First commit

exercises/ch02/correct_board.txt

@@ -0,0 +1,8 @@
+X - - - - - - -
+- - - - X - - -
+- - - - - - - X
+- - - - - X - -
+- - X - - - - -
+- - - - - - X -
+- X - - - - - -
+- - - X - - - -

exercises/ch02/ex1.lua

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+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)
+        os.exit(0)
+    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)

exercises/ch02/ex2.lua

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+N = 8 -- board size
+
+-- check whether position (n,c) is free from attacks
+local 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
+local 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
+
+local function reverse(a, s, e)
+    for i = s, e / 2 do
+        local counter_i = e - (i - 1)
+        local tmp = a[i]
+        a[i] = a[counter_i]
+        a[counter_i] = tmp
+    end
+end
+
+local function generatePermutations()
+    local p1 = { 1, 2, 3, 4, 5, 6, 7, 8}
+    local ps = {p1}
+
+    while true do
+        local newP = {}
+        local last_p = ps[#ps]
+        for i = 1, #last_p do
+            newP[i] = last_p[i]
+        end
+
+        local k = nil
+        for i = #newP, 1, -1 do
+            if newP[i + 1] == nil then
+                goto continue
+            end
+            if newP[i] < newP[i + 1] then
+                k = i
+                break
+            end
+            ::continue::
+        end
+        if k == nil then
+            break
+        end
+
+        local l = nil
+        for i = #newP, 1, -1 do
+            if newP[k] < newP[i] then
+                l = i
+                break
+            end
+        end
+
+        if l == nil then
+            print("ERROR: l was nil")
+            os.exit(1)
+        end
+
+        local tmp = newP[k]
+        newP[k] = newP[l]
+        newP[l] = tmp
+
+        reverse(newP, k + 1, #newP)
+
+        print(k, l)
+
+        table.insert(ps, newP)
+    end
+
+    return ps
+end
+
+local perms = generatePermutations()
+for i = 1, #perms do
+    print(table.unpack(perms[i]))
+end
+
+print(#perms)

exercises/ch02/orig.lua

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+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)

exercises/ch02/reverse.lua

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+local function reverse(a, s, e)
+    for i = s, e / 2 do
+        local counter_i = e - (i - 1)
+        local tmp = a[i]
+        a[i] = a[counter_i]
+        a[counter_i] = tmp
+    end
+end
+
+local a = {5, 3, 8, 1}
+reverse(a, 1, #a)
+print(table.unpack(a))