import sys
from typing import NamedTuple, Callable

# Folding function.
def fold[T, U](f: Callable[[U, T], U], z: U, l: list[T]) -> U:
    # This is a simple for loop that accumulates a value and then returns it.
    for x in l:
        z = f(z, x)
    return z

# This is the state of the memory.
class State(NamedTuple):
    faults: int
    hits: int
    order: dict[int, list[int]]
    page_table: set[int]
    physical_capacity: int

    # Increase hits by 1.
    def hit(s):
        return State(s.faults, s.hits + 1, s.order, s.page_table, s.physical_capacity)

    # Increase faults by 1.
    def fault(s):
        return State(s.faults + 1, s.hits, s.order, s.page_table, s.physical_capacity)

    # Updates the indices in the state.
    def update(s):
        # This is the recursive function that decreases the indices.
        def rec(order: dict[int, list[int]], page: int) -> dict[int, list[int]]:
            # If the page appears again:
            if order[page] != []:
                # Decrease all of the indices
                tmp = [x - 1 for x in order[page]]
                # If the first index is 0, skip it
                if tmp[0] == 0:
                    return order | {page: tmp[1:]}
                # Else, just use the decreased indices
                else:
                    return order | {page: tmp}
            # In the case where the page doesn't appear again, just return the
            # order.
            else:
                return order
        return State(s.faults, s.hits, fold(rec, s.order.copy(), s.order), s.page_table, s.physical_capacity)

    # Frees up a spot in the page table depending on the order.
    def evict(s):
        # These are the candidates to get removed.
        opts = [(page, s.order[page]) for page in s.page_table]

        # If some of the candidates don't appear again, simply remove them from
        # the page table.
        empty = [a for a in opts if a[1] == []]
        if empty != []:
            page = empty[0][0]
            return State(s.faults, s.hits, s.order, s.page_table - {page}, s.physical_capacity)
        else:
            # Otherwise, pick the candidate that appears last.
            page, lst = sorted([a for a in opts if a[1] != []], key = lambda x: x[1], reverse = True)[0]
            return State(s.faults, s.hits, s.order | {page: lst[1:]}, s.page_table - {page}, s.physical_capacity)

    # Inserts a page into the page table.
    def insert(s, page: int):
        return State(s.faults, s.hits, s.order, s.page_table | {page}, s.physical_capacity)

# This is the algorithm that is used to calculate the faults and hits.
def optimal(state: State, access: tuple[str,int]) -> State:
    # The read 
    page = access[1]
    # If the page is in the page table, then this is a page hit.
    if page in state.page_table:
        return state.update().hit()
    else:
        # Otherwise this is a page fault, and depending on whether the page
        # table is full or not, some space has to be made.
        if len(state.page_table) == state.physical_capacity:
            return state.evict().insert(page).update().fault()
        else:
            return state.insert(page).update().fault()

# This function calculates when they next page will be loaded into physical
# memory. The existence and reliance on this function in order to execute the
# rest of the algorithm is what make this algorithm impossible to implement.
def preprocess(accesses: list[tuple[str,int]]) -> dict[int,list[int]]:
    # The accumulating function: if the page is not in the pages that have been
    # seen, initialize it with 0. Otherwise, add the newest index to it.
    def f(seen, x):
        index, (_, page) = x
        if page not in seen:
            return seen | {page: []}
        else:
            return seen | {page: seen[page] + [index]}

    # Fold over the accesses with the accumulating function.
    return fold(f, dict(), list(enumerate(accesses)))


def main():
    # Please provide the correct number of arguments.
    if len(sys.argv) != 3:
        print("USAGE:", sys.argv[0], "number_of_pages", "file_path")
        print("\twhere:\n\t\tnumber_of_pages : int\n\t\tfile_path : string")

    # The file path is the second argument.
    file_path = sys.argv[2]

    # This opens the file and parses the accesses.
    accesses = []
    with open(file_path) as f:
        accesses = [(x.split(":")[0], int(x.split(":")[1])) for x in f.read().split()]

    # The limit is the first argument.
    limit = int(sys.argv[1])
    # The result of this computation will be a fold over the accesses, with the
    # the following state and using the optimal algorithm.
    res = fold(optimal,
        State(faults = 0, hits = 0, order = preprocess(accesses), page_table = set(), physical_capacity = limit),
        accesses)

    # Print the results!
    print("Faults:", res.faults, "\nHits:", res.hits)

main()