cin>>num[i];
        }
        build(,n,);
        for(int i = ;i < q;i ++){
            cin>>c>>x>>y;
            if(c == 'Q'){
                x++;y++;
                cout<<query(x,y,,n,)<<endl;
            }
            else{
                x++;
                update(x,y,,n,);
            }
        }
    }
    return ;
}