ALGORITHM READING NOTE

Counting Sort

Counting sort avoids comparisons. It counts how many times each key appears, then reconstructs the output in key order.

TYPEAlgorithmCATEGORYSortingDEPTHBeginnerTYPICAL COMPLEXITYO(n + k)

SHORT INTERVIEW ANSWER

Start with this mental model

Counting sort avoids comparisons. It counts how many times each key appears, then reconstructs the output in key order.

SIMPLE EXPLANATION

How it works, without unnecessary jargon

It is powerful when keys are integers in a reasonably small range.

Its complexity depends on n plus the key range k, so a huge sparse range can make it wasteful.

EXECUTION

Read the algorithm as a sequence of decisions

Understand what one pass/partition/merge guarantees.

Track which region is already finalized.

Reason about comparisons, swaps/moves and extra memory.

A small example to keep in mind

Read a tiny input by hand and write down the state after every important operation. For Counting Sort, the goal is to make the invariant visible rather than to memorize code.

READABLE JAVASCRIPT IMPLEMENTATIONJavaScript

function countingSort(a, max = Math.max(...a)) {
  const count = Array(max + 1).fill(0);
  for (const x of a) count[x]++;
  const out = [];
  for (let value = 0; value < count.length; value++) {
    for (let c = 0; c < count[value]; c++) out.push(value);
  }
  return out;
}

How to read this code

Do not memorize the syntax. Follow the state that changes on each line and connect it to the invariant described above.

COMPLEXITY

O(n + k)

Do not quote this complexity mechanically. Ask which operation or input dimension it describes, then derive the cost from the loops, recursion depth, data-structure operations and any preprocessing assumptions.

WHEN TO USE IT

Good fit

Choose based on input size, order, key range, stability and memory limits.

COMMON MISTAKES

What usually goes wrong

Comparing only average Big-O.
Forgetting stability, in-place behavior, recursion depth or key-domain assumptions.

HOW TO EXPLAIN IT IN AN INTERVIEW

A professional answer shape

Explain why it can beat the comparison-sorting lower bound: it uses assumptions about the key domain rather than only pairwise comparisons.

Problem→Core idea→Invariant / state→Big-O→Trade-off

QUICK INTERVIEW CHECK

What problem does Counting Sort solve?

Counting sort avoids comparisons. It counts how many times each key appears, then reconstructs the output in key order.

What should I mention about complexity?

Its typical cost here is O(n + k), but a complete answer should connect that cost to the representation, input constraints and the dominant operations.

What is the most common mistake?

Comparing only average Big-O.

Continue readingStable sortingIn-place sortingDivide and conquer

function countingSort(a, max = Math.max(...a)) { const count = Array(max + 1).fill(0); for (const x of a) count[x]++; const out = []; for (let value = 0; value < count.length; value++) { for (let c = 0; c < count[value]; c++) out.push(value); } return out; }