Rikka with Maximum Subsegment Sum

Author: Macesuted

QOJ/11521.cpp

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+/**
+ * @file 11521.cpp
+ * @author Macesuted ([email protected])
+ * @date 2025-09-12
+ *
+ * @copyright Copyright (c) 2025
+ *
+ */
+
+#include <bits/stdc++.h>
+using namespace std;
+
+#ifndef LOCAL
+#define endl '\n'
+#endif
+
+bool mem1;
+
+#define maxn 100005
+
+int64_t a[maxn], f[maxn], sl[maxn], sr[maxn];
+uint64_t fsum[maxn], slsum[maxn];
+
+uint64_t solve(int l, int r) {
+    if (l == r) return a[l];
+    int mid = (l + r) >> 1;
+    uint64_t ans = solve(l, mid) + solve(mid + 1, r);
+
+    int64_t sum = 0, maxv = a[mid];
+    for (int i = mid; i >= l; i--) f[i] = maxv = max(maxv, sum = max(sum, (int64_t)0) + a[i]);
+    sum = 0, maxv = a[mid + 1];
+    for (int i = mid + 1; i <= r; i++) f[i] = maxv = max(maxv, sum = max(sum, (int64_t)0) + a[i]);
+
+    sum = 0, maxv = a[mid];
+    for (int i = mid; i >= l; i--) sr[i] = maxv = max(maxv, sum += a[i]);
+    sum = 0, maxv = a[mid + 1];
+    for (int i = mid + 1; i <= r; i++) sl[i] = maxv = max(maxv, sum += a[i]);
+
+    slsum[mid] = fsum[mid] = 0;
+    for (int i = mid + 1; i <= r; i++) slsum[i] = slsum[i - 1] + sl[i], fsum[i] = fsum[i - 1] + f[i];
+
+    for (int i = mid; i >= l; i--) {
+        int p = lower_bound(f + mid + 1, f + r + 1, f[i]) - f;
+
+        auto calc = [&](int xl, int xr, int64_t v) -> uint64_t {
+            int c = lower_bound(sl + xl, sl + xr + 1, v - sr[i]) - sl;
+            uint64_t ret = 0;
+            if (xl <= c - 1) ret += (uint64_t)v * ((c - 1) - xl + 1);
+            if (c <= xr) ret += (uint64_t)sr[i] * (xr - c + 1) + slsum[xr] - slsum[c - 1];
+            return ret;
+        };
+
+        if (mid + 1 <= p - 1) ans += calc(mid + 1, p - 1, f[i]);
+        if (p <= r) {
+            int xl = p - 1, xr = r + 1;
+            while (xl + 1 < xr) {
+                int mid = (xl + xr) >> 1;
+                (sr[i] + sl[mid] >= f[mid] ? xl : xr) = mid;
+            }
+            if (p <= xl) ans += (uint64_t)sr[i] * (xl - p + 1) + slsum[xl] - slsum[p - 1];
+            if (xr <= r) ans += fsum[r] - fsum[xl];
+        }
+    }
+
+    return ans;
+}
+
+void solve(void) {
+    int n;
+    cin >> n;
+    for (int i = 1; i <= n; i++) cin >> a[i];
+    cout << solve(1, n) << endl;
+    return;
+}
+
+bool mem2;
+
+int main() {
+    ios::sync_with_stdio(false), cin.tie(nullptr);
+#ifdef LOCAL
+    cerr << "Memory Cost: " << abs(&mem1 - &mem2) / 1024. / 1024. << "MB" << endl;
+#endif
+
+    int _ = 1;
+    while (_--) solve();
+
+#ifdef LOCAL
+    cerr << "Time Cost: " << clock() * 1000. / CLOCKS_PER_SEC << "MS" << endl;
+#endif
+    return 0;
+}