Beyond Basic Backtracking

Explore sophisticated backtracking techniques that solve complex computational problems efficiently.

Sudoku Solver: A Complex Backtracking Example

func solveSudoku(board [][]byte) bool {
    for row := 0; row < 9; row++ {
        for col := 0; col < 9; col++ {
            if board[row][col] == '.' {
                for num := byte('1'); num <= byte('9'); num++ {
                    if isValidMove(board, row, col, num) {
                        board[row][col] = num
                        
                        if solveSudoku(board) {
                            return true
                        }
                        
                        board[row][col] = '.'  // Backtrack
                    }
                }
                return false
            }
        }
    }
    return true
}

func isValidMove(board [][]byte, row, col int, num byte) bool {
    // Check row, column, and 3x3 sub-box
    // Implementation details...
}
            

Graph Coloring Problem

func graphColoring(graph [][]int, m int) []int {
    colors := make([]int, len(graph))
    
    if colorGraph(graph, m, colors, 0) {
        return colors
    }
    
    return nil
}

func colorGraph(graph [][]int, m int, colors []int, vertex int) bool {
    if vertex == len(graph) {
        return true
    }
    
    for color := 1; color <= m; color++ {
        if isValidColor(graph, vertex, colors, color) {
            colors[vertex] = color
            
            if colorGraph(graph, m, colors, vertex+1) {
                return true
            }
            
            colors[vertex] = 0  // Backtrack
        }
    }
    
    return false
}

func isValidColor(graph [][]int, vertex int, colors []int, color int) bool {
    // Check adjacent vertices' colors
    // Implementation details...
}
            

Generating Permutations

func generatePermutations(arr []int) [][]int {
    var result [][]int
    backtrackPermutations(arr, 0, &result)
    return result
}

func backtrackPermutations(arr []int, start int, result *[][]int) {
    if start == len(arr) {
        perm := make([]int, len(arr))
        copy(perm, arr)
        *result = append(*result, perm)
        return
    }
    
    for i := start; i < len(arr); i++ {
        arr[start], arr[i] = arr[i], arr[start]
        backtrackPermutations(arr, start+1, result)
        arr[start], arr[i] = arr[i], arr[start]  // Backtrack
    }
}
            

Conclusion

Backtracking is a powerful technique for solving complex combinatorial problems by systematically exploring all potential solutions.