Reading and tracing code

Understand the idea

Tracing means recording state after each relevant statement. Keep the input, current position, variables, and output separate. A trace is a small execution proof, not a guess about what the code seems to do.

Work through an example

On [4,1,7,2], write i/value/best: initial/-/4, 1/1/4, 2/7/7, 3/2/7. Read the assignment only when the branch is true.

Time and space complexity

A manual trace takes O(n) rows; a program need not store that trace to compute the answer.

Why it works

Each row follows from the previous state plus exactly one executed operation.

Common mistakes

• Do not update both branches in your notes.
• Reassigning a variable and mutating a list are different state changes.

Chapter lab · Python implementation

Our running task is to find the largest value in a sequence. A program turns a precise input/output contract into small state changes. Read the example from the top, predict each update, and run its assertions. Python examples use ordinary built-in types; statements inside an indented block belong to that block.

This shared lab connects the chapter's topics. Follow the current lesson's worked example first, then trace the complete implementation. Additional algorithms described in topic exercises are variations you can implement independently.

def largest(values):
    if not values:
        return None
    best = values[0]
    for value in values[1:]:
        if value > best:
            best = value
    return best

def largest_without_slice(values):
    if not values:
        return None
    best = values[0]
    for i in range(1, len(values)):
        best = max(best, values[i])
    return best

Run and test the lab

Copy the implementation and these assertions into a Python 3 file and run it. An assertion failure means the actual result differs from the expectation. Add the current topic's exercise and boundary tests to deepen your understanding.

assert largest([]) is None
assert largest([-8, -3, -5]) == -3
assert largest_without_slice([4, 1, 7, 2]) == 7
assert largest_without_slice([0]) == 0