Range maximum query III | Segment tree with repair

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Time limit：1s

Memory limit：64MB

Problem Description

Given a sequence A of length n, q queries are given, and each query may be one of two operations.
1 lr indicates the maximum value in the range of the subscript l and r of the query array.
2 pos val indicates the a in the array The value of [pos] is changed to val.
Data scale guarantee:
-1e ⁶ <=A[i]≤1e ⁶
1<=l<=r<=n
1<=n, q<=100000

Input

The first line of input is n, q represents the length of the sequence and the number of queries. The
second line is the number of n. The
next q lines each give an operation.

Output

For operation 1, give the maximum value of the interval

Sample Input

Sample Output

5
8

Segment tree with trimming

AC code:

#include<cstdio>
#include<iostream>
using namespace std;
int n,m,x[100005];          //原数组
struct Node{
    
    
    int l,r,w;                              //区间左右端点和区间最大值
};
Node tree[400005];                          //线段树
void build(int num,int l,int r){
    
                //建树
    if(l == r){
    
                 //相等说明已经到了叶子节点
        tree[num].l = l,tree[num].r = r,tree[num].w = x[l];return;
    }
    int mid = (l + r) >> 1;
    int lc = num << 1;      //乘2是左子树
    int rc = num << 1 | 1;  //乘2或1是右子树
    build(lc,l,mid);        //建左子树
    build(rc,mid + 1,r);  //建右子树
    tree[num].l = l,tree[num].r = r,tree[num].w = max(tree[lc].w,tree[rc].w);return;//保存左右子树的最大子（区间最大）
}
int find(int num,int l,int r){
    
              //查找区间最大
    if(tree[num].l == l && tree[num].r == r)//找到目标区间
        return tree[num].w;
    int mid = (tree[num].l + tree[num].r) >> 1;
    int lc = num << 1;
    int rc = num << 1 | 1;
    if(l > mid)    //继续在右子树找
        return find(rc,l,r);
    else if(r <= mid)    //继续在左子树找
        return find(lc,l,r);
    else return max(find(lc,l,mid),find(rc,mid + 1,r)); //左子树找一段，右子树找一段
}
void pick(int num,int l,int val){
    
           //修改并更新线段树
    if(tree[num].l == l && tree[num].r == l){
    
    
        tree[num].w = val;return;
    }
    int mid = (tree[num].l + tree[num].r) >> 1;
    int lc = num << 1;
    int rc = num << 1 | 1;
    if(l > mid)
        pick(rc,l,val);
    else
        pick(lc,l,val);
    tree[num].w = max(tree[lc].w,tree[rc].w);return;
}
int main(){
    
    
    scanf("%d %d",&n,&m);
    for(int i = 1;i <= n;++i)
        scanf("%d",x + i);
    build(1,1,n);
    while(m--){
    
    
        int a,b,c;
        scanf("%d %d %d",&a,&b,&c);
        if(a == 1)
            printf("%d\n",find(1,b,c));
        else
            pick(1,b,c);
    }
    return 0;
}