Difference of Squares in Lua

문제

참고할 자료와 개념

• Learn Lua in Y Minutes

for 문

• Programming in Lua : 4.3.4 - Numeric for

local total = 0
for i = 1, 10 do -- 마지막의 10을 포함합니다.
	total = total + i -- lua에는 += 이 없습니다
end
print(total) --> 55

함수 정의하기

• Programming in Lua : 5 - Functions

function add(a,b)
	return a + b
end -- 중괄호는 없고 function으로 시작해서 end로 끝납니다.

print(add(1,1)) --> 2

일급함수와 클로저

• Programming in Lua : 6 - More about Functions

function add3(a) return add(a, 3) end
print(add3(1)) --> 4

add2 = function (a) return add(a, 2) end
print(add2(1)) --> 3

풀이된 예제

명령형

local function square_of_sum(n)
	local result = 0
	for i=1, n do
		result = result + i
	end
	return result * result
end

local function sum_of_squares(n)
	local result = 0
	for i=1, n do
		result = result + i * i
	end
	return result
end

local function difference_of_squares(n)
	return square_of_sum(n) - sum_of_squares(n)
end

return {
	square_of_sum = square_of_sum,
	sum_of_squares = sum_of_squares,
	difference_of_squares = difference_of_squares
}

함수형

--    > return square(4)
--    16
local function square(n)
	return n * n
end

--    > return sum({1,2,3})
--    6
local function sum(arr)
	local result = 0
	for _, v in pairs(arr) do
		result = result + v
	end
	return result
end

--    > return map({1,2,3}, function (x) return 2 * x end)
--    {2,4,6}
local function map(table, f)
	local t = {}
	for k,v in pairs(table) do
		t[k] = f(v)
	end
	return t
end

--    > return range(3)
--    {1,2,3}
local function range(n)
	local a = {}    -- new array
	for i=1, n do
		a[i] = i
	end
	return a
end

local function square_of_sum(n)
	return square(sum(range(n)))
end

local function sum_of_squares(n)
	return sum(map(range(n), square))
end

local function difference_of_squares(n)
	return square_of_sum(n) - sum_of_squares(n)
end

return {
	square_of_sum = square_of_sum,
	sum_of_squares = sum_of_squares,
	difference_of_squares = difference_of_squares
}

함수형 라이브러리

local f = require( 'fun')

local function square(n)
	return n * n
end

local function square_of_sum(n)
	return square(f.sum(f.range(1, n)))
end

local function sum_of_squares(n)
	return f.sum(f.map(square, f.range(1, n)))
end

local function difference_of_squares(n)
	return square_of_sum(n) - sum_of_squares(n)
end

return {
	square_of_sum = square_of_sum,
	sum_of_squares = sum_of_squares,
	difference_of_squares = difference_of_squares
}

수학

• 수학방 : 등차수열의 합 공식
• 수학방 : 자연수 거듭제곱의 합 공식, 유도

local function square_of_sum(n)
	local total = n * (1 + n) / 2
	return total * total
end

local function sum_of_squares(n)
	return n * (n + 1) * (2 * n + 1) / 6
end

local function difference_of_squares(n)
	return square_of_sum(n) - sum_of_squares(n)
end

return {
	square_of_sum = square_of_sum,
	sum_of_squares = sum_of_squares,
	difference_of_squares = difference_of_squares
}