{ "id": "sorting/radix-sort", "version": 1, "deterministic": true, "url": "/dsa/sorting/radix-sort", "topic": { "slug": "sorting", "title": "Sorting" }, "title": "Radix Sort", "tagline": "Sort by the last digit first. It sounds backwards, and it's the only way it works.", "vizKind": "bars", "complexity": { "time": { "best": "O(d × n)", "average": "O(d × n)", "worst": "O(d × n)" }, "space": "O(n + b)", "growth": "linear", "note": "d passes over n items, where d is the number of digits and b the base (10 here). On fixed-width keys d is a small constant, so this is effectively linear — genuinely faster than n log n. On values with wildly different lengths, d starts to hurt." }, "code": { "javascript": "// Sort by the last digit. Then the next. Then the next.\nfunction radixSort(a) {\n const maxValue = Math.max(...a);\n\n for (let exp = 1; Math.floor(maxValue / exp) > 0; exp *= 10) {\n a = countingSortByDigit(a, exp);\n }\n return a;\n}\n\nfunction countingSortByDigit(a, exp) {\n const buckets = Array.from({ length: 10 }, () => []);\n\n // Stability is everything: earlier items stay earlier.\n for (const v of a) {\n const digit = Math.floor(v / exp) % 10;\n buckets[digit].push(v);\n }\n\n return buckets.flat();\n}", "python": "# Sort by the last digit. Then the next. Then the next.\ndef radix_sort(a):\n max_value = max(a)\n exp = 1\n\n while max_value // exp > 0:\n a = counting_sort_by_digit(a, exp)\n exp *= 10\n\n return a\n\n\ndef counting_sort_by_digit(a, exp):\n buckets = [[] for _ in range(10)]\n\n # Stability is everything: earlier items stay earlier.\n for v in a:\n digit = (v // exp) % 10\n buckets[digit].append(v)\n\n return [v for bucket in buckets for v in bucket]\n", "java": "// Sort by the last digit. Then the next. Then the next.\nint[] radixSort(int[] a) {\n int maxValue = Arrays.stream(a).max().getAsInt();\n\n for (int exp = 1; maxValue / exp > 0; exp *= 10) {\n a = countingSortByDigit(a, exp);\n }\n return a;\n}\n\nint[] countingSortByDigit(int[] a, int exp) {\n List> buckets = new ArrayList<>();\n for (int d = 0; d < 10; d++) buckets.add(new ArrayList<>());\n\n // Stability is everything: earlier items stay earlier.\n for (int v : a) {\n int digit = (v / exp) % 10;\n buckets.get(digit).add(v);\n }\n\n return flatten(buckets);\n}", "cpp": "// Sort by the last digit. Then the next. Then the next.\nvector radixSort(vector a) {\n int maxValue = *max_element(a.begin(), a.end());\n\n for (int exp = 1; maxValue / exp > 0; exp *= 10) {\n a = countingSortByDigit(a, exp);\n }\n return a;\n}\n\nvector countingSortByDigit(vector& a, int exp) {\n vector> buckets(10);\n\n // Stability is everything: earlier items stay earlier.\n for (int v : a) {\n int digit = (v / exp) % 10;\n buckets[digit].push_back(v);\n }\n\n vector out;\n for (auto& b : buckets) for (int v : b) out.push_back(v);\n return out;\n}" }, "defaultInput": [ 170, 45, 75, 90, 24, 2, 66 ], "defaultTarget": null, "inputHint": "Units digit first, then tens, then hundreds. Each pass must be stable.", "pitfalls": [ { "wrong": "Sorting from the most significant digit first.", "right": "Each pass would destroy the last one's work. Least-significant-first, combined with stability, is what makes the passes accumulate instead of fight." }, { "wrong": "Using an unstable sort for each digit pass.", "right": "Stability is not a nice-to-have here — it's the load-bearing wall. Break it and the algorithm is simply wrong." }, { "wrong": "Forgetting negative numbers.", "right": "Digits don't have signs. Split into negatives and positives, sort separately, and reverse the negatives — or the minus signs will be silently ignored." } ], "quiz": [ { "q": "Why does radix sort start with the LAST digit?", "options": [ "It's arbitrary — either end works", "Because each stable pass preserves the previous pass's work, so the ordering accumulates", "Because the last digit is most important", "To save memory" ], "answer": 1, "why": "Least-significant-first plus stability means numbers that tie on the current digit keep the order the previous pass gave them. Every pass builds on the last instead of destroying it." }, { "q": "What breaks radix sort completely?", "options": [ "Duplicate values", "Using an unstable sort for each digit pass", "A large number of items", "Already-sorted input" ], "answer": 1, "why": "Stability is load-bearing. If a pass reorders numbers that tie on the current digit, it wipes out everything the earlier passes established, and the result is just wrong." }, { "q": "What's radix sort's complexity, and when does it beat n log n?", "options": [ "O(n²), never", "O(d × n) — it beats n log n when d (the number of digits) is a small constant", "O(n log n), the same as merge sort", "O(log n), always" ], "answer": 1, "why": "d passes over n items. On fixed-width keys like IDs or dates, d is a small constant, making it effectively linear and genuinely faster than any comparison sort." } ], "problems": [ { "name": "Sort an Array", "difficulty": "Medium", "url": "https://leetcode.com/problems/sort-an-array/" }, { "name": "Maximum Gap", "difficulty": "Medium", "url": "https://leetcode.com/problems/maximum-gap/" }, { "name": "Sort Colors", "difficulty": "Medium", "url": "https://leetcode.com/problems/sort-colors/" } ], "trace": { "note": "Each frame is one immutable step: data snapshot, pointers, per-index roles, executing code line, and a one-sentence explanation.", "length": 29, "frames": [ { "data": [ { "id": "c0-170", "value": 170 }, { "id": "c1-45", "value": 45 }, { "id": "c2-75", "value": 75 }, { "id": "c3-90", "value": 90 }, { "id": "c4-24", "value": 24 }, { "id": "c5-2", "value": 2 }, { "id": "c6-66", "value": 66 } ], "pointers": [], "highlights": [], "codeLine": 2, "variables": { "n": 7, "maxValue": 170 }, "explanation": "Radix sort never compares whole numbers either. It sorts by one digit at a time — starting with the LAST digit, which sounds backwards and is exactly the trick.", "stats": { "comparisons": 0, "swaps": 0 }, "accent": "active" }, { "data": [ { "id": "c0-170", "value": 170 }, { "id": "c1-45", "value": 45 }, { "id": "c2-75", "value": 75 }, { "id": "c3-90", "value": 90 }, { "id": "c4-24", "value": 24 }, { "id": "c5-2", "value": 2 }, { "id": "c6-66", "value": 66 } ], "pointers": [], "highlights": [], "codeLine": 5, "variables": { "pass": "units", "exp": 1 }, "explanation": "Pass over the units digit. Drop each number into the bucket for its units digit, keeping ties in their current order.", "stats": { "comparisons": 0, "swaps": 0 }, "accent": "pivot" }, { "data": [ { "id": "c0-170", "value": 170 }, { "id": "c1-45", "value": 45 }, { "id": "c2-75", "value": 75 }, { "id": "c3-90", "value": 90 }, { "id": "c4-24", "value": 24 }, { "id": "c5-2", "value": 2 }, { "id": "c6-66", "value": 66 } ], "pointers": [ { "name": "i", "index": 0 } ], "highlights": [ { "index": 0, "role": "compare" } ], "codeLine": 18, "variables": { "value": 170, "digit": 0, "bucket": 0 }, "explanation": "170 — its units digit is 0, so it goes into bucket 0.", "stats": { "comparisons": 1, "swaps": 0 }, "accent": "compare" }, { "data": [ { "id": "c0-170", "value": 170 }, { "id": "c1-45", "value": 45 }, { "id": "c2-75", "value": 75 }, { "id": "c3-90", "value": 90 }, { "id": "c4-24", "value": 24 }, { "id": "c5-2", "value": 2 }, { "id": "c6-66", "value": 66 } ], "pointers": [ { "name": "i", "index": 1 } ], "highlights": [ { "index": 1, "role": "compare" } ], "codeLine": 18, "variables": { "value": 45, "digit": 5, "bucket": 5 }, "explanation": "45 — its units digit is 5, so it goes into bucket 5.", "stats": { "comparisons": 2, "swaps": 0 }, "accent": "compare" }, { "data": [ { "id": "c0-170", "value": 170 }, { "id": "c1-45", "value": 45 }, { "id": "c2-75", "value": 75 }, { "id": "c3-90", "value": 90 }, { "id": "c4-24", "value": 24 }, { "id": "c5-2", "value": 2 }, { "id": "c6-66", "value": 66 } ], "pointers": [ { "name": "i", "index": 2 } ], "highlights": [ { "index": 2, "role": "compare" } ], "codeLine": 18, "variables": { "value": 75, "digit": 5, "bucket": 5 }, "explanation": "75 — its units digit is 5, so it goes into bucket 5.", "stats": { "comparisons": 3, "swaps": 0 }, "accent": "compare" }, { "data": [ { "id": "c0-170", "value": 170 }, { "id": "c1-45", "value": 45 }, { "id": "c2-75", "value": 75 }, { "id": "c3-90", "value": 90 }, { "id": "c4-24", "value": 24 }, { "id": "c5-2", "value": 2 }, { "id": "c6-66", "value": 66 } ], "pointers": [ { "name": "i", "index": 3 } ], "highlights": [ { "index": 3, "role": "compare" } ], "codeLine": 18, "variables": { "value": 90, "digit": 0, "bucket": 0 }, "explanation": "90 — its units digit is 0, so it goes into bucket 0.", "stats": { "comparisons": 4, "swaps": 0 }, "accent": "compare" }, { "data": [ { "id": "c0-170", "value": 170 }, { "id": "c1-45", "value": 45 }, { "id": "c2-75", "value": 75 }, { "id": "c3-90", "value": 90 }, { "id": "c4-24", "value": 24 }, { "id": "c5-2", "value": 2 }, { "id": "c6-66", "value": 66 } ], "pointers": [ { "name": "i", "index": 4 } ], "highlights": [ { "index": 4, "role": "compare" } ], "codeLine": 18, "variables": { "value": 24, "digit": 4, "bucket": 4 }, "explanation": "24 — its units digit is 4, so it goes into bucket 4.", "stats": { "comparisons": 5, "swaps": 0 }, "accent": "compare" }, { "data": [ { "id": "c0-170", "value": 170 }, { "id": "c1-45", "value": 45 }, { "id": "c2-75", "value": 75 }, { "id": "c3-90", "value": 90 }, { "id": "c4-24", "value": 24 }, { "id": "c5-2", "value": 2 }, { "id": "c6-66", "value": 66 } ], "pointers": [ { "name": "i", "index": 5 } ], "highlights": [ { "index": 5, "role": "compare" } ], "codeLine": 18, "variables": { "value": 2, "digit": 2, "bucket": 2 }, "explanation": "2 — its units digit is 2, so it goes into bucket 2.", "stats": { "comparisons": 6, "swaps": 0 }, "accent": "compare" }, { "data": [ { "id": "c0-170", "value": 170 }, { "id": "c1-45", "value": 45 }, { "id": "c2-75", "value": 75 }, { "id": "c3-90", "value": 90 }, { "id": "c4-24", "value": 24 }, { "id": "c5-2", "value": 2 }, { "id": "c6-66", "value": 66 } ], "pointers": [ { "name": "i", "index": 6 } ], "highlights": [ { "index": 6, "role": "compare" } ], "codeLine": 18, "variables": { "value": 66, "digit": 6, "bucket": 6 }, "explanation": "66 — its units digit is 6, so it goes into bucket 6.", "stats": { "comparisons": 7, "swaps": 0 }, "accent": "compare" }, { "data": [ { "id": "c0-170", "value": 170 }, { "id": "c3-90", "value": 90 }, { "id": "c5-2", "value": 2 }, { "id": "c4-24", "value": 24 }, { "id": "c1-45", "value": 45 }, { "id": "c2-75", "value": 75 }, { "id": "c6-66", "value": 66 } ], "pointers": [], "highlights": [], "codeLine": 21, "variables": { "pass": "units", "order": "170 90 2 24 45 75 66" }, "explanation": "Tip the buckets out, 0 through 9. The list is now sorted by its units digit — and, crucially, numbers that tied on this digit are still in the order the last pass left them. That stability is what stops this pass from wrecking the previous one.", "stats": { "comparisons": 7, "swaps": 1 }, "accent": "swap" }, { "data": [ { "id": "c0-170", "value": 170 }, { "id": "c3-90", "value": 90 }, { "id": "c5-2", "value": 2 }, { "id": "c4-24", "value": 24 }, { "id": "c1-45", "value": 45 }, { "id": "c2-75", "value": 75 }, { "id": "c6-66", "value": 66 } ], "pointers": [], "highlights": [], "codeLine": 5, "variables": { "pass": "tens", "exp": 10 }, "explanation": "Pass over the tens digit. Drop each number into the bucket for its tens digit, keeping ties in their current order.", "stats": { "comparisons": 7, "swaps": 1 }, "accent": "pivot" }, { "data": [ { "id": "c0-170", "value": 170 }, { "id": "c3-90", "value": 90 }, { "id": "c5-2", "value": 2 }, { "id": "c4-24", "value": 24 }, { "id": "c1-45", "value": 45 }, { "id": "c2-75", "value": 75 }, { "id": "c6-66", "value": 66 } ], "pointers": [ { "name": "i", "index": 0 } ], "highlights": [ { "index": 0, "role": "compare" } ], "codeLine": 18, "variables": { "value": 170, "digit": 7, "bucket": 7 }, "explanation": "170 — its tens digit is 7, so it goes into bucket 7.", "stats": { "comparisons": 8, "swaps": 1 }, "accent": "compare" }, { "data": [ { "id": "c0-170", "value": 170 }, { "id": "c3-90", "value": 90 }, { "id": "c5-2", "value": 2 }, { "id": "c4-24", "value": 24 }, { "id": "c1-45", "value": 45 }, { "id": "c2-75", "value": 75 }, { "id": "c6-66", "value": 66 } ], "pointers": [ { "name": "i", "index": 1 } ], "highlights": [ { "index": 1, "role": "compare" } ], "codeLine": 18, "variables": { "value": 90, "digit": 9, "bucket": 9 }, "explanation": "90 — its tens digit is 9, so it goes into bucket 9.", "stats": { "comparisons": 9, "swaps": 1 }, "accent": "compare" }, { "data": [ { "id": "c0-170", "value": 170 }, { "id": "c3-90", "value": 90 }, { "id": "c5-2", "value": 2 }, { "id": "c4-24", "value": 24 }, { "id": "c1-45", "value": 45 }, { "id": "c2-75", "value": 75 }, { "id": "c6-66", "value": 66 } ], "pointers": [ { "name": "i", "index": 2 } ], "highlights": [ { "index": 2, "role": "compare" } ], "codeLine": 18, "variables": { "value": 2, "digit": 0, "bucket": 0 }, "explanation": "2 — its tens digit is 0, so it goes into bucket 0.", "stats": { "comparisons": 10, "swaps": 1 }, "accent": "compare" }, { "data": [ { "id": "c0-170", "value": 170 }, { "id": "c3-90", "value": 90 }, { "id": "c5-2", "value": 2 }, { "id": "c4-24", "value": 24 }, { "id": "c1-45", "value": 45 }, { "id": "c2-75", "value": 75 }, { "id": "c6-66", "value": 66 } ], "pointers": [ { "name": "i", "index": 3 } ], "highlights": [ { "index": 3, "role": "compare" } ], "codeLine": 18, "variables": { "value": 24, "digit": 2, "bucket": 2 }, "explanation": "24 — its tens digit is 2, so it goes into bucket 2.", "stats": { "comparisons": 11, "swaps": 1 }, "accent": "compare" }, { "data": [ { "id": "c0-170", "value": 170 }, { "id": "c3-90", "value": 90 }, { "id": "c5-2", "value": 2 }, { "id": "c4-24", "value": 24 }, { "id": "c1-45", "value": 45 }, { "id": "c2-75", "value": 75 }, { "id": "c6-66", "value": 66 } ], "pointers": [ { "name": "i", "index": 4 } ], "highlights": [ { "index": 4, "role": "compare" } ], "codeLine": 18, "variables": { "value": 45, "digit": 4, "bucket": 4 }, "explanation": "45 — its tens digit is 4, so it goes into bucket 4.", "stats": { "comparisons": 12, "swaps": 1 }, "accent": "compare" }, { "data": [ { "id": "c0-170", "value": 170 }, { "id": "c3-90", "value": 90 }, { "id": "c5-2", "value": 2 }, { "id": "c4-24", "value": 24 }, { "id": "c1-45", "value": 45 }, { "id": "c2-75", "value": 75 }, { "id": "c6-66", "value": 66 } ], "pointers": [ { "name": "i", "index": 5 } ], "highlights": [ { "index": 5, "role": "compare" } ], "codeLine": 18, "variables": { "value": 75, "digit": 7, "bucket": 7 }, "explanation": "75 — its tens digit is 7, so it goes into bucket 7.", "stats": { "comparisons": 13, "swaps": 1 }, "accent": "compare" }, { "data": [ { "id": "c0-170", "value": 170 }, { "id": "c3-90", "value": 90 }, { "id": "c5-2", "value": 2 }, { "id": "c4-24", "value": 24 }, { "id": "c1-45", "value": 45 }, { "id": "c2-75", "value": 75 }, { "id": "c6-66", "value": 66 } ], "pointers": [ { "name": "i", "index": 6 } ], "highlights": [ { "index": 6, "role": "compare" } ], "codeLine": 18, "variables": { "value": 66, "digit": 6, "bucket": 6 }, "explanation": "66 — its tens digit is 6, so it goes into bucket 6.", "stats": { "comparisons": 14, "swaps": 1 }, "accent": "compare" }, { "data": [ { "id": "c5-2", "value": 2 }, { "id": "c4-24", "value": 24 }, { "id": "c1-45", "value": 45 }, { "id": "c6-66", "value": 66 }, { "id": "c0-170", "value": 170 }, { "id": "c2-75", "value": 75 }, { "id": "c3-90", "value": 90 } ], "pointers": [], "highlights": [], "codeLine": 21, "variables": { "pass": "tens", "order": "2 24 45 66 170 75 90" }, "explanation": "Tip the buckets out, 0 through 9. The list is now sorted by its tens digit — and, crucially, numbers that tied on this digit are still in the order the last pass left them. That stability is what stops this pass from wrecking the previous one.", "stats": { "comparisons": 14, "swaps": 2 }, "accent": "swap" }, { "data": [ { "id": "c5-2", "value": 2 }, { "id": "c4-24", "value": 24 }, { "id": "c1-45", "value": 45 }, { "id": "c6-66", "value": 66 }, { "id": "c0-170", "value": 170 }, { "id": "c2-75", "value": 75 }, { "id": "c3-90", "value": 90 } ], "pointers": [], "highlights": [], "codeLine": 5, "variables": { "pass": "hundreds", "exp": 100 }, "explanation": "Pass over the hundreds digit. Drop each number into the bucket for its hundreds digit, keeping ties in their current order.", "stats": { "comparisons": 14, "swaps": 2 }, "accent": "pivot" }, { "data": [ { "id": "c5-2", "value": 2 }, { "id": "c4-24", "value": 24 }, { "id": "c1-45", "value": 45 }, { "id": "c6-66", "value": 66 }, { "id": "c0-170", "value": 170 }, { "id": "c2-75", "value": 75 }, { "id": "c3-90", "value": 90 } ], "pointers": [ { "name": "i", "index": 0 } ], "highlights": [ { "index": 0, "role": "compare" } ], "codeLine": 18, "variables": { "value": 2, "digit": 0, "bucket": 0 }, "explanation": "2 — its hundreds digit is 0, so it goes into bucket 0.", "stats": { "comparisons": 15, "swaps": 2 }, "accent": "compare" }, { "data": [ { "id": "c5-2", "value": 2 }, { "id": "c4-24", "value": 24 }, { "id": "c1-45", "value": 45 }, { "id": "c6-66", "value": 66 }, { "id": "c0-170", "value": 170 }, { "id": "c2-75", "value": 75 }, { "id": "c3-90", "value": 90 } ], "pointers": [ { "name": "i", "index": 1 } ], "highlights": [ { "index": 1, "role": "compare" } ], "codeLine": 18, "variables": { "value": 24, "digit": 0, "bucket": 0 }, "explanation": "24 — its hundreds digit is 0, so it goes into bucket 0.", "stats": { "comparisons": 16, "swaps": 2 }, "accent": "compare" }, { "data": [ { "id": "c5-2", "value": 2 }, { "id": "c4-24", "value": 24 }, { "id": "c1-45", "value": 45 }, { "id": "c6-66", "value": 66 }, { "id": "c0-170", "value": 170 }, { "id": "c2-75", "value": 75 }, { "id": "c3-90", "value": 90 } ], "pointers": [ { "name": "i", "index": 2 } ], "highlights": [ { "index": 2, "role": "compare" } ], "codeLine": 18, "variables": { "value": 45, "digit": 0, "bucket": 0 }, "explanation": "45 — its hundreds digit is 0, so it goes into bucket 0.", "stats": { "comparisons": 17, "swaps": 2 }, "accent": "compare" }, { "data": [ { "id": "c5-2", "value": 2 }, { "id": "c4-24", "value": 24 }, { "id": "c1-45", "value": 45 }, { "id": "c6-66", "value": 66 }, { "id": "c0-170", "value": 170 }, { "id": "c2-75", "value": 75 }, { "id": "c3-90", "value": 90 } ], "pointers": [ { "name": "i", "index": 3 } ], "highlights": [ { "index": 3, "role": "compare" } ], "codeLine": 18, "variables": { "value": 66, "digit": 0, "bucket": 0 }, "explanation": "66 — its hundreds digit is 0, so it goes into bucket 0.", "stats": { "comparisons": 18, "swaps": 2 }, "accent": "compare" }, { "data": [ { "id": "c5-2", "value": 2 }, { "id": "c4-24", "value": 24 }, { "id": "c1-45", "value": 45 }, { "id": "c6-66", "value": 66 }, { "id": "c0-170", "value": 170 }, { "id": "c2-75", "value": 75 }, { "id": "c3-90", "value": 90 } ], "pointers": [ { "name": "i", "index": 4 } ], "highlights": [ { "index": 4, "role": "compare" } ], "codeLine": 18, "variables": { "value": 170, "digit": 1, "bucket": 1 }, "explanation": "170 — its hundreds digit is 1, so it goes into bucket 1.", "stats": { "comparisons": 19, "swaps": 2 }, "accent": "compare" }, { "data": [ { "id": "c5-2", "value": 2 }, { "id": "c4-24", "value": 24 }, { "id": "c1-45", "value": 45 }, { "id": "c6-66", "value": 66 }, { "id": "c0-170", "value": 170 }, { "id": "c2-75", "value": 75 }, { "id": "c3-90", "value": 90 } ], "pointers": [ { "name": "i", "index": 5 } ], "highlights": [ { "index": 5, "role": "compare" } ], "codeLine": 18, "variables": { "value": 75, "digit": 0, "bucket": 0 }, "explanation": "75 — its hundreds digit is 0, so it goes into bucket 0.", "stats": { "comparisons": 20, "swaps": 2 }, "accent": "compare" }, { "data": [ { "id": "c5-2", "value": 2 }, { "id": "c4-24", "value": 24 }, { "id": "c1-45", "value": 45 }, { "id": "c6-66", "value": 66 }, { "id": "c0-170", "value": 170 }, { "id": "c2-75", "value": 75 }, { "id": "c3-90", "value": 90 } ], "pointers": [ { "name": "i", "index": 6 } ], "highlights": [ { "index": 6, "role": "compare" } ], "codeLine": 18, "variables": { "value": 90, "digit": 0, "bucket": 0 }, "explanation": "90 — its hundreds digit is 0, so it goes into bucket 0.", "stats": { "comparisons": 21, "swaps": 2 }, "accent": "compare" }, { "data": [ { "id": "c5-2", "value": 2 }, { "id": "c4-24", "value": 24 }, { "id": "c1-45", "value": 45 }, { "id": "c6-66", "value": 66 }, { "id": "c2-75", "value": 75 }, { "id": "c3-90", "value": 90 }, { "id": "c0-170", "value": 170 } ], "pointers": [], "highlights": [], "codeLine": 21, "variables": { "pass": "hundreds", "order": "2 24 45 66 75 90 170" }, "explanation": "Tip the buckets out, 0 through 9. The list is now sorted by its hundreds digit — and, crucially, numbers that tied on this digit are still in the order the last pass left them. That stability is what stops this pass from wrecking the previous one.", "stats": { "comparisons": 21, "swaps": 3 }, "accent": "swap" }, { "data": [ { "id": "c5-2", "value": 2 }, { "id": "c4-24", "value": 24 }, { "id": "c1-45", "value": 45 }, { "id": "c6-66", "value": 66 }, { "id": "c2-75", "value": 75 }, { "id": "c3-90", "value": 90 }, { "id": "c0-170", "value": 170 } ], "pointers": [], "highlights": [ { "index": 0, "role": "sorted" }, { "index": 1, "role": "sorted" }, { "index": 2, "role": "sorted" }, { "index": 3, "role": "sorted" }, { "index": 4, "role": "sorted" }, { "index": 5, "role": "sorted" }, { "index": 6, "role": "sorted" } ], "codeLine": 8, "variables": { "passes": 3, "comparisons": 0 }, "explanation": "Sorted, in 3 passes and zero comparisons. Radix sort is O(d × n) where d is the number of digits — so on a big pile of fixed-width keys it genuinely beats n log n. Try it on numbers of wildly different lengths and the d starts to hurt.", "stats": { "comparisons": 21, "swaps": 3 }, "accent": "sorted" } ] } }