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143 lines
4.0 KiB
Lua
143 lines
4.0 KiB
Lua
--- General stateless utility algorithms
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--
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-- @module gear.algo
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-- @copyright 2022 The DoubleFourteen Code Forge
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-- @author Lorenzo Cogotti
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local floor = math.floor
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local min, max = math.min, math.max
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local algo = {}
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--- Clamp x within range [a,b] (where b >= a).
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--
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-- @number x value to clamp.
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-- @number a interval lower bound (inclusive).
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-- @number b interval upper bound (includive).
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-- @treturn number clamped value.
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function algo.clamp(x, a, b) return min(max(x, a), b) end
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--- Fast remove from array.
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--
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-- Replace 'array[i]' with last array's element and
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-- discard array's tail.
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--
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-- @tparam table array
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-- @int i
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function algo.removefast(array, i)
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local n = #array
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array[i] = array[n] -- NOP if i == n
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array[n] = nil
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end
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local function lt(a, b) return a < b end
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local function _insertionsort(array, lo, hi, less)
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for i = lo+1,hi do
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local k = lo
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local v = array[i]
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for j = i,lo+1,-1 do
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local el = array[j-1]
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if less(v, el) then
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array[j] = el
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else
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k = j
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break
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end
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end
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array[k] = v
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end
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end
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--- Sort array using Insertion Sort - O(n^2).
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--
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-- Provides the most basic sorting algorithm around.
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-- Performs better than regular table.sort() for small arrays
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-- (~100 elements).
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--
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-- @tparam table array array to be sorted.
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-- @tparam[opt=operator <] function less comparison function, takes 2 arguments,
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-- returns true if its first argument is
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-- less than its second argument,
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-- false otherwise.
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function algo.insertionsort(array, less)
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_insertionsort(array, 1, #array, less or lt)
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end
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--- Binary search last element where
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-- what <= array[i] - also known as lower bound.
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--
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-- @tparam table array an array sorted according to the less function.
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-- @param what the comparison argument.
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-- @tparam[opt=operator <] function less sorting criterium, a function taking 2 arguments,
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-- returns true if the first argument
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-- is less than the second argument,
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-- false otherwise.
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--
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-- @treturn int the greatest index i, where what <= array[i].
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-- If no such element exists, it returns an out of bounds index
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-- such that array[i] == nil.
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function algo.bsearchl(array, what, less)
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less = less or lt
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local lo, hi = 1, #array
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local ofs, mid = -1, hi
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while mid > 0 do
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mid = floor(hi / 2)
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-- array[lo+mid] <= what <-> what >= array[lo+mid]
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-- <-> not what < array[lo+mid]
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if not less(what, array[lo+mid]) then
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lo = lo + mid
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ofs = 0 -- at least one element where array[lo+mid] <= what
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end
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hi = hi - mid
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end
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return lo + ofs
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end
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--- Binary search first element where
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-- what >= array[i] - also known as upper bound.
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--
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-- @tparam table array an array sorted according to the less function.
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-- @param what the comparison argument.
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-- @tparam[opt=operator <] function less sorting criterium,
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-- a function taking 2 arguments,
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-- returns true if the first argument
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-- is less than the second argument,
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-- false otherwise.
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--
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-- @treturn int the smallest index i, where what >= array[i].
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-- If no such element exists, it returns an out of bounds index
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-- such that array[i] == nil.
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function algo.bsearchr(array, what, less)
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less = less or lt
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local lo, hi = 1, #array
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local ofs, mid = -1, hi
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while mid > 0 do
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mid = floor(hi / 2)
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-- array[lo+mid] >= what <-> not array[lo+mid] < what
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if not less(array[lo+mid], what) then
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ofs = 0
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else
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lo = lo + mid
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ofs = 1
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end
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hi = hi - mid
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end
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return lo + ofs
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end
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return algo
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