Rezolvare

Iată rezolvarea de 100 de puncte pentru problema doubletrouble:

#include <vector>
#include <cstdint>
#include <fstream>
using namespace std;

// the minimum energy for a distance and a given number of spells
int64_t energy(int64_t x, int64_t spells) {
    int64_t a = x / spells;
    int64_t r = x % spells;
    return (spells - r)*a*a + r*(a + 1)*(a + 1);
}

int main() {
    ifstream        f("doubletrouble.in");
    ofstream        g("doubletrouble.out");
    int             N; f >> N;
    int64_t         E; f >> E;
    vector<int>     P(N+1), S(N+1), C(N+1), X;

    // compute the initial position for each potion
    for (int i = 1; i <= N; i++) {
        int v; f >> v; P[v] = i;
    }

    // compute the Fenwick array -- add 1 to all elements
    for (int i = 1; i <= N; i++) {
        for (int k = i; k <= N; k += k & -k) S[k]++;
    }

    // for each potion, find the distance to its desired position
    for (int i = 1; i <= N; i++) {
        int x = 0;
        for (int k = P[i]; k <= N; k += k & -k) S[k]--;
        for (int k = P[i]; k  > 0; k -= k & -k) x += S[k];
        C[x]++;
    }

    // extract all distinct distances
    for (int i = 1; i <= N; i++) if (C[i]) X.push_back(i);

    // binary search for the delta of the optimal solution
    int64_t spells  = -1;
    for (int64_t lo = 1, hi = 1LL*N*N; lo <= hi;) {
        int64_t delta = (lo + hi)/2, cnt = 0, e = 0, s = 0;
        int     u = 1, v = 1;
        for (int i = 0; i < X.size(); i++) {
            // update u and v -- the lower and the upper bound
            while (u < X[i] && energy(X[i], u) - energy(X[i], u + 1)  > delta) u++;
            v = max(v, u);
            while (v < X[i] && energy(X[i], v) - energy(X[i], v + 1) >= delta) v++;

            // update the used energy and the number of spells
            e += C[X[i]]*energy(X[i], v);
            s += C[X[i]]*v;

            // in case we have a range, (u, v] producing delta, then keep track of these values,
            // since later they might save a few spells, by trading a spell for delta units of energy
            if (v > 1 && energy(X[i], v - 1) - energy(X[i], v) == delta) cnt += C[X[i]]*(v - u);
        }

        if (e <= E) {
            spells = s - min((E - e)/delta, cnt);
            lo = delta + 1;
        } else {
            hi = delta - 1;
        }
    }
    g << spells;

    return 0;
}