algorithm-class/算法周更班/class_2022_05_2_week/Code05_RedAndWhiteSquares.java

package class_2022_05_2_week;

// 来自网易
// 小红拿到了一个大立方体，该大立方体由1*1*1的小方块拼成，初始每个小方块都是白色。
// 小红可以每次选择一个小方块染成红色
// 每次小红可能选择同一个小方块重复染色
// 每次染色以后，你需要帮小红回答出当前的白色连通块数
// 如果两个小方块共用同一个面，且颜色相同，则它们是连通的
// 给定n、m、h，表示大立方体的长、宽、高
// 给定k次操作，每一次操作用(a, b, c)表示在大立方体的该位置进行染色
// 返回长度为k的数组，表示每一次操作后，白色方块的连通块数
// n * m * h <= 10 ^ 5，k <= 10 ^ 5
public class Code05_RedAndWhiteSquares {

	// 暴力方法
	// 时间复杂度(k * n * m * h);
	public static int[] blocks1(int n, int m, int h, int[][] ops) {
		int k = ops.length;
		int[][][] cube = new int[n][m][h];
		int value = 1;
		int[] ans = new int[k];
		for (int i = 0; i < k; i++) {
			cube[ops[i][0]][ops[i][1]][ops[i][2]] = -1;
			for (int x = 0; x < n; x++) {
				for (int y = 0; y < m; y++) {
					for (int z = 0; z < h; z++) {
						if (cube[x][y][z] != -1 && cube[x][y][z] != value) {
							ans[i]++;
							infect(cube, x, y, z, value);
						}
					}
				}
			}
			value++;
		}
		return ans;
	}

	public static void infect(int[][][] cube, int a, int b, int c, int change) {
		if (a < 0 || a == cube.length || b < 0 || b == cube[0].length || c < 0 || c == cube[0][0].length
				|| cube[a][b][c] == -1 || cube[a][b][c] == change) {
			return;
		}
		cube[a][b][c] = change;
		infect(cube, a - 1, b, c, change);
		infect(cube, a + 1, b, c, change);
		infect(cube, a, b - 1, c, change);
		infect(cube, a, b + 1, c, change);
		infect(cube, a, b, c - 1, change);
		infect(cube, a, b, c + 1, change);
	}

	// 最优解
	// O(k + n * m * h)
	public static int[] blocks2(int n, int m, int h, int[][] ops) {
		int k = ops.length;
		int[][][] red = new int[n][m][h];
		for (int[] op : ops) {
			red[op[0]][op[1]][op[2]]++;
		}
		UnionFind uf = new UnionFind(n, m, h, red);
		int[] ans = new int[k];
		for (int i = k - 1; i >= 0; i--) {
			ans[i] = uf.sets;
			int x = ops[i][0];
			int y = ops[i][1];
			int z = ops[i][2];
			if (--red[x][y][z] == 0) {
				// x, y ,z 这个格子，变白，建立自己的小集合
				// 然后6个方向，集合该合并合并
				uf.finger(x, y, z);
			}
		}
		return ans;
	}

	public static class UnionFind {
		public int n;
		public int m;
		public int h;
		public int[] father;
		public int[] size;
		public int[] help;
		public int sets;

		public UnionFind(int a, int b, int c, int[][][] red) {
			n = a;
			m = b;
			h = c;
			int len = n * m * h;
			father = new int[len];
			size = new int[len];
			help = new int[len];
			for (int x = 0; x < n; x++) {
				for (int y = 0; y < m; y++) {
					for (int z = 0; z < h; z++) {
						if (red[x][y][z] == 0) {
							finger(x, y, z);
						}
					}
				}
			}
		}

		public void finger(int x, int y, int z) {
			// x，y，z
			// 一维数值
			int i = index(x, y, z);
			father[i] = i;
			size[i] = 1;
			sets++;
			union(i, x - 1, y, z);
			union(i, x + 1, y, z);
			union(i, x, y - 1, z);
			union(i, x, y + 1, z);
			union(i, x, y, z - 1);
			union(i, x, y, z + 1);
		}

		private int index(int x, int y, int z) {
			return z * n * m + y * n + x;
		}

		private void union(int i, int x, int y, int z) {
			if (x < 0 || x == n || y < 0 || y == m || z < 0 || z == h) {
				return;
			}
			int j = index(x, y, z);
			if (size[j] == 0) {
				return;
			}
			i = find(i);
			j = find(j);
			if (i != j) {
				if (size[i] >= size[j]) {
					father[j] = i;
					size[i] += size[j];
				} else {
					father[i] = j;
					size[j] += size[i];
				}
				sets--;
			}
		}

		private int find(int i) {
			int s = 0;
			while (i != father[i]) {
				help[s++] = i;
				i = father[i];
			}
			while (s > 0) {
				father[help[--s]] = i;
			}
			return i;
		}

	}

	// 为了测试
	public static int[][] randomOps(int n, int m, int h) {
		int size = (int) (Math.random() * (n * m * h)) + 1;
		int[][] ans = new int[size][3];
		for (int i = 0; i < size; i++) {
			ans[i][0] = (int) (Math.random() * n);
			ans[i][1] = (int) (Math.random() * m);
			ans[i][2] = (int) (Math.random() * h);
		}
		return ans;
	}

	// 为了测试
	public static void main(String[] args) {
		int size = 10;
		int testTime = 5000;
		System.out.println("测试开始");
		for (int i = 0; i < testTime; i++) {
			int n = (int) (Math.random() * size) + 1;
			int m = (int) (Math.random() * size) + 1;
			int h = (int) (Math.random() * size) + 1;
			int[][] ops = randomOps(n, m, h);
			int[] ans1 = blocks1(n, m, h, ops);
			int[] ans2 = blocks2(n, m, h, ops);
			for (int j = 0; j < ops.length; j++) {
				if (ans1[j] != ans2[j]) {
					System.out.println("出错了!");
				}
			}
		}
		System.out.println("测试结束");

		// 立方体达到10^6规模
		int n = 100;
		int m = 100;
		int h = 100;
		int len = n * m * h;
		// 操作条数达到10^6规模
		int[][] ops = new int[len][3];
		for (int i = 0; i < len; i++) {
			ops[i][0] = (int) (Math.random() * n);
			ops[i][1] = (int) (Math.random() * m);
			ops[i][2] = (int) (Math.random() * h);
		}
		long start = System.currentTimeMillis();
		blocks2(n, m, h, ops);
		long end = System.currentTimeMillis();
		System.out.println("运行时间(毫秒) : " + (end - start));

	}

}