IOI '20 - Biscuits (9pts)

#include "biscuits.h"
#include <bits/stdc++.h>

using namespace std;

const int MX = 60;

long long count_tastiness(long long x, vector<long long> a) {
    int k = a.size();
    long long maxSum = 0;
    for (int i = 0; i < k; ++i) {
        maxSum += (1LL << i) * a[i];
    }
    k = 1;
    long long p = 1;
    while (p < maxSum) ++k, p <<= 1;
    while (a.size() < k) a.push_back(0);

    auto possible = [&k, &a, &maxSum, &x](const bitset<MX> &y) {
        long long need = 0; // as a multiple of current power of two
        for (int i = k-1; i >= 0; --i) {
            if (y[i]) need += x;
            long long use = min(need, a[i]);
            need -= use;
            need <<= 1;
            if (need > maxSum) return false;
        }
        return !need;
    };

    bitset<MX> y = 0;
    long long ans = 1;
    bool foundNext = true;
    while (foundNext) {
        foundNext = false;
        bitset<MX> z = y;
        // find next highest y-value that works
        for (int i = 0; i < k; ++i) {
            if (y[i]) {z[i] = 0; continue;}
            // change a 0 into a 1, and set all smaller bits to 0
            z[i] = 1;
            if (possible(z)) {
                ++ans, y = z;
                foundNext = true;
                break;
            }
            z[i] = 0;
        }
    }
    return ans;
}