# lab12.py
# YOUR NAME(S) AND NETID(S) HERE
# DATE COMPLETED HERE
"""Loop functions (with invariants) for lab 11"""


def isprime(p):
    """Returns: True if p a prime, False otherwise
    
    i.e. p is at least 2 and is divisible by only 1 and itself
    
    Precondition: p is an int"""
    assert type(p) == int, `p`+' is not an int'
    
    if p < 2:
        return False    # CHANGE THIS EXPRESSION, IF NECESSARY
    
    # Return False if some integer in 2..p-1 divides p
    k = 0               # CHANGE THIS EXPRESSION, IF NECESSARY
    
    # inv: p is not divisible by integers in 2..k-1
    while k < p:
        if False:       # CHANGE THIS EXPRESSION
            return False
        
        # Increment to next position
        k= k+1
    
    # no integer in 2..p-1 divides p
    return False        # CHANGE THIS EXPRESSION, IF NECESSARY


def count_letter(c, s):
    """Returns: number of times character c appears in string s
    
    Precondition: s, c are strings. len(c) == 1"""
    assert type(s) == str, `s`+' is not a string'
    assert type(c) == str and len(c) == 1, `c`+' is not a character'
    
    # INITIALIZE LOOP VARIABLES HERE
    
    # inv: x is number of times c appears in s[0..k-1]
    while True:             # CHANGE THIS EXPRESSION
        if False:           # CHANGE THIS EXPRESSION
            x = x+1
        
        # Increment to next position
        k = k + 1
    
    return 0 # CHANGE THIS, IF NECESSARY



# OPTIONAL FUNCTIONS
def primes(n,m):
    """Returns: a list that contains each prime between n and m.
    
    Example: primes(3,12) returns [3,5,7,11]
             primes(-1,13) returns [2,3,5,7,11,13]

    Precondition: n, m are ints with m >= n."""
    assert type(n) == int, `n`+' is not an int'
    assert type(m) == int, `m`+' is not an int'
    assert n <= m, 'range ['+`n`+','+`m`+'] is invalid'
    
    x = NONE              # CHANGE THIS EXPRESSION
    c = 0                 # CHANGE THIS EXPRESSION

    # inv: list x contains each prime in n..c-1
    while c <= 0:         # CHANGE THIS EXPRESSION
        if False:         # CHANGE THIS EXPRESSION
            x.append(0)   # CHANGE THIS COMMAND

        # Increment to next position
        c = c + 1

    # post: list x contains contains each prime in n..m
    return x


def count_all_letters(s1, s2):
    """Returns: number of times the characters in s1 appear in s2

    Each letter in s1 is treated separately.  Duplicates in s1
    are ignored (but not ignored in s2).

    Example: count_all_letters('ac', 'aaab') is 3
    Example: count_all_letters('aeiou', word) gives the number of
    vowels in string word (for some definitions of vowels)

    Precondition: s1, s2 are strings"""
    assert type(s1) == str, `s1`+' is not a string'
    assert type(s2) == str, `s2`+' is not a string'
    # STUB: IMPLEMENT ME
    # Hint1: Don't nest one while loop in another; 
    # use count_letter as a helper function
    # Hint2: You need to find the unique elements 
    # of s1 at the same time that you are counting
    return 0 # CHANGE THIS, IF NECESSARY