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Fix formatting issues in searching.md
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notes/searching.md

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

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