Counting Sort
Counting sort avoids comparisons. It counts how many times each key appears, then reconstructs the output in key order.
ابدأ بهذا النموذج الذهني
Counting sort avoids comparisons. It counts how many times each key appears, then reconstructs the output in key order.
كيف يعمل، بلا مصطلحات زائدة
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.
اقرأ الخوارزمية كسلسلة من القرارات
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;
}لا تحفظ الصياغة. تتبع الحالة التي تتغير في كل سطر واربطها بالثابت الموضح أعلاه.
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Do not quote this complexity mechanically.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.
مناسب لـ
- Choose based on input size, order, key range, stability and memory limits.
ما الذي يسوء عادةً
- Comparing only average Big-O.
- Forgetting stability, in-place behavior, recursion depth or key-domain assumptions.
صيغة إجابة احترافية
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.
ماذا يجب أن أذكر عن التعقيد؟
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.
ما الخطأ الأكثر شيوعاً؟
Comparing only average Big-O.