# bin, binr¶

Binary search

x bin  y    bin[x;y]
x binr y    binr[x;y]

Where

• x is a sorted list
• y is a list or atom of exactly the same type (no type promotion)

returns the index of the last item in x which is ≤y. The result is -1 for y less than the first item of x. binr binary search right, introduced in V3.0 2012.07.26, gives the index of the first item in x which is ≥y.

They use a binary-search algorithm, which is generally more efficient on large data than the linear-search algorithm used by ? (Find).

The items of x should be sorted ascending although bin does not verify that; if the items are not sorted ascending, the result is undefined. y can be either an atom or a simple list of the same type as the left argument.

The result r can be interpreted as follows: for an atom y, r is an integer atom whose value is either a valid index of x or -1. In general:

r[i]=-1            iff y[i]<x[0]
r[i]=j             iff last j such that x[j]<=y[i]<=x[j+1]
r[i]=n-1           iff x[n-1]<=y[i]

and

r[j]=x bin y[j]    for all j in index of y

Essentially bin gives a half-open interval on the left.

bin and binr are right-atomic: their results have the same count as y.

bin also operates on tuples and table columns and is the function used in aj and lj.

If x is not sorted the result is undefined.

## Three-column argument¶

bin and ? on three columns find all equijoins on the first two cols and then do bin or ? respectively on the third column. bin assumes the third column is sorted within the equivalence classes of the first two column pairs (but need not be sorted overall).

q)0 2 4 6 8 10 bin 5
2
q)0 2 4 6 8 10 bin -10 0 4 5 6 20
-1 0 2 2 3 5

If the left argument items are not distinct the result is not the same as would be obtained with ?:

q)1 2 3 3 4 bin 2 3
1 3
q)1 2 3 3 4 ? 2 3
1 2

## Sorted third column¶

bin detects the special case of three columns with the third column having a sorted attribute. The search is initially constrained by the first column, then by the sorted third column, and then by a linear search through the remaining second column. The performance difference is visible in this example:

q)n:1000000;t:([]a:p#asc n?2;b:#asc n?1000;c:asc n?100000)
q)\t t bin t
194
q)update#c fromt; / remove the sort attr from column c
q)\t t bin t
3699`