线段数模板

单点更新：

#include<cstdio>
#include<iostream>
#include<string>
#include<cmath>
using namespace std;
const int MAXNODE = 1 << 19;
const int MAX = 2e5 + 10;
typedef struct Node
{
    int left;
    int right;
    int value;
};
Node node[MAXNODE];
int father[MAX];//记录位置
void BuildTree(int i,int left,int right)//构造线段数和初始化
{
    node[i].left = left;
    node[i].right = right;
    node[i].value = 0;
    if(left == right)
    {
        father[left] = i;
        return ;
    }
    else
    {
        int temp = (left + right) / 2.0;
        BuildTree(i << 1,left,temp);
        BuildTree((i << 1) + 1,temp + 1,right);
    }
}
void Update(int ri)//更新
{
    if(ri == 1)
        return ;
    int fi = ri / 2;
    int a = node[fi << 1].value;
    int b = node[(fi << 1) + 1].value;
    node[fi].value = a + b;
    Update(fi);
}
int M;
void query(int i,int l,int r)//询问查找
{
    if(node[i].left == l && node[i].right == r)
    {
      M += node[i].value;
      return ;
    }
    i = i << 1;
    if(l <= node[i].right)
    {
        if(r <= node[i].right)
        {
            query(i,l,r);
        }
        else
        {
            query(i,l,node[i].right);
        }
    }
    i += 1;
    if(r >= node[i].left)
    {
        if(l >= node[i].left)
        {
            query(i,l,r);
        }
        else
        {
            query(i,node[i].left,r);
        }
    }
}
int main()
{
    ios::sync_with_stdio(false);//不用会T，或者使用scanf printf
    int T;
    cin >> T;
    int t = 1;
    while(T--)
    {
        cout << "Case " << t++  << ':'<< endl;
        int n;
        cin >> n;
        BuildTree(1,1,n);
        for(int i = 1;i <= n; ++i)
        {
            int v;
            cin >> v;
            node[father[i]].value = v;//将值存入最底层
            Update(father[i]);
        }
        string s;
        while(cin >> s && s[0] != 'E')
        {

            int a,b;
            cin >> a >> b;
            if(s[0] == 'Q')
            {
                M = 0;
                query(1,a,b);
                cout << M << endl;
            }
            if(s[0] == 'A')
            {
                node[father[a]].value += b;
                Update(father[a]);
            }
            if(s[0] == 'S')
            {
                node[father[a]].value -= b;
                Update(father[a]);
            }
        }
    }
}

单点更新（回溯）：

#include<cstdio>
#include<iostream>
#include<string>
const int MAXN = 2e5 + 10;
using namespace std;
#define lson l,m,i << 1
#define rson m + 1,r,i << 1 | 1
typedef struct Node
{
    int l,r;
    int mid()
    {
        return (l + r) / 2.0;
    }
    int value;
};
Node node[MAXN << 2];
void push_up(int i)
{
    node[i].value = max(node[i << 1].value,node[i << 1 | 1].value);
}
void Build(int l,int r,int i)
{
    node[i].l = l;
    node[i].r = r;
    node[i].value = 0;
    if(l == r)
    {
        cin >> node[i].value;
        return ;
    }
    int m = node[i].mid();
    Build(lson);
    Build(rson);
    push_up(i);
}
int M;
void query(int l,int r,int i)
{
    if(node[i].l == l && node[i].r == r)
    {
      M = max(node[i].value,M);
      return ;
    }
    int m = node[i].mid();
    if(r <= m)
        query(l,r,i << 1);
    else
        if(l > m)
            query(l,r,i << 1 | 1);
        else
        {
            query(lson);
            query(rson);
        }
}
void update(int l,int r,int i,int v,int num)
{
    if(l == r && l == num)
    {
        node[i].value = v;
        return ;
    }
    int m = node[i].mid();
    if(m >= num)
        update(l,m,i << 1,v,num);
    else
        update(m + 1,r,i << 1 | 1,v,num);
    push_up(i);

}
int main()
{
    ios::sync_with_stdio(false);
    int n,m,a,b;
    string s;
    while(cin >> n >> m)
    {
        Build(1,n,1);
        while(m--)
        {
            cin >> s >> a >>b;
            if(s[0] == 'Q')
            {
                M = 0;
                query(a,b,1);
                cout << M << endl;
            }
            else
            {
                update(1,n,1,b,a);
            }
        }
    }
}

线段数区间求和（延迟标记）

#include<cstdio>
#include<iostream>
using namespace std;
const int N = 1e5 + 10;
typedef long long LL;
typedef struct Node
{
    int l;
    int r;
    int mid()
    {
        return (l + r) / 2.0;
    }
};
LL ans;
Node node[N << 2];//为什么乘4
LL add[N << 2];// 延迟标记数组
LL sum[N << 2];//每个节点的sum
void PushUp(int i);
#define lson i << 1,l,m
#define rson i << 1 | 1,m + 1,r
void build(int i,int l,int r)//建树并完成初始化
{
    node[i].l = l;
    node[i].r = r;
    sum[i] = 0;
    add[i] = 0;
    if(l == r)
    {
        cin >> sum[i];//在内部输入，为叶子节点
        return ;//一定要写return！！！
    }

    int m = node[i].mid();
    build(lson);//只想下更新sum
    build(rson);
    PushUp(i);//递归回去完成区间的更新.
}
void PushUp(int i) // 建树递归返回时更新。
{
    sum[i] = sum[i << 1] + sum[i << 1 | 1];
}
void PushDown(int i,int L) // L为区间长度 （延迟标记）
{
    if(add[i])
    {
        add[i << 1] += add[i];
        add[i << 1 | 1] += add[i];
        sum[i << 1] += add[i] * (L - (L >> 1)); // 易错
        sum[i << 1 | 1] += add[i] * (L >> 1);
        add[i] = 0;
    }
}
void update(int v,int l,int r,int i)//更新操作，区间【l,r】加值v
{
    if(node[i].l == l && node[i].r == r)//当找到目标区间时，
    {
        sum[i] += (LL)v * (r - l + 1);//更新当前节点的值，
        add[i] += v;//延迟标记+V
        return ;
    }

    PushDown(i,node[i].r - node[i].l + 1);// 因为没有匹配到合适的区间,向下寻找,检查这个区间是否有标记.
    int m = node[i].mid();//如果有标记,说明应该先把之前的标记量给计算出,再进行寻找.
    if(r <= m)
    {
        update(v,l,r,i << 1);
    }
    else
    {
        if(l > m)
            update(v,l,r,i << 1 | 1);
        else
        {
            update(v,l,m,i << 1);
            update(v,m + 1,r,i << 1 | 1);
        }
    }
    PushUp(i);//递归返回
}
void query(int l,int r,int i) //查询
{
    if(node[i].l == l && node[i].r == r)
    {
        ans +=  sum[i];
        return ;
    }
    PushDown(i,node[i].r - node[i].l + 1);
    int m = node[i].mid();
    if(r <= m)
         query(l,r,i << 1 );
    else
    {
        if(l > m)
            query(l,r,i << 1 | 1);
        else
        {
            query(l,m,i << 1);
            query(m + 1,r,i << 1 | 1);
        }
    }
}
int main()
{
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    int n,m;
    while(cin >> n >> m)
    {
        build(1,1,n);
        string s;
        while(m--)
        {
            int a,b,c;
            cin >> s;
            if(s[0] == 'Q')
            {
                ans = 0;
                cin >> a >> b;
                query(a,b,1);
                cout << ans << endl;
            }
            else
            {
                cin >> a >> b >> c;
                update(c,a,b,1);
            }
        }
    }
}