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CSES Problem Set/Prefix Sum Queries.cpp

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+/* Problem URL: https://cses.fi/problemset/task/2166 */
+
+#include <bits/stdc++.h>
+#include <ext/pb_ds/assoc_container.hpp>
+#include <ext/pb_ds/tree_policy.hpp>
+
+using namespace std;
+using namespace __gnu_pbds;
+
+template <class T, class comp = less<>>
+using ordered_set = tree<T, null_type , comp , rb_tree_tag , tree_order_statistics_node_update>;
+
+#define V vector
+
+#define rmin(a, b) a = min(a, b)
+#define rmax(a, b) a = max(a, b)
+
+#define rep(i, lim) for (int i = 0; i < (lim); i++)
+#define nrep(i, s, lim) for (int i = s; i < (lim); i++)
+
+#define repv(i, v) for (auto &i : (v))
+#define fillv(v) for (auto &itr_ : (v)) { cin >> itr_; }
+#define sortv(v) sort(v.begin(), v.end())
+#define all(v) (v).begin(), (v).end()
+
+using vi = vector<int>;
+using vvi = vector<vi>;
+using vvvi = vector<vvi>;
+using vvvvi = vector<vvvi>;
+
+using ll = long long;
+
+using vl = vector<ll>;
+using vvl = vector<vl>;
+using vvvl = vector<vvl>;
+using vvvvl = vector<vvvl>;
+
+template<class v>
+auto operator<<(ostream &os, const vector<v> &vec)->ostream& {
+    os << vec[0];
+    for (size_t i = 1; i < vec.size(); i++) {
+        os << ' ' << vec[i];
+    }
+    os << '\n';
+    return os;
+}
+
+template<class v>
+auto operator>>(istream &is, vector<v> &vec)->istream& {
+    for (auto &i : vec) {
+        is >> i;
+    }
+    return is;
+}
+
+template<class v>
+auto operator<<(ostream &os, const vector<vector<v>> &vec)->ostream& {
+    for (auto &i : vec) {
+        os << i[0];
+        for (size_t j = 1; j < i.size(); j++) {
+            os << ' ' << i[j];
+        }
+        os << '\n';
+    }
+    return os;
+}
+
+template<class v>
+auto operator>>(istream  &is, vector<vector<v>> &vec)->istream& {
+    for (auto &i : vec) {
+        for (auto &j : i) {
+            is >> j;
+        }
+    }
+    return is;
+}
+
+int main()
+{
+    ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    int n, q;
+    cin >> n >> q;
+
+    vl fds(n);
+
+    cin >> fds;
+
+    ll oo = INT64_MAX >> 1;
+
+    while (__builtin_popcount(n) != 1) {
+        n++;
+        fds.push_back(0);
+    }
+
+    vl seg(n * 2);
+    vl pref(n * 2);
+    vl lazy(n * 2);
+
+    auto propagate = [&](int i, int l, int r) {
+        if (lazy[i] == 0) {
+            return;
+        }
+
+        if (i >= n) {
+            seg[i] += lazy[i];
+            lazy[i] = 0;
+            return; 
+        }
+
+        seg[i] += lazy[i];
+        lazy[i * 2] += lazy[i];
+        lazy[i * 2 + 1] += lazy[i];
+        lazy[i] = 0;
+    };
+
+    function<void(int, int, int, int, int, ll)> update = [&](int i, int l, int r, int tl, int tr, ll v) {
+        propagate(i, l, r);
+
+        if (l > tr || r < tl) {
+            return;
+        }
+
+        if (l >= tl && r <= tr) {
+            lazy[i] += v;
+            propagate(i, l, r);
+            return;
+        }
+
+        int mid = (l + r) >> 1;
+
+        update(i * 2, l, mid, tl, tr, v);
+        update(i * 2 + 1, mid + 1, r, tl, tr, v);
+
+        seg[i] = max(seg[i * 2], seg[i * 2 + 1]);
+    };
+
+    function<void(int, ll)> updatepref = [&](int i, ll v) {
+        i += n;
+        pref[i] = v;
+
+        for (i >>= 1; i > 0; i >>= 1) {
+            pref[i] = pref[i * 2] + pref[i * 2 + 1];
+        }
+    };
+
+    function<ll(int, int, int, int, int)> query = [&](int i, int l, int r, int tl, int tr) {
+        if (l > tr || r < tl) {
+            return -oo;
+        }
+
+        propagate(i, l, r);
+
+        if (l >= tl && r <= tr) {
+            return seg[i];
+        }
+
+        int mid = (l + r) >> 1;
+
+        return max(query(i * 2, l, mid, tl, tr), query(i * 2 + 1, mid + 1, r, tl, tr));
+    };
+
+    function<ll(int, int, int, int, int)> prefquery = [&](int i, int l, int r, int tl, int tr) {
+        if (l > tr || r < tl) {
+            return 0LL;
+        }
+
+        propagate(i, l, r);
+
+        if (l >= tl && r <= tr) {
+            return pref[i];
+        }
+
+        int mid = (l + r) >> 1;
+
+        return prefquery(i * 2, l, mid, tl, tr) + prefquery(i * 2 + 1, mid + 1, r, tl, tr);
+    };
+
+    rep(i, n) {
+        update(1, 0, n - 1, i, n - 1, fds[i]);
+        pref[i + n] = fds[i];
+    }
+
+    for (int i = n - 1; i > 0; i--) {
+        pref[i] = pref[i * 2] + pref[i * 2 + 1];
+    }
+
+    while (q--) {
+        int op;
+        cin >> op;
+        
+        if (op == 1) {
+            int k, u;
+            cin >> k >> u;
+            k--;
+
+            update(1, 0, n - 1, k, n - 1, u);
+            update(1, 0, n - 1, k, n - 1, -fds[k]);
+            updatepref(k, u);
+            fds[k] = u;
+            continue;
+        }
+
+        int a, b;
+        cin >> a >> b;
+        a--, b--;
+
+        cout << max(query(1, 0, n - 1, a, b) - prefquery(1, 0, n - 1, 0, a - 1), 0LL) << '\n';
+    }
+}