From bb078d798b1ebc59aa61f7d056fa7c45a2a72d7d Mon Sep 17 00:00:00 2001
From: Reza Behzadan <rbehzadan@gmail.com>
Date: Wed, 20 May 2020 14:40:38 +0430
Subject: [PATCH] import sudoku logic codes

---
 boards.lua |  38 ++++++++++++++++++
 check.lua  | 116 +++++++++++++++++++++++++++++++++++++++++++++++++++++
 demo.lua   |   0
 sudoku.lua |  44 ++++++++++++++++++++
 utils.lua  |  28 +++++++++++++
 5 files changed, 226 insertions(+)
 create mode 100644 boards.lua
 create mode 100644 check.lua
 create mode 100644 demo.lua
 create mode 100644 sudoku.lua
 create mode 100644 utils.lua

diff --git a/boards.lua b/boards.lua
new file mode 100644
index 0000000..562cc2a
--- /dev/null
+++ b/boards.lua
@@ -0,0 +1,38 @@
+board = {{}, {}}
+
+board[1].problem = {
+    {5, 3, 0, 0, 7, 0, 0, 0, 0},
+    {6, 0, 0, 1, 9, 5, 0, 0, 0},
+    {0, 9, 8, 0, 0, 0, 0, 6, 0},
+    {8, 0, 0, 0, 6, 0, 0, 0, 3},
+    {4, 0, 0, 8, 0, 3, 0, 0, 1},
+    {7, 0, 0, 0, 2, 0, 0, 0, 6},
+    {0, 6, 0, 0, 0, 0, 2, 8, 0},
+    {0, 0, 0, 4, 1, 9, 0, 0, 5},
+    {0, 0, 0, 0, 8, 0, 0, 7, 9},
+}
+
+board[1].solution = {
+    {5, 3, 4, 6, 7, 8, 9, 1, 2},
+    {6, 7, 2, 1, 9, 5, 3, 4, 8},
+    {1, 9, 8, 3, 4, 2, 5, 6, 7},
+    {8, 5, 9, 7, 6, 1, 4, 2, 3},
+    {4, 2, 6, 8, 5, 3, 7, 9, 1},
+    {7, 1, 3, 9, 2, 4, 8, 5, 6},
+    {9, 6, 1, 5, 3, 7, 2, 8, 4},
+    {2, 8, 7, 4, 1, 9, 6, 3, 5},
+    {3, 4, 5, 2, 8, 6, 1, 7, 9},
+}
+
+
+board[2].problem = {
+    {8, 0, 0, 0, 5, 0, 0, 0, 7},
+    {0, 6, 1, 0, 0, 0, 0, 0, 0},
+    {3, 7, 0, 0, 0, 0, 0, 6, 8},
+    {0, 0, 0, 6, 0, 0, 8, 0, 0},
+    {0, 1, 0, 0, 9, 0, 0, 2, 0},
+    {0, 3, 0, 2, 0, 0, 0, 9, 0},
+    {0, 8, 0, 0, 0, 7, 0, 0, 0},
+    {0, 0, 0, 0, 0, 0, 4, 0, 1},
+    {0, 0, 5, 0, 0, 0, 9, 8, 3},
+}
diff --git a/check.lua b/check.lua
new file mode 100644
index 0000000..a1383c3
--- /dev/null
+++ b/check.lua
@@ -0,0 +1,116 @@
+local function checkCT(ct)
+    local r = {}
+    for i = 1, 8 do
+        for j = i+1, 9 do
+            if ct[i] == ct[j] and ct[i] ~= 0 then
+                table.insert(r, {i, j})
+            end
+        end
+    end
+    if #r > 0 then return false, r end
+    return true
+end
+
+local function findThisTable(this, that)
+    for i = 1, #that do
+        if #that[i] == #this then
+            local flag = true
+            for j = 1, #this do
+                if this[j] ~= that[i][j] then flag = false; break end
+            end
+            if flag then return true, i end
+        end
+    end
+    return false
+end
+
+function check(board)
+    local rr = {}
+    for x = 1, 9 do
+        local ct = {}
+        for y = 1, 9 do
+            ct[y] = board[x][y]
+        end
+        local ok, r = checkCT(ct)
+        if not ok then
+            for _, p in ipairs(r) do
+                local t = {x, p[1], x, p[2], board[x][p[1]]}
+                if not findThisTable(t, rr) then
+                    table.insert(rr, t)
+                end
+            end
+        end
+    end
+    for y = 1, 9 do
+        local ct = {}
+        for x = 1, 9 do
+            ct[x] = board[x][y]
+        end
+        local ok, r = checkCT(ct)
+        if not ok then
+            for _, p in ipairs(r) do
+                local t = {p[1], y, p[2], y, board[p[1]][y]}
+                if not findThisTable(t, rr) then
+                    table.insert(rr, t)
+                end
+            end
+        end
+    end
+    for i = 0, 2 do
+        for j = 0, 2 do
+            local ct = {}
+            for x = 1, 3 do
+                for y = 1, 3 do
+                    ct[(x-1)*3+y] = board[x+i*3][y+j*3]
+                end
+            end
+            local ok, r = checkCT(ct)
+            if not ok then
+                for _, p in ipairs(r) do
+                    local x1 = ((p[1] - 1) // 3 + 1) + i * 3
+                    local y1 = ((p[1] - 1) % 3 + 1) + j * 3
+                    local x2 = ((p[2] - 1) // 3 + 1) + i * 3
+                    local y2 = ((p[2] - 1) % 3 + 1) + j * 3
+                    local t = {x1, y1, x2, y2, board[x1][y1]}
+                    if not findThisTable(t, rr) then
+                        table.insert(rr, t)
+                    end
+                end
+            end
+        end
+    end
+    if #rr > 0 then
+        return false, rr
+    end
+    return true
+end
+
+function checkSolved(board)
+    local r = {}
+    for i = 1, 9 do
+        for j = 1, 9 do
+            if board[i][j] < 1 or board[i][j] > 9 then
+                table.insert(r, {i, j, board[i][j]})
+            end
+        end
+    end
+    local ok, rr = check(board)
+    if #r > 0 or (rr and #rr > 0) then
+        return false, r, rr
+    end
+    return true
+end
+
+function pcheck(board)
+    local ok, r, rr = checkSolved(board)
+    if ok then
+        print("Board is solved!")
+        return 
+    end
+    for _, p in ipairs(r) do
+        print(S("(%d, %d) = %d", unpack(p)))
+    end
+    for _, p in ipairs(rr) do
+        print(S("(%d, %d) = (%d, %d) = %d", unpack(p)))
+    end
+end
diff --git a/demo.lua b/demo.lua
new file mode 100644
index 0000000..e69de29
diff --git a/sudoku.lua b/sudoku.lua
new file mode 100644
index 0000000..70ee9e4
--- /dev/null
+++ b/sudoku.lua
@@ -0,0 +1,44 @@
+require "utils"
+
+function calValidOptions(b, x, y)
+    if b[x][y] ~= 0 then return {} end
+    local elm
+    local u = {}
+    local v = {}
+    for i = 1, 9 do
+        elm = b[x][i]
+        if elm ~= 0 and find(u, elm) == 0 then
+            table.insert(u, elm)
+        end
+        elm = b[i][y]
+        if elm ~= 0 and find(u, elm) == 0 then
+            table.insert(u, elm)
+        end
+    end
+    local xc = ((x - 1) // 3) * 3
+    local yc = ((y - 1) // 3) * 3
+    for i = 1, 3 do
+        for j = 1, 3 do
+            elm = b[i+xc][j+yc]
+            if elm ~= 0 and find(u, elm) == 0 then
+                table.insert(u, elm)
+            end
+        end
+    end
+    for i = 1, 9 do
+        if find(u, i) == 0 then table.insert(v, i) end
+    end
+    return v
+end
+
+function buildSearchSpace(b)
+    local s = {}
+    for i = 1, 9 do
+        s[i] = {}
+        for j = 1, 9 do
+            s[i][j] = calValidOptions(b, i, j)
+        end
+    end
+    return s
+end
+
diff --git a/utils.lua b/utils.lua
new file mode 100644
index 0000000..a16c2e7
--- /dev/null
+++ b/utils.lua
@@ -0,0 +1,28 @@
+function find(array, element)
+    local index = 0
+    for i = 1, #array do
+        if array[i] == element then
+            index = i
+            break
+        end
+    end
+    return index
+end
+
+function showBoard(board)
+    for row = 1, 9 do
+        print(table.concat(board[row], " "))
+    end
+end
+
+function cloneBoard(b)
+    local c = {}
+    for i = 1, 9 do
+        c[i] = {}
+        for j = 1, 9 do
+            c[i][j] = b[i][j]
+        end
+    end
+    return c
+end
+