{ "id": "hashing/hash-map", "version": 1, "deterministic": true, "url": "/dsa/hashing/hash-map", "topic": { "slug": "hashing", "title": "Hashing" }, "title": "Hash Map", "tagline": "Turn a key straight into a location — the structure behind almost everything.", "vizKind": "hash", "complexity": { "time": { "best": "O(1)", "average": "O(1)", "worst": "O(n)" }, "space": "O(n)", "growth": "constant", "note": "Insert and lookup are O(1) on average — one hash, one jump, a glance at a short chain. The worst case is O(n): if every key collides into one bucket, that bucket becomes a plain list you have to scan. A good hash function keeps that from happening." }, "code": { "javascript": "const BUCKETS = 5;\n\nfunction insert(table, key) {\n const i = key % BUCKETS;\n table[i].push(key);\n}\n\nfunction has(table, key) {\n const i = key % BUCKETS;\n for (const k of table[i]) {\n if (k === key) return true;\n }\n return false;\n}", "python": "BUCKETS = 5\n\ndef insert(table, key):\n i = key % BUCKETS\n table[i].append(key)\n\n\ndef has(table, key):\n i = key % BUCKETS\n for k in table[i]:\n if k == key:\n return True\n return False\n", "java": "static final int BUCKETS = 5;\n\nvoid insert(List> table, int key) {\n int i = key % BUCKETS;\n table.get(i).add(key);\n}\n\nboolean has(List> table, int key) {\n int i = key % BUCKETS;\n for (int k : table.get(i)) {\n if (k == key) return true;\n }\n return false;\n}", "cpp": "const int BUCKETS = 5;\n\nvoid insert(vector>& table, int key) {\n int i = key % BUCKETS;\n table[i].push_back(key);\n}\n\nbool has(vector>& table, int key) {\n int i = key % BUCKETS;\n for (int k : table[i]) {\n if (k == key) return true;\n }\n return false;\n}" }, "defaultInput": [ 17, 22, 3, 8, 12, 27 ], "defaultTarget": 12, "inputHint": "Keys get hashed into 5 buckets. Watch for collisions that share a bucket.", "pitfalls": [ { "wrong": "Assuming lookups are always O(1).", "right": "Only on average. Pile every key into one bucket — a bad hash, or an attacker feeding you worst-case keys — and it degrades to scanning a list, O(n)." }, { "wrong": "Expecting keys to come back in the order you inserted them.", "right": "A hash map scatters keys by their hash, not by insertion order. If you need order, that's a different tool (or a linked hash map)." }, { "wrong": "Forgetting to handle collisions.", "right": "Two keys will eventually share a bucket. Without chaining (or another scheme), the second one overwrites the first and you silently lose data." } ], "quiz": [ { "q": "How does a hash map find a key so fast?", "options": [ "It searches every bucket quickly", "It calculates the key's bucket directly with a hash", "It keeps the keys sorted", "It remembers where everything is in a list" ], "answer": 1, "why": "The hash turns the key into a bucket index by arithmetic, so you jump straight there. No searching — that's what makes it O(1) on average." }, { "q": "Two different keys hash to the same bucket. What is that called, and is it a problem?", "options": [ "A crash — the map breaks", "A collision — expected, and handled by chaining", "A duplicate — one key is lost", "Impossible — hashes are unique" ], "answer": 1, "why": "It's a collision, and it's completely normal. Chaining stores both keys in the same bucket's list, so nothing is lost as long as chains stay short." }, { "q": "When does a hash map's lookup degrade to O(n)?", "options": [ "When it holds more than 100 items", "When many keys collide into the same bucket", "Never — it's always O(1)", "When the keys are large numbers" ], "answer": 1, "why": "If a bad hash sends everything to one bucket, that bucket is just a list you must scan end to end — O(n). Good hash functions spread keys evenly to prevent this." } ], "problems": [ { "name": "Two Sum", "difficulty": "Easy", "url": "https://leetcode.com/problems/two-sum/" }, { "name": "Contains Duplicate", "difficulty": "Easy", "url": "https://leetcode.com/problems/contains-duplicate/" }, { "name": "Group Anagrams", "difficulty": "Medium", "url": "https://leetcode.com/problems/group-anagrams/" } ], "trace": { "note": "Each frame is one immutable step: data snapshot, pointers, per-index roles, executing code line, and a one-sentence explanation.", "length": 17, "frames": [ { "data": { "buckets": [ { "entries": [] }, { "entries": [] }, { "entries": [] }, { "entries": [] }, { "entries": [] } ] }, "pointers": [], "highlights": [], "codeLine": 1, "variables": {}, "explanation": "A hash map turns a key straight into a location. Instead of searching for where something is, it calculates where it must be — so lookups are almost instant, no matter how much you store.", "stats": { "comparisons": 0, "swaps": 0 } }, { "data": { "buckets": [ { "entries": [] }, { "entries": [] }, { "role": "active", "entries": [] }, { "entries": [] }, { "entries": [] } ], "probe": { "key": 17, "hash": 2 } }, "pointers": [], "highlights": [], "codeLine": 4, "variables": { "key": 17, "hash": "17 % 5 = 2" }, "explanation": "Where does 17 go? Compute 17 % 5 = 2. So 17 belongs in bucket 2 — no searching, just arithmetic.", "stats": { "comparisons": 0, "swaps": 0 }, "accent": "compare" }, { "data": { "buckets": [ { "entries": [] }, { "entries": [] }, { "role": "active", "entries": [ { "id": "e0-17", "key": 17, "role": "found" } ] }, { "entries": [] }, { "entries": [] } ] }, "pointers": [], "highlights": [], "codeLine": 5, "variables": { "key": 17, "bucket": 2, "collision": false }, "explanation": "Bucket 2 was empty, so 17 drops straight in.", "stats": { "comparisons": 0, "swaps": 0 }, "accent": "found" }, { "data": { "buckets": [ { "entries": [] }, { "entries": [] }, { "role": "active", "entries": [ { "id": "e0-17", "key": 17 } ] }, { "entries": [] }, { "entries": [] } ], "probe": { "key": 22, "hash": 2 } }, "pointers": [], "highlights": [], "codeLine": 4, "variables": { "key": 22, "hash": "22 % 5 = 2" }, "explanation": "Where does 22 go? Compute 22 % 5 = 2. So 22 belongs in bucket 2 — no searching, just arithmetic.", "stats": { "comparisons": 0, "swaps": 0 }, "accent": "compare" }, { "data": { "buckets": [ { "entries": [] }, { "entries": [] }, { "role": "active", "entries": [ { "id": "e0-17", "key": 17 }, { "id": "e1-22", "key": 22, "role": "found" } ] }, { "entries": [] }, { "entries": [] } ] }, "pointers": [], "highlights": [], "codeLine": 5, "variables": { "key": 22, "bucket": 2, "collision": true }, "explanation": "Bucket 2 already has something — a collision. That's fine: just chain 22 onto the end of the bucket's list.", "stats": { "comparisons": 0, "swaps": 0 }, "accent": "swap" }, { "data": { "buckets": [ { "entries": [] }, { "entries": [] }, { "entries": [ { "id": "e0-17", "key": 17 }, { "id": "e1-22", "key": 22 } ] }, { "role": "active", "entries": [] }, { "entries": [] } ], "probe": { "key": 3, "hash": 3 } }, "pointers": [], "highlights": [], "codeLine": 4, "variables": { "key": 3, "hash": "3 % 5 = 3" }, "explanation": "Where does 3 go? Compute 3 % 5 = 3. So 3 belongs in bucket 3 — no searching, just arithmetic.", "stats": { "comparisons": 0, "swaps": 0 }, "accent": "compare" }, { "data": { "buckets": [ { "entries": [] }, { "entries": [] }, { "entries": [ { "id": "e0-17", "key": 17 }, { "id": "e1-22", "key": 22 } ] }, { "role": "active", "entries": [ { "id": "e2-3", "key": 3, "role": "found" } ] }, { "entries": [] } ] }, "pointers": [], "highlights": [], "codeLine": 5, "variables": { "key": 3, "bucket": 3, "collision": false }, "explanation": "Bucket 3 was empty, so 3 drops straight in.", "stats": { "comparisons": 0, "swaps": 0 }, "accent": "found" }, { "data": { "buckets": [ { "entries": [] }, { "entries": [] }, { "entries": [ { "id": "e0-17", "key": 17 }, { "id": "e1-22", "key": 22 } ] }, { "role": "active", "entries": [ { "id": "e2-3", "key": 3 } ] }, { "entries": [] } ], "probe": { "key": 8, "hash": 3 } }, "pointers": [], "highlights": [], "codeLine": 4, "variables": { "key": 8, "hash": "8 % 5 = 3" }, "explanation": "Where does 8 go? Compute 8 % 5 = 3. So 8 belongs in bucket 3 — no searching, just arithmetic.", "stats": { "comparisons": 0, "swaps": 0 }, "accent": "compare" }, { "data": { "buckets": [ { "entries": [] }, { "entries": [] }, { "entries": [ { "id": "e0-17", "key": 17 }, { "id": "e1-22", "key": 22 } ] }, { "role": "active", "entries": [ { "id": "e2-3", "key": 3 }, { "id": "e3-8", "key": 8, "role": "found" } ] }, { "entries": [] } ] }, "pointers": [], "highlights": [], "codeLine": 5, "variables": { "key": 8, "bucket": 3, "collision": true }, "explanation": "Bucket 3 already has something — a collision. That's fine: just chain 8 onto the end of the bucket's list.", "stats": { "comparisons": 0, "swaps": 0 }, "accent": "swap" }, { "data": { "buckets": [ { "entries": [] }, { "entries": [] }, { "role": "active", "entries": [ { "id": "e0-17", "key": 17 }, { "id": "e1-22", "key": 22 } ] }, { "entries": [ { "id": "e2-3", "key": 3 }, { "id": "e3-8", "key": 8 } ] }, { "entries": [] } ], "probe": { "key": 12, "hash": 2 } }, "pointers": [], "highlights": [], "codeLine": 4, "variables": { "key": 12, "hash": "12 % 5 = 2" }, "explanation": "Where does 12 go? Compute 12 % 5 = 2. So 12 belongs in bucket 2 — no searching, just arithmetic.", "stats": { "comparisons": 0, "swaps": 0 }, "accent": "compare" }, { "data": { "buckets": [ { "entries": [] }, { "entries": [] }, { "role": "active", "entries": [ { "id": "e0-17", "key": 17 }, { "id": "e1-22", "key": 22 }, { "id": "e4-12", "key": 12, "role": "found" } ] }, { "entries": [ { "id": "e2-3", "key": 3 }, { "id": "e3-8", "key": 8 } ] }, { "entries": [] } ] }, "pointers": [], "highlights": [], "codeLine": 5, "variables": { "key": 12, "bucket": 2, "collision": true }, "explanation": "Bucket 2 already has something — a collision. That's fine: just chain 12 onto the end of the bucket's list.", "stats": { "comparisons": 0, "swaps": 0 }, "accent": "swap" }, { "data": { "buckets": [ { "entries": [] }, { "entries": [] }, { "role": "active", "entries": [ { "id": "e0-17", "key": 17 }, { "id": "e1-22", "key": 22 }, { "id": "e4-12", "key": 12 } ] }, { "entries": [ { "id": "e2-3", "key": 3 }, { "id": "e3-8", "key": 8 } ] }, { "entries": [] } ], "probe": { "key": 27, "hash": 2 } }, "pointers": [], "highlights": [], "codeLine": 4, "variables": { "key": 27, "hash": "27 % 5 = 2" }, "explanation": "Where does 27 go? Compute 27 % 5 = 2. So 27 belongs in bucket 2 — no searching, just arithmetic.", "stats": { "comparisons": 0, "swaps": 0 }, "accent": "compare" }, { "data": { "buckets": [ { "entries": [] }, { "entries": [] }, { "role": "active", "entries": [ { "id": "e0-17", "key": 17 }, { "id": "e1-22", "key": 22 }, { "id": "e4-12", "key": 12 }, { "id": "e5-27", "key": 27, "role": "found" } ] }, { "entries": [ { "id": "e2-3", "key": 3 }, { "id": "e3-8", "key": 8 } ] }, { "entries": [] } ] }, "pointers": [], "highlights": [], "codeLine": 5, "variables": { "key": 27, "bucket": 2, "collision": true }, "explanation": "Bucket 2 already has something — a collision. That's fine: just chain 27 onto the end of the bucket's list.", "stats": { "comparisons": 0, "swaps": 0 }, "accent": "swap" }, { "data": { "buckets": [ { "entries": [] }, { "entries": [] }, { "role": "active", "entries": [ { "id": "e0-17", "key": 17 }, { "id": "e1-22", "key": 22 }, { "id": "e4-12", "key": 12 }, { "id": "e5-27", "key": 27 } ] }, { "entries": [ { "id": "e2-3", "key": 3 }, { "id": "e3-8", "key": 8 } ] }, { "entries": [] } ], "probe": { "key": 12, "hash": 2 } }, "pointers": [], "highlights": [], "codeLine": 9, "variables": { "lookup": 12, "hash": "12 % 5 = 2" }, "explanation": "Now look up 12. Same trick: 12 % 5 = 2, so if it's anywhere, it's in bucket 2. We ignore the other 4 buckets entirely.", "stats": { "comparisons": 0, "swaps": 0 }, "accent": "compare" }, { "data": { "buckets": [ { "entries": [] }, { "entries": [] }, { "role": "active", "entries": [ { "id": "e0-17", "key": 17, "role": "compare" }, { "id": "e1-22", "key": 22 }, { "id": "e4-12", "key": 12 }, { "id": "e5-27", "key": 27 } ] }, { "entries": [ { "id": "e2-3", "key": 3 }, { "id": "e3-8", "key": 8 } ] }, { "entries": [] } ] }, "pointers": [], "highlights": [], "codeLine": 11, "variables": { "checking": 17, "target": 12 }, "explanation": "17 isn't 12. Check the next entry in this bucket's chain.", "stats": { "comparisons": 1, "swaps": 0 }, "accent": "compare" }, { "data": { "buckets": [ { "entries": [] }, { "entries": [] }, { "role": "active", "entries": [ { "id": "e0-17", "key": 17 }, { "id": "e1-22", "key": 22, "role": "compare" }, { "id": "e4-12", "key": 12 }, { "id": "e5-27", "key": 27 } ] }, { "entries": [ { "id": "e2-3", "key": 3 }, { "id": "e3-8", "key": 8 } ] }, { "entries": [] } ] }, "pointers": [], "highlights": [], "codeLine": 11, "variables": { "checking": 22, "target": 12 }, "explanation": "22 isn't 12. Check the next entry in this bucket's chain.", "stats": { "comparisons": 2, "swaps": 0 }, "accent": "compare" }, { "data": { "buckets": [ { "entries": [] }, { "entries": [] }, { "role": "active", "entries": [ { "id": "e0-17", "key": 17 }, { "id": "e1-22", "key": 22 }, { "id": "e4-12", "key": 12, "role": "found" }, { "id": "e5-27", "key": 27 } ] }, { "entries": [ { "id": "e2-3", "key": 3 }, { "id": "e3-8", "key": 8 } ] }, { "entries": [] } ] }, "pointers": [], "highlights": [], "codeLine": 11, "variables": { "checking": 12, "target": 12 }, "explanation": "12 is here. Found it after checking just 3 entries — only the ones that share its bucket.", "stats": { "comparisons": 3, "swaps": 0 }, "accent": "found" } ] } }