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## Search Functions and Hash Tables

Primitive dyadic search functions, such as ⍳ (index of) and ∊ (membership) have a principal argument in which items of the other subject argument are located.

In the case of ⍳, the principal argument is the one on the left and in the case of ∊, it is the one on the right. The following table shows the principal (P) and subject (s) arguments for each of the functions.

P ⍳ s |
Index of |

s ∊ P |
Membership |

s ∩ P |
Intersection |

P ∪ s |
Union |

s ~ P |
Without |

P {(↓⍺)⍳↓⍵} s |
Matrix Iota (idiom) |

P∘⍋ and P∘⍒ |
Sort |

The Dyalog APL implementation of these functions already uses a technique known as hashing to improve performance over a simple linear search. (Note that ⍷ (find) does not employ the same hashing technique, and is excluded from this discussion.)

Building a hash table for the principal argument takes a significant time but is rewarded by a considerably quicker search for each item in the subject. Unfortunately, the hash table is discarded each time the function completes and must be reconstructed for a subsequent call (even if its principal argument is identical to that in the previous one).

For optimal performance of repeated search operations, the hash table may be retained between calls, by binding the function with its principal argument using the primitive ∘ (compose) operator. The retained hash table is then used directly whenever this monadic derived function is applied to a subject argument.

Notice that retaining the hash table pays off only on a second or subsequent application of the derived function. This usually occurs in one of two ways: either the derived function is named for later (and repeated) use, as in the first example below or it is applied repeatedly as the operand of a primitive or defined operator, as in the second example.

#### Example: naming a derived function.

words←'red' 'ylo' 'grn' 'brn' 'blu' 'pnk' 'blk'
find←words∘⍳ ⍝ monadic find function
find'blk' 'blu' 'grn' 'ylo' ⍝
7 5 3 2
find'grn' 'brn' 'ylo' 'red' ⍝ fast find
3 4 2 1

#### Example: repeated application by (¨) each operator.

∊∘⎕A¨'This' 'And' 'That'
1 0 0 0 1 0 0 1 0 0 0