|
|
package class24;
|
|
|
|
|
|
import java.util.ArrayList;
|
|
|
import java.util.List;
|
|
|
|
|
|
public class Code04_Painting {
|
|
|
// 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
|
|
|
|
|
|
public static int minColors(int N, int M) {
|
|
|
// 颜色数量是i
|
|
|
for (int i = 2; i < N * M; i++) {
|
|
|
int[][] matrix = new int[N][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
|
|
|
public static boolean can(int[][] matrix, int N, int M, int pNum) {
|
|
|
int all = N * M;
|
|
|
int every = all / pNum;
|
|
|
ArrayList<Integer> rest = new ArrayList<>();
|
|
|
rest.add(0);
|
|
|
for (int i = 1; i <= pNum; i++) {
|
|
|
rest.add(every);
|
|
|
}
|
|
|
return process(matrix, N, M, pNum, 0, 0, rest);
|
|
|
}
|
|
|
|
|
|
public static boolean process(int[][] matrix, int N, int M, int pNum, int row, int col, List<Integer> rest) {
|
|
|
if (row == N) {
|
|
|
return true;
|
|
|
}
|
|
|
if (col == M) {
|
|
|
return process(matrix, N, M, pNum, row + 1, 0, rest);
|
|
|
}
|
|
|
int left = col == 0 ? 0 : matrix[row][col - 1];
|
|
|
int up = row == 0 ? 0 : matrix[row - 1][col];
|
|
|
for (int color = 1; color <= pNum; color++) {
|
|
|
if (color != left && color != up && rest.get(color) > 0) {
|
|
|
int count = rest.get(color);
|
|
|
rest.set(color, count - 1);
|
|
|
matrix[row][col] = color;
|
|
|
if (process(matrix, N, M, pNum, row, col + 1, rest)) {
|
|
|
return true;
|
|
|
}
|
|
|
rest.set(color, count);
|
|
|
matrix[row][col] = 0;
|
|
|
}
|
|
|
}
|
|
|
return false;
|
|
|
}
|
|
|
|
|
|
public static void main(String[] args) {
|
|
|
// 根据代码16行的提示，打印出答案，看看是答案是哪个因子
|
|
|
for (int N = 2; N < 10; N++) {
|
|
|
for (int M = 2; M < 10; M++) {
|
|
|
System.out.println("N = " + N);
|
|
|
System.out.println("M = " + M);
|
|
|
System.out.println("ans = " + minColors(N, M));
|
|
|
System.out.println("===========");
|
|
|
}
|
|
|
}
|
|
|
// 打印答案，分析可知，是N*M最小的质数因子，原因不明，也不重要
|
|
|
// 反正打表法猜出来了
|
|
|
}
|
|
|
|
|
|
}
|
