# file: lists.py
#
# author: Bob Muller
# date: November 6, 2007
#
# This module has some simple functions operating on lists.
# These functions were covered in class on Nov. 6, 2007.

import random

def length(lst):
    if lst == []:
        return 0
    else:
        return 1 + length(lst[1:])

# A series of three -many- functions which return lists of various
# kinds.
#
def manyOnes(n):
    if n == 0:
        return []
    else:
        return [1] + manyOnes(n - 1)

def manyOf(m,n):
    if m == 0:
        return []
    else:
        return [n] + manyOf(m - 1,n)

def manyRandoms(m,n):
    if m == 0:
        return []
    else:
        return [int(n * random.random())] + manyRandoms(m - 1,n)

# printAll accepts a list and prints all the elements, one per line.
#
def printAll(lst):
    if lst == []:
        return
    else:
        print lst[0]
        printAll(lst[1:])

# member accepts an item and a list and returns True if the item
# is in the list. Otherwise it returns False.
#
def member(item, lst):
    if lst == []:
        return False
    else:
        return (item == lst[0]) | member(item, lst[1:])

# rember accepts an item and a list and returns the list with the
# first occurrence of the item removed.
#
def rember(item, lst):
    if lst == []:
        return []
    else:
        if item == lst[0]:
            return lst[1:]
        else:
            return [lst[0]] + rember(item, lst[1:])

# countAll accepts an integer m and a list of integers lst. It returns
# the number of times that m occurs in lst.
#
def countAll(m,lst):
    if lst == []:
        return 0
    else:
        if m == lst[0]:
            return 1 + countAll(m,lst[1:])
        else:
            return countAll(m,lst[1:])

# frequency accepts two integers m and n. It first generates a list of m
# random numbers. Each random number is between 0 and n - 1. frequency
# returns a list of frequency counts of the numbers.
#
# NB: This function is a little different than the one handed out and
# covered in class on Tuesday Nov. 6.
#
def frequency(m,n):

    # generate a list of n zeros. This list will be used as counters.
    #
    counts = manyOf(n,0)
    
    i = 0

    while i < m:
        j = int(random.random() * n)
        counts[j] = counts[j] + 1
        i = i + 1

    return counts