# Linear Conditionals

#### Resources

Conditional statements are a very powerful tool for programmers to use. So far in this lab, we’ve explored simple conditional statements, including the if statement and if-else statement in Python. However, up to this point we’ve only looked at how we can use a single conditional statement at a time in a program, which can be very limiting. Now we’re going to explore how we can combine conditional statements in a variety of different ways to build even more complex programs. These combined, or nested conditional statements, are commonly used across all programming languages, but learning how to build and debug them takes time and practice. We’ll work through several examples, and then you’ll get a chance to try it yourself.

## Linear Conditional Statements

To explore the various ways we can use conditional statements in code, let’s start by examining the same problem using three different techniques. We’ll use the classic Rock Paper Scissors game. In this game, two players simultaneously make one of three hand gestures, and then determine a winner based on the following diagram:

For example, if the first player displays a balled fist, representing rock and the second player displays a flat hand, representing paper, then the second player wins because “paper covers rock” according to the rules. If the players both display the same symbol, the game is considered a tie.

So, to make this work, we’re going to write a Python program that reads two inputs representing the symbols, and then we’ll use some conditional statements to determine which player wins. A basic skeleton of this program is shown below:

p1 = input("Enter \"rock\", \"paper\", or \"scissors\" for player 1: ")
p2 = input("Enter \"rock\", \"paper\", or \"scissors\" for player 2: ")

# determine the winner

Our goal, therefore, is to replace the comment # determine the winner with a set of conditional statements and print statements to accomplish this goal.

## Linear Conditional Statements

First, let’s try to write this program using what we already know. We’ve already learned how to use conditional statements, and it is completely possible to write this program using just a set of linear conditional statements and nothing else. So, to do this, we need to determine each possible combination of inputs, and then write an if statement for each one. Since there are $3$ possible inputs for each player, we know there are $3 * 3 = 9$ possible combinations:

Player 1 Player 2 Output
rock rock tie
rock paper player 2 wins
rock scissors player 1 wins
paper rock player 1 wins
paper paper tie
paper scissors player 2 wins
scissors rock player 2 wins
scissors paper player 1 wins
scissors scissors tie

We also have to deal with a final option where one player or the other inputs an invalid value. So, in total, we’ll have $10$ conditional statements in our program!

Let’s first try to make a quick flowchart of this program. Since we need $10$ conditional statements, our flowchart will have $10$ of the diamond-shaped decision nodes. Unfortunately, that would make a very large flowchart, so we’ll only include the first three decision nodes in the flowchart shown here:

As we can see, this flowchart is very tall, and just consists of one decision node after another. Thankfully, we should know how to implement this in code based on what we’ve previously learned. Below is a full implementation of this program in Python, using just linear conditional statements:

p1 = input("Enter \"rock\", \"paper\", or \"scissors\" for player 1: ")
p2 = input("Enter \"rock\", \"paper\", or \"scissors\" for player 2: ")

if p1 == "rock" and p2 == "rock":
print("tie")
if p1 == "rock" and p2 == "paper":
print("player 2 wins")
if p1 == "rock" and p2 == "scissors":
print("player 1 wins")
if p1 == "paper" and p2 == "rock":
print("player 1 wins")
if p1 == "paper" and p2 == "paper":
print("tie")
if p1 == "paper" and p2 == "scissors":
print("player 2 wins")
if p1 == "scissors" and p2 == "rock":
print("player 2 wins")
if p1 == "scissors" and p2 == "paper":
print("player 1 wins")
if p1 == "scissors" and p2 == "scissors":
print("tie")
if not (p1 == "rock" or p1 == "paper" or p1 == "scissors") or not (p2 == "rock" or p2 == "paper" or p2 == "scissors"):
print("error")

This program seems a bit complex, but if we step through it one step at a time it should be easy to follow. For example, if the user inputs "scissors" for player 1 and "rock" for player 2, we just have to find the conditional statement that matches that input and print the correct output. Since we were careful about how we wrote the Boolean expressions for these conditional statements, we know that it is only possible for one of them to evaluate to true. So, we’d say that those Boolean expressions are mutually exclusive, since it is impossible for two of them to be true at the same time.

Things get a bit more difficult in the last conditional statement. Here, we want to make sure the user has not input an invalid value for either player. Unfortunately, the only way to do that using linear conditional statements is to explicitly check each possible value and make sure that the user did not input that value. This can seem pretty redundant, and it indeed is! As we’ll see later in this lab, there are better ways we can structure this program to avoid having to explicitly list all possible inputs when checking for an invalid one.

Before moving on, it is always a good idea to run this code yourself, either directly in Python or using Python Tutor, to make sure you understand how it works and what it does.

## Alternative Version

There is an alternative way we can write this program using linear if statements. Instead of having an if statement for each possible combination of inputs, we can instead have a single if statement for each possible output, and construct more complex Boolean expressions that are used in each if statement. Here’s what that would look like in Python:

p1 = input("Enter \"rock\", \"paper\", or \"scissors\" for player 1: ")
p2 = input("Enter \"rock\", \"paper\", or \"scissors\" for player 2: ")

if (p1 == "rock" and p2 == "rock") or (p1 == "paper" and p2 == "paper") or (p1 == "scissors" and p2 == "scissors"):
print("tie")
if (p1 == "rock" and p2 == "paper") or (p1 == "paper" and p2 == "scissors") or (p1 == "scissors" and p2 == "rock"):
print("player 2 wins")
if (p1 == "rock" and p2 == "scissors") or (p1 == "paper" and p2 == "rock") or (p1 == "scissors" and p2 == "paper"):
print("player 1 wins")
if not (p1 == "rock" or p1 == "paper" or p1 == "scissors") or not (p2 == "rock" or p2 == "paper" or p2 == "scissors"):
print("error")

In this example, we now have just four if statements, but each one now requires a Boolean expression that includes multiple parts. So, this program is simultaneously more and less complex than the previous example. It has fewer lines of code, but each line can be much trickier to understand and debug.

Again, feel free to run this code in either Python Tutor or directly in Python to confirm that it works and make sure you understand it before continuing.

In terms of style, both of these options are pretty much equivalent - there’s no reason to choose one over the other. However, we’ll see later in this lab, there are much better ways we can write this program using chaining and nesting with conditional statements.

1. File:Rock-paper-scissors.svg. (2020, November 18). Wikimedia Commons, the free media repository. Retrieved 16:57, February 28, 2022 from https://commons.wikimedia.org/w/index.php?title=File:Rock-paper-scissors.svg&oldid=513212597↩︎