import time


def simple_cut_rod(p, n):
    if n == 0:
        return 0
    q = float('-inf')
    for i in range(1, n + 1):
        q = max(q, p[i] + simple_cut_rod(p, n - i))
    return q


def _memoized_cut_rod_aux(p, n, r):
    if r[n] >= 0:
        return r[n]
    if n == 0:
        q = 0
    else:
        q = float('-inf')
        for i in range(1, n + 1):
            q = max(q, p[i] + _memoized_cut_rod_aux(p, n - i, r))
    r[n] = q
    return q


def memoized_cut_rod(p, n):
    r = [float('-inf')] * (n + 1)
    return _memoized_cut_rod_aux(p, n, r)


def bottom_up_cut_rod(p, n):
    r = [0] * (n + 1)
    for j in range(1, n + 1):
        q = float('-inf')
        for i in range(1, j + 1):
            q = max(q, p[i] + r[j - i])
        r[j] = q
    return r[n]


def main():
    n = int(input("Enter number of Inches: "))

    with open("Cut Rod Problem/Cut Rod Problem/Data.txt", encoding="utf-8-sig") as f:
        price_data = f.read().split()

    # 1-indexed: prices[0] unused, prices[i] = price for length i
    prices = [0] + [int(x) for x in price_data]

    start = time.perf_counter()
    best_price = memoized_cut_rod(prices, n)
    # best_price = bottom_up_cut_rod(prices, n)
    # best_price = simple_cut_rod(prices, n)
    elapsed = time.perf_counter() - start

    print(f"Best Revenue is upto : {best_price}")
    print(f"Time Elapsed : {elapsed:.9f}s")


if __name__ == "__main__":
    main()