gear/algo.lua

219 lines
6.1 KiB
Lua

--- General stateless utility algorithms
--
-- @module gear.algo
-- @copyright 2022 The DoubleFourteen Code Forge
-- @author Lorenzo Cogotti
local floor = math.floor
local min, max = math.min, math.max
local algo = {}
--- Clamp x within range [a,b] (where b >= a).
--
-- @number x value to clamp.
-- @number a interval lower bound (inclusive).
-- @number b interval upper bound (inclusive).
-- @treturn number clamped value.
function algo.clamp(x, a, b) return min(max(x, a), b) end
--- Sign function.
--
-- @number x value whose sign should be returned.
-- @treturn number sign of x, -1 if negative, 1 if positive, 0 otherwise.
function algo.sign(x) return x > 0 and 1 or x < 0 and -1 or 0 end
--- Fast remove from array.
--
-- Replace 'array[i]' with last array's element and
-- discard array's tail.
--
-- @tparam table array
-- @int i
function algo.removefast(array, i)
local n = #array
array[i] = array[n] -- NOP if i == n
array[n] = nil
end
local function lt(a, b) return a < b end
local function _insertionsort(array, lo, hi, less)
for i = lo+1,hi do
local k = lo
local v = array[i]
for j = i,lo+1,-1 do
local el = array[j-1]
if less(v, el) then
array[j] = el
else
k = j
break
end
end
array[k] = v
end
end
--- Sort array using Insertion Sort - O(n^2).
--
-- Provides the most basic sorting algorithm around.
-- Performs better than regular table.sort() for small arrays
-- (~100 elements).
--
-- @tparam table array array to be sorted.
-- @tparam[opt=operator <] function less comparison function, takes 2 arguments,
-- returns true if its first argument is
-- less than its second argument,
-- false otherwise.
function algo.insertionsort(array, less)
_insertionsort(array, 1, #array, less or lt)
end
--- Binary search last element where
-- what <= array[i] - also known as lower bound.
--
-- @tparam table array an array sorted according to the less function.
-- @param what the comparison argument.
-- @tparam[opt=operator <] function less sorting criterium, a function taking 2 arguments,
-- returns true if the first argument
-- is less than the second argument,
-- false otherwise.
--
-- @treturn int the greatest index i, where what <= array[i].
-- If no such element exists, it returns an out of bounds index
-- such that array[i] == nil.
function algo.bsearchl(array, what, less)
less = less or lt
local lo, hi = 1, #array
local ofs, mid = -1, hi
while mid > 0 do
mid = floor(hi / 2)
-- array[lo+mid] <= what <-> what >= array[lo+mid]
-- <-> not what < array[lo+mid]
if not less(what, array[lo+mid]) then
lo = lo + mid
ofs = 0 -- at least one element where array[lo+mid] <= what
end
hi = hi - mid
end
return lo + ofs
end
--- Binary search first element where
-- what >= array[i] - also known as upper bound.
--
-- @tparam table array an array sorted according to the less function.
-- @param what the comparison argument.
-- @tparam[opt=operator <] function less sorting criterium,
-- a function taking 2 arguments,
-- returns true if the first argument
-- is less than the second argument,
-- false otherwise.
--
-- @treturn int the smallest index i, where what >= array[i].
-- If no such element exists, it returns an out of bounds index
-- such that array[i] == nil.
function algo.bsearchr(array, what, less)
less = less or lt
local lo, hi = 1, #array
local ofs, mid = -1, hi
while mid > 0 do
mid = floor(hi / 2)
-- array[lo+mid] >= what <-> not array[lo+mid] < what
if not less(array[lo+mid], what) then
ofs = 0
else
lo = lo + mid
ofs = 1
end
hi = hi - mid
end
return lo + ofs
end
local function merge(array, lo, mid, hi, less, workspace)
local i, j, k
i = 1
-- Copy first half of array to auxiliary array
for j = lo,mid do
workspace[i] = array[j]
i = i + 1
end
i = 1
j = mid + 1
k = lo
while k < j and j <= hi do
local v = array[j]
local el = workspace[i]
if less(v, el) then
array[k] = v
j = j + 1
else
array[k] = el
i = i + 1
end
k = k + 1
end
-- Copy back any remaining elements of first half
for k = k,j-1 do
array[k] = workspace[i]
i = i + 1
end
end
local function mergesort(array, lo, hi, less, workspace)
if hi - lo < 72 then
_insertionsort(array, lo, hi, less)
else
local mid = floor((lo + hi)/2)
mergesort(array, lo, mid, less, workspace)
mergesort(array, mid + 1, hi, less, workspace)
merge(array, lo, mid, hi, less, workspace)
end
end
--- Array stable sort, uses Merge Sort - O(n*log(n)).
--
-- Algorithm is a slightly altered version of stable_sort(),
-- posted on Lua-L by Steve Fisher on 02 May 2013 22:10:50
-- https://lua-users.org/lists/lua-l/2013-05/msg00038.html
--
-- This implementation uses an auxiliary buffer of size O(n/2).
--
-- @tparam table array Array to be sorted.
-- @tparam[opt=operator <] function less comparison function, takes 2 arguments,
-- returns true if its first argument is
-- less than its second argument,
-- false otherwise.
-- @tparam[opt={}] table use an existing workspace buffer instead of allocating one.
function algo.stablesort(array, less, workspace)
local n = #array
less = less or lt
workspace = workspace or {}
workspace[floor((n+1)/2)] = array[1] -- preallocate some room
mergesort(array, 1, n, less, workspace)
end
return algo