Introduction to Computer Science I

Turn a problem into a precise algorithm

Before writing syntax, state the inputs, outputs, and rules that connect them. An algorithm is a finite procedure whose steps are unambiguous at the chosen level of detail. Decomposition separates a large task into smaller contracts: read records, validate them, calculate a result, then present it. Trace a tiny example by hand before coding. If you cannot predict the required output for an empty input or a boundary value, the problem specification needs more work. Correctness means satisfying the contract for every allowed input, rather than merely finishing without an exception.

References: COMP 1405/1005 A/B/C — Fall 2026 course outline · Python Software Foundation — The Python Tutorial

Values, types, assignment, and state

A variable name refers to a value; assignment updates that binding. In Python, an integer supports exact whole-number arithmetic, while a float approximates real values with finite precision. Strings represent text and require explicit conversion when numerical input is expected. Distinguish equality from identity and from assignment. Evaluate the right side before changing the left side: after x = 4 and x = x + 3, x is 7. A state table listing each variable after every statement is a reliable way to diagnose an incorrect calculation.

distance_m = 1250
time_s = 250
speed_m_per_s = distance_m / time_s
print(speed_m_per_s)  # 5.0

References: COMP 1405/1005 A/B/C — Fall 2026 course outline · Python Software Foundation — The Python Tutorial

Branching, loops, and invariants

A conditional chooses a path using a Boolean expression. Test compound expressions with a truth table and remember that the order of overlapping branches matters. A loop repeats an operation while maintaining a useful statement called an invariant. When summing a list, the accumulator equals the sum of all elements already visited. Establish this before the loop, preserve it in each iteration, and use termination to obtain the final result. Watch for off-by-one errors: range(n) produces n indices starting at zero, so its final index is n minus one.

References: COMP 1405/1005 A/B/C — Fall 2026 course outline · Python Software Foundation — The Python Tutorial

Lists, strings, dictionaries, and aliasing

Choose a collection according to the operations the program needs. A list preserves position; a dictionary associates keys with values; a string is an immutable sequence of characters. Indexing selects one element, whereas slicing creates a subsequence. Mutating an aliased list is visible through both names: b = a does not copy a. With nested lists, copying only the outer list still shares inner rows. Draw the references when reasoning about such code. Empty collections, absent keys, duplicate values, and uneven row lengths deserve explicit handling.

References: COMP 1405/1005 A/B/C — Fall 2026 course outline · Python Software Foundation — The Python Tutorial

Functions, scope, and recursive decomposition

A function gives a name to a calculation and defines an interface through parameters and a return value. Prefer returning a result to printing it when callers must reuse the value. Local variables belong to a call; separate calls have separate local state. A recursive function solves a smaller instance using the same contract. It needs a base case and a measure that decreases toward that case. For a list total, remove one element per recursive call. A missing decrease can cause unbounded recursion even when the base-case code exists.

References: COMP 1405/1005 A/B/C — Fall 2026 course outline · Python Software Foundation — The Python Tutorial

Testing, searching, and a worked trace

Consider finding the first reading above 20 in [18, 20, 23, 19]. A linear scan rejects indices 0 and 1, then returns 2. The invariant is that no earlier index qualifies. If nothing qualifies, return a documented sentinel such as None. Linear search takes up to n comparisons; binary search reduces the remaining interval repeatedly but requires sorted input. Sorting first costs time and can change positions. Design tests around the specification: empty input, a match first, a match last, no match, and repeated qualifying values.

def first_above(values, limit):
    for index, value in enumerate(values):
        if value > limit:
            return index
    return None

References: COMP 1405/1005 A/B/C — Fall 2026 course outline · Python Software Foundation — The Python Tutorial

Practice & worked answers

Original exercises for this guide.

Public notes & references

Course sources establish the scope above. Reference materials support the explanations; linked lecture notes and books remain with their authors.

• COMP 1405/1005 A/B/C — Fall 2026 course outline ↗Course scope · Fall 2026
• Python Software Foundation — The Python Tutorial ↗Primary reference · Public reference; checked 2026-11-05