Data Structures & Sets

Complete the set-based collision system. Fill each blank with the correct set operation or data structure expression.

# Build a set for O(1) membership testing
snake_set = ▢1(snake)

# In the update step:
snake.insert(0, new_head)
snake_set.▢2(new_head)

if not ate_food:
    tail = snake.pop()
    snake_set.▢3(tail)   # remove tail from set

# Self-collision check (O(1)):
body_set = set(snake[▢4:])     # exclude head (index 0)
alive = new_head ▢5 body_set

# Score with high-score tracking:
score = ▢6
if ate_food:
    score["player"] ▢7= 1
    if score["player"] > score[▢8]:
        score["high"] = score["player"]

The set-based code below has 3 bugs. Type the corrected line for each.

snake_set = set(snake)
snake.insert(0, new_head)
snake_set.add(new_head)

if not ate_food:
    tail = snake.pop()
    snake_set.remove(tail)       # Bug 1 – can raise KeyError

body_set = set(snake)            # Bug 2 – includes head
alive = new_head not in body_set

score["player"] + 1              # Bug 3 – doesn't save the result

Write a function `check_alive(snake, new_head, wall_death)` that returns `True` if the snake is alive after the move. It should check self-collision using a set AND optionally wall collision.

def check_alive(snake, new_head, wall_death=False):
    hx, hy = new_head
    # Check wall collision if wall_death is True
    # YOUR CODE here

    # Check self-collision using a set of body positions (exclude head)
    # YOUR CODE here

    return True  # replace with correct logic

**Performance experiment:** Write a script that creates a list of 1 000 (x, y) tuples, then times 100 000 membership checks using both a list and a set. Print the ratio. Paste your timing code and results.

Answer each prompt thoughtfully. There are no right or wrong answers — this is your own reflection.