@@ -832,7 +832,7 @@ Path followed:
832832* Simple and cache-friendly; clusters form (“primary clustering”) which can slow probes.
833833* Deletion uses ** tombstones** to keep probe chains intact.
834834* Performance depends sharply on load factor; keep α well below 1 (e.g., α ≤ 0.7).
835- * Expected search \ ~ $O(1)$ at low α; degrades as clusters grow.
835+ * Expected search~ $O(1)$ at low α; degrades as clusters grow.
836836
837837#### Open Addressing — Quadratic Probing
838838
@@ -1293,7 +1293,7 @@ T₂: [ ][20 ][ ][10 ][15 ]
12931293
12941294* Lookups probe at ** most two places** (with two hashes) → excellent constant factors.
12951295* Inserts may trigger a chain of evictions; detect cycles and ** rehash** with new functions.
1296- * High load factors achievable (e.g., \ ~ 0.5–0.9 depending on variant and number of hashes/tables).
1296+ * High load factors achievable (e.g.,~ 0.5–0.9 depending on variant and number of hashes/tables).
12971297* Deletions are easy (remove key); no tombstones, but ensure invariants remain.
12981298* Sensitive to hash quality; poor hashes increase cycle risk.
12991299
@@ -1416,7 +1416,7 @@ All ones → **MAYBE PRESENT** (could be a **false positive**)
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14171417* Answers: ** maybe present** / ** definitely not present** ; never false negatives (without deletions).
14181418* False-positive rate is tunable via bit-array size ** m** , number of hashes ** k** , and items ** n** ; more space & good ** k** → lower FPR.
1419- * Time: $O(k)$ per insert/lookup; Space: \ ~ m bits.
1419+ * Time: $O(k)$ per insert/lookup; Space:~ m bits.
14201420* No deletions in the basic form; duplicates are harmless (idempotent sets).
14211421* Union = bitwise OR; intersection = bitwise AND (for same m,k,hashes).
14221422* Choose independent, well-mixed hash functions to avoid correlated bits.
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