05 Loops and Repetition

The Four Parts of a Loop

A loop repeats a block of instructions so that a program can process many values or continue an action until a condition changes. A well-designed loop normally has four parts:

1. Initialization establishes the starting value or data source.

2. Condition or stopping rule determines whether another repetition should occur.

3. Loop body contains the instructions performed during each iteration.

4. Progress or update changes the program state so that the loop can eventually stop.

A useful design question is: what information must the program remember from one iteration to the next? That information might be a count, a running total, a best value, a current position, or the state of a search.

Takeaway

Before writing a loop, identify its starting state, repeated work, stopping rule, and path toward progress.

Choosing Between while and for Loops

A while loop checks its condition before each iteration and runs only while that condition is true. It is appropriate when the number of repetitions is not known in advance, such as repeatedly requesting input until it is valid or until a correct password is entered.

The condition should describe when the loop may continue, and the body should change something related to that condition. For example, a counter that starts at $1$ and increases by $1$ after each iteration eventually makes the condition $\text{count} \leq 5$ false.

A for loop is designed to process each item in an iterable, such as a list of names, or each value generated by range(). Use it when the program should perform an action once for every item or repeat a known number of times.

The ending value of range() is not included. Thus, range(2, 11, 2) generates $2$, $4$, $6$, $8$, and $10$. When both an index and an item are needed, enumerate() provides them together and avoids manually maintaining an index.

Choose a for loop when processing a collection, iterating through a range, or repeating a known number of times. Choose a while loop when the stopping point depends on input or changing state.

Takeaway

Use the loop form that matches the stopping information available before the loop begins.

Counters, Accumulators, and Search

A counter records how many times an event occurs. Initialize it before the loop, and increase it only when the event being counted happens. For example, when examining a list of numbers, an even-number counter should increase only when the remainder condition identifies an even value.

Counters can track categories at the same time. Separate variables can count positive values, negative values, and zero values, with exactly one category updated for each item.

An accumulator combines values into one result. A sum usually starts at $0$, while a product starts at $1$, because these are the identity values for addition and multiplication. An accumulator can also build a string or collect a result in a list.

Search and aggregation often use the same general pattern:

1. Initialize the state, such as a count, total, or candidate answer.

2. Examine one item during each iteration.

3. Update the state when the item provides relevant information.

4. Use the final state as the result.

To find a largest value, begin with an initial candidate, compare each remaining value with it, and replace the candidate whenever a larger value is found.

Takeaway

Update a counter or accumulator at the exact point where the current item contributes to the result.

Controlling Loop Execution

break immediately ends the innermost loop. It is useful when a search has found its target or when continuing would perform unnecessary work.

continue skips the remainder of the current iteration and starts the next one. It can simplify filtering: a loop may skip unwanted values and process only the values that remain. In a while loop, however, continue must not bypass the update that moves the loop toward termination.

Python also supports a loop else clause. The else block runs when the loop finishes normally, but not when the loop ends with break. This makes it useful for searches: break can report success, while else can report that every item was examined without success.

A sentinel value is a special value that means “stop.” An input loop can repeatedly read a response and use break when the response equals the sentinel. This is a deliberate use of while True, provided every possible path either makes progress or reaches a clear stopping action.

Takeaway

Use break for successful early termination, continue for deliberate filtering, and a sentinel value when input itself signals completion.

Nested Loops and Reliable Termination

A nested loop places one loop inside another. The inner loop completes all of its iterations for each iteration of the outer loop. This structure is useful for rows and columns, multiplication tables, grids, and comparisons between pairs of values.

If the outer loop runs $n$ times and the inner loop runs $m$ times for every outer iteration, the loop body executes approximately $n \times m$ times. Nested loops can therefore require substantially more work than a single loop as the input grows.

A break inside a nested loop exits only the innermost loop. The outer loop continues with its next iteration unless it has its own stopping logic.

An infinite loop never reaches its stopping condition. In a while loop, check that the controlling value is initialized, that the body updates it, and that the update moves toward making the condition false. Also consider whether every possible input can eventually produce termination.

When debugging, temporarily display control variables and count iterations. If the loop does not finish, check whether the condition is always true, an update is missing, an update moves in the wrong direction, or continue skips a required update.

Takeaway

Analyze nested-loop cost and verify a reliable path toward termination before running a loop on large or unpredictable input.