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Lesson 5 of 8

Match stopping and pruning to the question

Existence, one witness, counts, and enumeration need different return rules.

Understand the idea

An existence search may return after finding one answer. A counting search must add the results of disjoint branches; an enumeration must visit and output every answer. Reject a partial choice only after proving that none of its completions can succeed.

Trace a small example

For [0, 0] and target 0, all four subsets work. Returning 1 as soon as the current sum is zero would miss three. For signed [5, −4] and target 1, pruning when the current sum exceeds 1 would wrongly discard the successful pair.

Conditions and cost

The common sum > target prune requires that future choices cannot decrease the sum. Even with valid pruning, worst-case work can remain exponential. When returning a witness early, restore shared state or copy the answer before undoing it.

Pause & predict

Is sum > target a valid prune when remaining values can be negative?

Choose an answer
Try it yourself

Turn the idea into code

Count subsets of [0, 1, 1] whose sum is 1.

Give me a hint

Choose one of the two 1 positions, then choose whether to include zero.

Show the explained solution

There are 2 × 2 = 4 subsets. Count at the leaf after all positions are decided, or use another equally justified counting rule.

Your notes

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Mark complete when you can explain it yourself.

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