How to stop function being called non stop in lua - lua

Question

I am busy reading the programming in lua 4th edition book and I am struggling with chapter two. The program essentially prints a chess board with 8 queens that are placed in a way that none of them can attack each other. What I am struggling to figure out is why it prints the boards multiple times.
I have went over the code step by step and once the print solution has finished printing the first board I thought it would just end the function and then jump back to the main but for some reason it keeps looping. I am also very new to lua and have just come from C so still getting used to it all.
Image of one of the boards it outputs. The Xs are the queens - https://ibb.co/KsT3R8X
N = 8 -- board size
-- check whether position (n,c) is free from attacks
function isplaceok (a, n, c)
for i = 1, n - 1 do -- for each queen already placed
if (a[i] == c) or -- same column?
(a[i] - i == c - n) or -- same diagonal?
(a[i] + i == c + n) then -- same diagonal?
return false -- place can be attacked
end
end
return true -- no attacks; place is OK
end
-- print a board
function printsolution (a)
for i = 1, N do -- for each row
for j = 1, N do -- and for each column
-- write "X" or "-" plus a space
io.write(a[i] == j and "X" or "-", " ")
end
io.write("\n")
end
io.write("\n")
end
-- add to board 'a' all queens from 'n' to 'N'
function addqueen (a, n)
if n > N then -- all queens have been placed?
printsolution(a)
else -- try to place n-th queen
for c = 1, N do
if isplaceok(a, n, c) then
a[n] = c -- place n-th queen at column 'c'
addqueen(a, n + 1)
end
end
end
end
-- run the program
addqueen({}, 1)

Answer 1

The program is printing all 92 possible solutions for the 8x8 chessboard.
Which is likely the intention, so it would appear to be working correctly.
To stop after we find 1 solution we can add a variable found to the program:
local found = false
-- print a board
function printsolution (a)
for i = 1, N do -- for each row
for j = 1, N do -- and for each column
-- write "X" or "-" plus a space
io.write(a[i] == j and "X" or "-", " ")
end
io.write("\n")
end
io.write("\n")
found = true
end
-- add to board 'a' all queens from 'n' to 'N'
function addqueen (a, n)
if n > N then -- all queens have been placed?
printsolution(a)
else -- try to place n-th queen
for c = 1, N do
if isplaceok(a, n, c) and found == false then
a[n] = c -- place n-th queen at column 'c'
addqueen(a, n + 1)
end
end
end
end
This found variable stops the continued recursion of the existing loops as we move back up the stack.
Now why is it that this code works this way, where are all the solutions coming from?
That has to do with the for loop in addqueen:
for c = 1, N do
if isplaceok(a, n, c) then
a[n] = c
addqueen(a, n + 1)
end
end
Each loop of the for loop sends the code deeper by recursively calling addqueen. The stack will never be deeper then 9 as that is the limit set by the N
The first solution after 114 calls to addqueen is this one:
X - - - - - - -
- - - - X - - -
- - - - - - - X
- - - - - X - -
- - X - - - - -
- - - - - - X -
- X - - - - - -
- - - X - - - -
The 5th solution is the first time we will have come back to our original call of addqueen, you can see the first X has moved from 1x1 to 1x2(n=1 c=2, second step of our original for loop):
- X - - - - - -
- - - X - - - -
- - - - - X - -
- - - - - - - X
- - X - - - - -
X - - - - - - -
- - - - - - X -
- - - - X - - -
In the end we call addqueen 1952 times for the program to check all the possible solutions.
You can adjust the code to print a value of the depth to get a better idea of how the stack looks as the program runs:
-- add to board 'a' all queens from 'n' to 'N'
function addqueen (a, n)
print(n .. "↓")
if n > N then -- all queens have been placed?
printsolution(a)
else -- try to place n-th queen
for c = 1, N do
if isplaceok(a, n, c) then
a[n] = c -- place n-th queen at column 'c'
addqueen(a, n + 1)
end
end
end
print(n - 1 .. "↑")
end