The Runtime Theory
mediumLeetCode#prefix-suffix#no-division

Product of Array Except Self

For every index, return the product of all values except the value at that index, without using division.

The Runtime Theory Team25 min read
Solve it

Solving happens on the judge — come back and mark it done

Sample cases

innums=[1,2,3,4]

out[24,12,8,6]

innums=[-1,1,0,-3,3]

out[0,0,9,0,0]

innums=[2,3]

out[3,2]

For every index, return the product of all values except the value at that index, without using division.

A good solution should

  • State the invariant or decision rule that makes the approach correct.
  • Explain the time and space complexity in terms of the input sizes and required output.
  • Handle empty, minimal, duplicate, and boundary-shaped inputs covered by the contract.

Reasoning prompt

Handle zero and negative values. Aim for linear time and constant auxiliary space beyond the output.

Use the linked judge for the canonical problem. The examples above are compact TRT checks; write additional cases before submitting, especially for the boundary that tends to break your chosen invariant.

More practice in this topic

easy · arraysContains Duplicatemedium · arraysEncode and Decode a List of Stringsmedium · arraysGroup Anagrams

One dispatch a week

The trace behind each problem, the tradeoff that explains it, and one technical dispatch per week — no noise.

One technical dispatch per week. No noise.

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