From 59ba2684f3ba3051522d84f827c109f9bab1b5f0 Mon Sep 17 00:00:00 2001
From: Yi Heng <yihengwang2000@gmail.com>
Date: Tue, 23 Jan 2024 00:57:07 -0500
Subject: [PATCH] Finished SolveSudoku

---
 sudoku.go | 67 +++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 67 insertions(+)

diff --git a/sudoku.go b/sudoku.go
index 06ab7d0..99be780 100644
--- a/sudoku.go
+++ b/sudoku.go
@@ -1 +1,68 @@
 package main
+
+const BOARD_SIZE = 9
+
+const EMPTY_CELL = 0
+
+func SolveSudoku(board [][]int) [][]int {
+	solveWrapper(board)
+	return board
+}
+
+// solveWrapper is a recursive helper function for solving the Sudoku puzzle. It returns true if it can be solved and false otherwise.
+func solveWrapper(board [][]int) bool {
+
+	// loop over every position of the board, ...
+	for row := 0; row < BOARD_SIZE; row++ {
+		for col := 0; col < BOARD_SIZE; col++ {
+			if board[row][col] == EMPTY_CELL {
+				// ... trying to place a valid number from 1 to 9 on every empty cell
+				for num := 1; num <= 9; num++ {
+					if !hasDuplicateNumbersIn3x3Grid(board, row, col, num) && !hasDuplicateNumbersInLine(board, row, col, num) {
+						board[row][col] = num // set the current number when it does not violate sudoku rules...
+						if solveWrapper(board) { // ... and determine if it can be part of the solution for the sudoku
+							return true
+						} else {
+							board[row][col] = EMPTY_CELL // if it cannot be part of the solution, reinitialize to empty cell
+						}
+					}
+				}
+
+				// when no number can be placed, backtrack by returning false
+				return false
+			}
+		}
+	}
+
+	// when every cell has been filled, return true
+	return true
+}
+
+// hasDuplicateNumbersInLine returns true if a duplicate exists horizontally/vertically at board[row][col] and false otherwise
+func hasDuplicateNumbersInLine(board [][]int, row, col, num int) bool {
+	for i := 0; i < BOARD_SIZE; i++ {
+		if board[row][i] == num || board[i][col] == num {
+			return true
+		}
+	}
+	return false
+}
+
+// hasDuplicateNumbersIn3x3Grid returns true if a duplicate exists in a 3x3 subgrid and false otherwise
+// It gets the middle of the 3x3 grid and iterates over all 9 possible locations through coordinates
+func hasDuplicateNumbersIn3x3Grid(board [][]int, row, col, num int) bool {
+	middleCellRowValue, middleCellColValue := row - row%3 + 1, col - col%3 + 1
+	offsets := [][2]int{
+		{-1, -1}, {-1, 0}, {-1, 1},
+		{0, -1}, {0, 0}, {0, 1},
+		{1, -1}, {1, 0}, {1, 1},
+	}
+	for _, offset := range offsets {
+		row, col = middleCellRowValue + offset[0], middleCellColValue + offset[1]
+		if board[row][col] == num {
+			return true
+		}
+	}
+	return false
+}
+