Counting Sort
Counting sort avoids comparisons. It counts how many times each key appears, then reconstructs the output in key order.
Beginne mit diesem mentalen Modell
Counting sort avoids comparisons. It counts how many times each key appears, then reconstructs the output in key order.
So funktioniert es – ohne unnötigen 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.
Lies den Algorithmus als Folge von Entscheidungen
Understand what one pass/partition/merge guarantees.
Track which region is already finalized.
Reason about comparisons, swaps/moves and extra memory.
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.
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;
}Lerne die Syntax nicht auswendig. Folge dem Zustand, der sich in jeder Zeile ändert, und verbinde ihn mit der oben beschriebenen Invariante.
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Do not quote this complexity mechanically.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.
Gut geeignet
- Choose based on input size, order, key range, stability and memory limits.
Was typischerweise schiefgeht
- Comparing only average Big-O.
- Forgetting stability, in-place behavior, recursion depth or key-domain assumptions.
Struktur einer professionellen Antwort
Explain why it can beat the comparison-sorting lower bound: it uses assumptions about the key domain rather than only pairwise comparisons.
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.
Was sollte ich zur Komplexität erwähnen?
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.
Was ist der häufigste Fehler?
Comparing only average Big-O.