线段树代码模板 → 点更新、区间查询

【算法代码】

#include<bits/stdc++.h>
using namespace std;

const int maxn=100005;
const int inf=0x3f3f3f3f;
int a[maxn];

struct node {
    int le,ri,mx; //mx represents the maximum value of interval [le,ri]
} tree[maxn*4]; //Segment tree needs 4 times the maxn space

void build(int k,int le,int ri) { //Create a segment tree
    tree[k].le=le; //k represents the node number of segment tree
    tree[k].ri=ri;
    if(le==ri) {
        tree[k].mx=a[le];
        return;
    }
    int mid,lson,rson;
    mid=(le+ri)/2; //The middle of the interval [le..ri]
    lson=k*2; //Left child subscript
    rson=k*2+1; //Right child subscript
    build(lson,le,mid);
    build(rson,mid+1,ri);
    tree[k].mx=max(tree[lson].mx,tree[rson].mx);
}

void update(int k,int i,int v) { //Point update: Change the value of a[i] to v
    if(tree[k].le==tree[k].ri && tree[k].le==i) { //Find leaf node a[i] with number i
        tree[k].mx=v;
        return;
    }
    int mid,lson,rson;
    mid=(tree[k].le+tree[k].ri)/2;
    lson=k*2;  //Left child subscript
    rson=k*2+1; //Right child subscript
    if(i<=mid) update(lson,i,v); //Go to the left subtree to update
    else update(rson,i,v); //Go to the right subtree to update
    tree[k].mx=max(tree[lson].mx,tree[rson].mx);
}

int query(int k,int le,int ri) { //Interval query: find the maximum value of the interval [le..ri]
    if(tree[k].le>=le && tree[k].ri<=ri) //Find interval [le..ri]
        return tree[k].mx;
    int mid,lson,rson;
    mid=(tree[k].le+tree[k].ri)/2;
    lson=k*2; //Left child subscript
    rson=k*2+1; //Right child subscript
    int iMAX=-inf; //Note: iMAX is a local variable
    if(le<=mid)
        iMAX=max(iMAX,query(lson,le,ri)); //Go to the left subtree to query
    if(ri>mid)
        iMAX=max(iMAX,query(rson,le,ri)); //Go to the right subtree to query
    return iMAX;
}

void print(int k) {
    if(tree[k].mx) {
        cout<<k<<"\t"<<tree[k].le<<"\t"<<tree[k].ri<<"\t"<<tree[k].mx<<"\t"<<endl;
        print(k<<1);
        print((k<<1)+1);
    }
}

int main() {
    int n;
    cin>>n;
    for(int i=1; i<=n; i++) cin>>a[i];

    build(1,1,n); //Create a segment tree
    print(1);

    int le,ri;
    cout<<"Enter the query interval [le..ri]:"<<endl;
    cin>>le>>ri;
    cout<<query(1,le,ri)<<endl;

    int idx,v;
    cout<<"Enter id idx and value v of an element to be modified:"<<endl;
    cin>>idx>>v;
    update(1,idx,v); //Change the value of a[idx] to v

    cout<<"Enter the query interval [le..ri] after updating:"<<endl;
    cin>>le>>ri;
    cout<<query(1,le,ri)<<endl;

    return 0;
}


/*
in:
10
5 3 7 2 12 1 6 4 8 15

out:
1       1       10      15
2       1       5       12
4       1       3       7
8       1       2       5
16      1       1       5
17      2       2       3
9       3       3       7
5       4       5       12
10      4       4       2
11      5       5       12
3       6       10      15
6       6       8       6
12      6       7       6
24      6       6       1
25      7       7       6
13      8       8       4
7       9       10      15
14      9       9       8
15      10      10      15
Enter the query interval [le..ri]:
3 7
12
Enter id idx and value v of an element to be modified:
8 11111
Enter the query interval [le..ri] after updating:
5 9
11111
*/