package main

import "fmt"

func main() {
    ret := minColors(4, 2)
    fmt.Println(ret)
}

// N * M的棋盘
// 每种颜色的格子数必须相同的
// 相邻格子染的颜色必须不同
// 所有格子必须染色
// 返回至少多少种颜色可以完成任务

func minColors(N int, M int) int {
    // 颜色数量是i
    for i := 2; i < N*M; i++ {
        matrix := make([][]int, N)
        for i := 0; i < N; i++ {
            matrix[i] = make([]int, M)
        }
        // 下面这一句可知，需要的最少颜色数i，一定是N*M的某个因子
        if (N*M)%i == 0 && can(matrix, N, M, i) {
            return i
        }
    }
    return N * M
}

// 在matrix上染色，返回只用pNum种颜色是否可以做到要求
func can(matrix [][]int, N int, M int, pNum int) bool {
    all := N * M
    every := all / pNum
    rest := make([]int, 0)
    rest = append(rest, 0)
    for i := 1; i <= pNum; i++ {
        rest = append(rest, every)
    }
    return process(matrix, N, M, pNum, 0, 0, rest)
}

func process(matrix [][]int, N int, M int, pNum int, row int, col int, rest []int) bool {
    if row == N {
        return true
    }
    if col == M {
        return process(matrix, N, M, pNum, row+1, 0, rest)
    }
    left := 0
    if col != 0 {
        left = matrix[row][col-1]
    }
    up := 0
    if row != 0 {
        up = matrix[row-1][col]
    }
    for color := 1; color <= pNum; color++ {
        if color != left && color != up && rest[color] > 0 {
            count := rest[color]
            rest[color] = count - 1
            matrix[row][col] = color
            if process(matrix, N, M, pNum, row, col+1, rest) {
                return true
            }
            rest[color] = count
            matrix[row][col] = 0
        }
    }
    return false
}

func twoSelectOne(c bool, a int, b int) int {
    if c {
        return a
    } else {
        return b
    }
}