#include <map>
#include <vector>

// Your new function as given to you by me, your boss.
int cut_log(const std::vector<int>& p, int n)
{
    std::map<int, int> cache;

    // Some array to store calculated values
    for (int j = 1; j <= n; j++) {
        cache[j] = (j < static_cast<int>(p.size())) ? p[j] : 0;

        for (int i = 1; i < j; i++) { // Two nested loops = Θ(n^2)
            cache[j] = std::max(cache[j], cache[i] + cache[j - i]);
        }
    }

    return cache[n];
}

#pragma region tests

#include <gtest/gtest.h>

static const std::vector<int>& p()
{
    static std::vector<int> _p({ 0, 1, 5, 8, 9, 10, 17, 17, 20, 24,
        30, 32, 35, 39, 43, 43, 45, 49, 50, 54,
        57, 60, 65, 68, 70, 74, 80, 81, 84, 85,
        87, 91, 95, 99, 101, 104, 107, 112, 115, 116,
        119, 121, 125, 129, 131, 134, 135, 140, 143, 145,
        151 });

    return _p;
}

TEST(sample, one)
{
    ASSERT_EQ(cut_log(p(), 1), 1);
}

TEST(sample, five)
{
    ASSERT_EQ(cut_log(p(), 5), 13);
}

TEST(sample, eight)
{
    ASSERT_EQ(cut_log(p(), 8), 22);
}

TEST(sample, ten)
{
    ASSERT_EQ(cut_log(p(), 10), 30);
}

TEST(sample, twenty_two)
{
    ASSERT_EQ(cut_log(p(), 22), 65);
}

int main(int argc, char** argv)
{
    ::testing::InitGoogleTest(&argc, argv);
    return RUN_ALL_TESTS();
}

#pragma endregion /* tests */