单点修改+区间求和

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#include<bits/stdc++.h>
#define endl '\n' 
using i64 = long long;
using namespace std;
signed main(){
    std::ios::sync_with_stdio(false);cin.tie(0);
    int n, m;
    cin >> n >> m;
    vector<i64> a(n + 1);
    auto add = [&](int x, i64 k) -> void
    {
        for (int i = x; i <= n; i += i & (-i))
            a[i] += k;
    };
    auto query = [&](int x) -> i64
    {
        i64 res = 0;
        for (int i = x; i; i -= i & (-i))
            res += a[i];
        return res;
    };
    for (int i = 1; i <= n; i++){
        int x;
        cin >> x;
        add(i, x);
    }
    while (m--){
        int opt;
        cin >> opt;
        if (opt == 1){
            int x;
            i64 k;
            cin >> x >> k;
            add(x, k);
        }
        else{
            int x, y;
            i64 ans;
            cin >> x >> y;
            ans = query(y) - query(x - 1);
            cout << ans << endl;
        }
    }
    return 0;
}

区间修改+单点查询

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#include<bits/stdc++.h>
#define endl '\n' 
using i64 = long long;
using namespace std;
signed main(){
    std::ios::sync_with_stdio(false);cin.tie(0);
    int n, m;
    cin >> n >> m;
    vector<i64> a(n + 1), diff(n + 1);
    for (int i = 1; i <= n; i++)
        cin >> a[i];
    auto add = [&](int x, i64 k) -> void
    {
        for (int i = x; i <= n; i += i & (-i))
            diff[i] += k;
    };
    auto query = [&](int x) -> i64
    {
        i64 res = 0;
        for (int i = x; i; i -= i & (-i))
            res += diff[i];
        return res;
    };
    while (m--){
        int opt;
        cin >> opt;
        if (opt == 1){
            int x, y;
            i64 k;
            cin >> x >> y >> k;
            add(x, k), add(y + 1, -k);
        }
        else{
            int x;
            i64 ans;
            cin >> x;
            ans = a[x] + query(x);
            cout << ans << endl;
        }
    }
    return 0;
}

区间修改+区间查询

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#include <bits/stdc++.h>
#define endl '\n'
using i64 = long long;
using namespace std;
signed main(){
    std::ios::sync_with_stdio(false);
    cin.tie(0);
    int n, q;
    cin >> n >> q;
    vector<i64> a(n + 1), b(n + 1), diff(n + 1), t(n + 1);
    for (int i = 1; i <= n; i++){
        cin >> a[i];
        b[i] = a[i] - a[i - 1];
    }
    auto add1 = [&](int x, i64 k) -> void
    {
        for (int i = x; i <= n; i += i & (-i)){
            diff[i] += k;
            t[i] += k * x;
        }
    };
    auto add2 = [&](int l, int r, i64 x) -> void
    {
        add1(l, x), add1(r + 1, -x);
    };
    auto query1 = [&](int x) -> i64
    {
        i64 res = 0;
        for (int i = x; i; i -= i & (-i))
            res += (x + 1) * diff[i] - t[i];
        return res;
    };
    auto query2 = [&](int l, int r) -> i64
    {
        return query1(r) - query1(l - 1);
    };
    for (int i = 1; i <= n; i++)
        add1(i, b[i]);
    while (q--){
        int opt;
        cin >> opt;
        if (opt == 1){
            int l, r;
            i64 x;
            cin >> l >> r >> x;
            add2(l, r, x);
        }
        else{
            int l, r;
            cin >> l >> r;
            cout << query2(l, r) << endl;
        }
    }
    return 0;
}