prefix sum, sparse table, RMQ

submissions/CSES/maximum-subarray-sum-ii.cpp

@@ -0,0 +1,68 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+#ifdef DEBUG
+#include "debug.cpp"
+#else
+#define dbg(...)
+#endif
+
+using ll = long long;
+
+#define F(expr) [](auto a, auto b) { return expr; }
+template <typename T, typename Op> struct SparseTable {
+  vector<vector<T>> st;
+  Op f;
+  const T id;
+  // Lazy loading constructor. Needs to call build!
+  SparseTable(Op op, const T neutral = T()) : st(), f(op), id(neutral) {}
+  SparseTable(const vector<T> &v, Op op = Op(), const T neutral = T()) : st(), f(op), id(neutral) { build(v); }
+  void build(const vector<T> &v) {
+    auto logn = 31-__builtin_clz((int)size(v));
+    st.resize(logn+1, vector<T>(v.size()));
+    st[0] = v;
+    for (int i = 1; i <= logn; i++)
+      for (int j = 0; j + (1 << i) <= (int)v.size(); j++)
+        st[i][j] = f(st[i-1][j], st[i-1][j+(1 << (i-1))]);
+  }
+  T query(int l, int r) const {
+    assert(l <= r);
+    auto lg = 31-__builtin_clz(r-l+1);
+    return f(st[lg][l], st[lg][r-(1<<lg)+1]);
+  }
+  // Non RMQ query
+  T query_complete(int l, int r) const {
+    assert(l <= r);
+    T acc = id;
+    for (int i = 31-__builtin_clz(size(st[0])); ~i; --i)
+      if ((1 << i) <= r - l + 1) {
+        acc = f(acc, st[i][l]);
+        l += 1 << i;
+      }
+    return acc;
+  }
+};
+
+void solve() {
+  int n, a, b;
+  cin >> n >> a >> b;
+  vector<ll> v(n);
+  for (auto &x : v) cin >> x;
+  vector<ll> pref(n+1);
+  partial_sum(begin(v), end(v), begin(pref)+1);
+  auto op = [](auto x, auto y) { return min(x, y); };
+  SparseTable<ll, decltype(op)> st(pref, op, LLONG_MAX);
+  ll res = LLONG_MIN;
+  for (int i = a; i <= n; i++)
+    res = max(res, pref[i]-st.query(max(i-b,0), i-a));
+  cout << res << '\n';
+}
+
+int32_t main() {
+  cin.tie(0)->sync_with_stdio(0);
+  int t = 1;
+  // cin >> t; cin.ignore();
+  for (auto i = 1; i <= t; i++) {
+    solve();
+  }
+}