CF1661F

contest/cf1661/F.cpp

@@ -0,0 +1,102 @@
+#include <bits/stdc++.h>
+
+using ll = long long int;
+
+const int MAXN = 2e5 + 19;
+
+int n, a[MAXN];
+ll m;
+
+struct Node {
+    int len, x;
+    ll value() const {
+        int t = x + 1, b = len / t, f = len % t;
+
+        return (ll)f * (b + 1) * (b + 1) + ll(t - f) * b * b;
+    }
+    ll benefit() const {
+        return value() - Node{len, x + 1}.value();
+    }
+    bool operator<(const Node &b) const {
+        return benefit() < b.benefit();
+    }
+} node[MAXN];
+
+int get(int len, ll b) {
+    int l = 0, r = len;
+    while (l < r) {
+        int mid = (l + r + 1) / 2;
+        if (Node{len, mid - 1}.benefit() >= b) {
+            l = mid;
+        } else {
+            r = mid - 1;
+        }
+    }
+    return l;
+}
+
+ll check(ll b) {
+    ll res = 0;
+    for (int i = 1; i <= n; ++i) {
+        res += Node{a[i] - a[i - 1], get(a[i] - a[i - 1], b)}.value();
+    }
+    return res;
+}
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    std::cin.tie(nullptr);
+
+    std::cin >> n;
+    for (int i = 1; i <= n; ++i) {
+        std::cin >> a[i];
+    }
+    std::cin >> m;
+
+    for (int i = 1; i <= n; ++i) {
+        node[i] = Node{a[i] - a[i - 1], 0};
+    }
+
+    ll t;
+    {
+        ll b = 0; // take all that benefit >= b
+        for (int i = 60; ~i; --i) {
+            if (check(b + (1ULL << i)) < m) {
+                b += 1ULL << i;
+            }
+        }
+        t = b + 1;
+    }
+
+    std::priority_queue<Node> q;
+    ll tot = check(t);
+    int ans = 0;
+    for (int i = 1; i <= n; ++i) {
+        q.push(Node{a[i] - a[i - 1], get(a[i] - a[i - 1], t)});
+        ans += get(a[i] - a[i - 1], t);
+    }
+
+    while (tot > m) {
+        auto [len, x] = q.top();
+        q.pop();
+
+        ll b = Node{len, x}.benefit();
+        int l = x + 1, r = len;
+        while (l < r) {
+            int mid = (l + r + 1) / 2;
+            if (Node{len, mid - 1}.benefit() == b && tot - b * (mid - x - 1) > m) {
+                l = mid;
+            } else {
+                r = mid - 1;
+            }
+        }
+        ans += l - x;
+        tot -= b * (l - x);
+
+        q.push(Node{len, l});
+    }
+
+    std::cout << ans << '\n';
+
+    return 0;
+}