问题
包含整数的二维矩阵 M 表示一个图片的灰度。你需要设计一个平滑器来让每一个单元的灰度成为平均灰度 (向下舍入) ，平均灰度的计算是周围的8个单元和它本身的值求平均，如果周围的单元格不足八个，则尽可能多的利用它们。
输入:
[[1,1,1],
[1,0,1],
[1,1,1]]输出:
[[0, 0, 0],
[0, 0, 0],
[0, 0, 0]]解释:
对于点 (0,0), (0,2), (2,0), (2,2): 平均(3/4) = 平均(0.75) = 0
对于点 (0,1), (1,0), (1,2), (2,1): 平均(5/6) = 平均(0.83333333) = 0
对于点 (1,1): 平均(8/9) = 平均(0.88888889) = 0
注意:
给定矩阵中的整数范围为 [0, 255]。
矩阵的长和宽的范围均为 [1, 150]。
Given a 2D integer matrix M representing the gray scale of an image, you need to design a smoother to make the gray scale of each cell becomes the average gray scale (rounding down) of all the 8 surrounding cells and itself. If a cell has less than 8 surrounding cells, then use as many as you can.
Input:
[[1,1,1],
[1,0,1],
[1,1,1]]Output:
[[0, 0, 0],
[0, 0, 0],
[0, 0, 0]]Explanation:
For the point (0,0), (0,2), (2,0), (2,2): floor(3/4) = floor(0.75) = 0
For the point (0,1), (1,0), (1,2), (2,1): floor(5/6) = floor(0.83333333) = 0
For the point (1,1): floor(8/9) = floor(0.88888889) = 0
Note:
The value in the given matrix is in the range of [0, 255].
The length and width of the given matrix are in the range of [1, 150].
示例
public class Program {
public static void Main(string[] args) {
int[,] nums = null;
nums = new int[,] { { 1, 1, 1 }, { 1, 0, 1 }, { 1, 1, 1 } };
var res = ImageSmoother(nums);
ShowArray(res);
Console.ReadKey();
}
private static void ShowArray(int[,] array) {
foreach(var num in array) {
Console.Write($"{num} ");
}
Console.WriteLine();
}
private static int[,] ImageSmoother(int[,] M) {
int[,] result = M.Clone() as int[,];
for(int i = 0; i < M.GetLength(0); i++) {
for(int j = 0; j < M.GetLength(1); j++) {
result[i, j] = ComputerSmoothValue(M, i, j);
}
}
return result;
}
private static int ComputerSmoothValue(int[,] M, int i, int j) {
//以某个数为中心，求9个数的平均值即可
//该题主要考查边界的处理
int count = 0;
int sum = 0;
for(int m = Math.Max(i - 1, 0); m <= Math.Min(i + 1, M.GetLength(0) - 1); m++) {
for(int n = Math.Max(j - 1, 0); n <= Math.Min(j + 1, M.GetLength(1) - 1); n++) {
count++;
sum += M[m, n];
}
}
return sum / count;
}
}以上给出1种算法实现，以下是这个案例的输出结果：
0 0 0 0 0 0 0 0 0分析：
假设原二维数组有m行，n列，ComputerSmoothValue的执行次数在最坏的情况会执行9次，ComputerSmoothValue执行的次数为m*n次，故以上算法的时间复杂度为： 。