Pattern1 Practice14 Interview

Choose / Explore / Unchoose

GuideCode Labs

Build candidates recursively, prune invalid states, and undo each choice during backtracking. Learn its decision rule, maintained state, Python cost model, and transfer from a focused drill to a full Interview Problem.

Recognize it when

Consider Choose / Explore / Unchoose when the prompt's constraints and required operations match this shape: Build candidates recursively, prune invalid states, and undo each choice during backtracking.

On this page · Treat the Path as Reversible State

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Treat the Path as Reversible State

The current path is shared mutable state describing decisions from root to the active search node. Sibling branches must begin from the same restored prefix.

Choose One Legal Move

Apply exactly one choice and update all state it owns before recursion. Choice order controls output order but should not change which valid solutions exist.

Trace Choice Lifecycles

Reference

def choice_lifecycle(choices):
    path=[]; events=[]
    for choice in choices:
        path.append(choice); events.append(["choose",path.copy()]); events.append(["undo",path.copy()]); path.pop()
    return events

Practice

Implement choice_lifecycle(choices). Return [choose,path] and [undo,path] for one decision depth.

def choice_lifecycle(choices):
    pass

Public tests

Undo each applied choice

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Explore Then Undo Exactly Once

After the recursive call, reverse every mutation from the choice—path append, used flag, counts, or board cell. Early returns need the same cleanup unless success intentionally terminates the entire search.

Generate Permutations

Reference

def permutations(values):
    result=[]; path=[]; used=[False]*len(values)
    def search():
        if len(path)==len(values): result.append(path.copy()); return
        for index,value in enumerate(values):
            if used[index]: continue
            used[index]=True; path.append(value); search(); path.pop(); used[index]=False
    search(); return result

Practice

Implement permutations(values). Return all permutations in choice order without mutating values.

def permutations(values):
    pass

Public tests

Restore path and availability

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Copy Only Complete Answers

Append a copy when recording a solution; appending the shared path itself makes every result reflect later mutations. Avoid copying at every internal node unless the simpler immutable-state approach is worth its cost.

Explain It in an Interview

Say: “The path is the current partial candidate. I choose, explore, and undo so the next sibling sees an identical prefix.” Then state terminal condition, duplicate policy, branching factor, maximum depth, and output-copy cost.

Python Version Note

Python 3.11+

The examples use the standard Python syntax and containers supported by the browser Judge; the Choose / Explore / Unchoose invariant is independent of a minor Python release.

Verify in Python docs

Complexity & Invariants

Interview bounds depend on the stated representation, input model, and real Python operations.

Operation	Average	Worst	Interview note
Choose / Explore / Unchoose decision loop	`O(c * (p + 1))`	`O(c * (p + 1))`	Each backtracking branch needs a path state that includes one choice but does not leak that choice into sibling branches. Before expanding each choice, path equals the original caller-owned prefix; every emitted candidate contains exactly one additional element.

Space

O(c * (p + 1)) for independent candidates for the focused Complete One Backtracking Frame implementation.

Assumptions

Appending one choice creates exactly one candidate extension, and copying it prevents later mutations from changing prior output. Popping restores the original path before the next choice, so all and only one-step branches are emitted.
The bound includes real Python operations; no repeated slicing, linear list membership, or hidden sorting is treated as free.

Invariants Worth Saying Aloud

State the precise Choose / Explore / Unchoose invariant before coding and preserve it after every update, traversal step, or recursive return.
The mutable path represents exactly the choices on the current recursion stack.
Sibling branches begin from identical parent state.
Each backtracking branch needs a path state that includes one choice but does not leak that choice into sibling branches. Preserve this property after every transition.
Before expanding each choice, path equals the original caller-owned prefix; every emitted candidate contains exactly one additional element. Preserve this property after every transition.

When To Use Or Avoid Choose / Explore / Unchoose

Use It When

Use Choose / Explore / Unchoose when the prompt exposes the ordering, monotonicity, recurrence, or constraint that makes this decision safe.
Use it when the mutable path represents exactly the choices on the current recursion stack.

Choose Another Tool When

Avoid Choose / Explore / Unchoose when its decision rule cannot eliminate work or preserve the required state.
Avoid forcing the label onto a prompt whose simpler direct scan already meets the constraints.

Common Pitfalls

These are the mistakes most likely to survive a happy-path example and fail a boundary case.

Moving state without a proof

Applying the pattern without proving its ordering, monotonicity, or window invariant can silently miss valid candidates.

Prevent it: Write the decision rule beside the loop and verify it against Complete One Backtracking Frame before optimizing.

Avoid

def expand_backtracking_frame(path, choices):
    pass

Use instead

def expand_backtracking_frame(path, choices):
    candidates = []
    for choice in choices:
        path.append(choice)
        candidates.append(path.copy())
        path.pop()
    return candidates

Where you will hit this: Complete One Backtracking Frame(opens in a new tab)

Breaking the maintained state

Never undoes the choice and stores the same mutable path object for every sibling candidate.

Prevent it: Use the public tests and preserve this state: The mutable path represents exactly the choices on the current recursion stack.

Avoid

def expand_backtracking_frame(path, choices):
    candidates = []
    for choice in choices:
        path.append(choice)
        candidates.append(path)
    return candidates

Use instead

def expand_backtracking_frame(path, choices):
    candidates = []
    for choice in choices:
        path.append(choice)
        candidates.append(path.copy())
        path.pop()
    return candidates

Where you will hit this: Complete One Backtracking Frame(opens in a new tab)

Hiding Python work in the hot path

Python slicing, copying, membership in lists, or repeated sorting inside the loop can invalidate the intended complexity.

Prevent it: Count every slice, copy, sort, membership check, and container update before claiming O(c * (p + 1)).

Avoid

def expand_backtracking_frame(path, choices):
    candidates = []
    for choice in choices:
        path.append(choice)
        candidates.append(path)
    return candidates

Use instead

def expand_backtracking_frame(path, choices):
    candidates = []
    for choice in choices:
        path.append(choice)
        candidates.append(path.copy())
        path.pop()
    return candidates

Where you will hit this: Path Sum II(opens in a new tab)

Reviewed References

Official Python documentation supports language behavior. Canonical problem pages provide additional practice context.

Python Compound Statements — Function Definitions(opens in a new tab)
python-docs · checked 2026-07-27
Python More on Lists(opens in a new tab)
python-docs · checked 2026-07-27

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