# Name:
# Kerberos:
# homework_2a.py
import math
import random

##### Template for Homework 2a, exercises 3.1-3.2  ######


# **********  Exercise 3.1 ********** 

# Define your rock paper scissors function here
def rps(player1, player2):
    '''
    Takes in two strings (rock, paper, or scissors) as input, 
    and gives the result of the game.
    '''
    # Validate the input (must be one of 'rock')
    if (player1 != 'rock' and player1 != 'paper' and player1!= 'scissors') or \
    (player2 != 'rock' and player2 != 'paper' and player2!= 'scissors'):
        return 'Invalid input.'
    if player1 == player2:
        return 'Tie!'
    elif player1 == 'rock' and player2 == 'scissors' or\
    player1 == 'scissors' and player2 == 'paper' or\
    player1 == 'paper' and player2 == 'rock':
        return 'Player 1 wins!'
    else:
        return 'Player 2 wins!'

    

# Test Cases for Exercise 3.1
assert rps('rock','scissors') == 'Player 1 wins!'
assert rps('rock','paper') == 'Player 2 wins!'
assert rps('rock','rock') == 'Tie!'
assert rps('nothing','err') == 'Invalid input.'

# *********** Exercise 3.2 ***********
## 1 - multadd function
def multadd(a, b, c):
    '''
    Takes in three numbers, and returns a * b + c.
    '''
    return a * b + c
    
## 2 - Equations

angle_test = multadd(math.cos(math.pi/4), 1.0/2, math.sin(math.pi/4))
print "sin(pi/4) + cos(pi/4)/2 is:"
print angle_test

ceiling_test = multadd(2, math.log(12, 7), math.ceil(276.0/19))
print "ceiling(276/19) + 2 log_7(12) is:"
print ceiling_test

## 3 - yikes function
## Using math.pow
def yikes(x):
    '''
    Takes in a number, and returns x*e^(-x) + (1 - e^(-x))^(1/2).
    '''
    return multadd(x, math.pow(math.e, -x), math.sqrt(1 - math.pow(math.e, -x)))

# Using **.
def yikes2(x):
    '''
    Takes in a number, and returns x*e^(-x) + (1 - e^(-x))^(1/2).
    '''
    return multadd(x, math.e**(-x), math.sqrt(1 - math.e**(-x)))

# Test Cases
x = 5
print "yikes(5) =", yikes(x)
print "yikes2(5)=", yikes2(x)