【算法】乱序检查

乱序检查。通过实验检查表中的乱序代码是否能够产生预期的效果。编写一个程序

ShuffleTest，接受命令行参数M和N，将大小为M的数组打乱N次且在每次打乱之前都将数组

重新初始化为a[i] = i。打印一个MxM的表格，对于所有的列j，行i表示的是i在打乱后

落到j的位置的次数。数组中的所有元素的值都应该接近于N/M。

乱序代码：（StdRandom来自http://algs4.cs.princeton.edu/code/stdlib.jar）

    /**
     * Rearrange the elements of a double array in random order.
     */
    public static void shuffle(double[] a) {
        int N = a.length;
        for (int i = 0; i < N; i++) {
            int r = i + uniform(N-i);     // between i and N-1
            double temp = a[i];
            a[i] = a[r];
            a[r] = temp;
        }
    }

实验代码：

package com.beyond.algs4.experiment;

import com.beyond.algs4.lib.StdIn;
import com.beyond.algs4.lib.StdOut;
import com.beyond.algs4.lib.StdRandom;

public class ShuffleTest {

    public static class RandomArray {
        private int M = 0;
        private int[] a = null;

        public int[] getA() {
            return a;
        }

        public void setA(int[] a) {
            this.a = a;
        }

        public RandomArray(int M) {
            this.M = M;
            this.a = new int[M];
            for (int i = 0; i < M; i++) {
                a[i] = i;
            }
        }
    }
    
    public static class RandomChecker {
        private double[][] matrix = null;
        public double[][] getMatrix() {
            return matrix;
        }


        private int M = 0;
        private int N = 0;
        
        public RandomChecker(int M, int N) {
            this.M = M;
            this.N = N;
            matrix = new double[M][];
            for (int i = 0; i < matrix.length; i++) {
                matrix[i] = new double[M];
            }
        }
        
        public void execute() {
            for (int n = 0; n < this.N; n++) {
                RandomArray c = new RandomArray(M);
                int[] a = c.getA();
                StdRandom.shuffle(a);
                for (int k = 0; k < a.length; k++) {
                    int i = a[k];
                    int j = k;
                    matrix[i][j] += 1;
                }
                
            }
        }
        
        public void print() {
            for (int i = 0; i < M; i++) {
                for (int j = 0; j < M; j++) {
                    StdOut.print(matrix[i][j] + "	");
                }
                StdOut.print("
");
            }
        }
    }
    
    public static class BadRandomChecker {
        private double[][] matrix = null;
        public double[][] getMatrix() {
            return matrix;
        }


        private int M = 0;
        private int N = 0;
        
        public BadRandomChecker(int M, int N) {
            this.M = M;
            this.N = N;
            matrix = new double[M][];
            for (int i = 0; i < matrix.length; i++) {
                matrix[i] = new double[M];
            }
        }
        
        public void execute() {
            for (int n = 0; n < this.N; n++) {
                RandomArray c = new RandomArray(M);
                int[] a = c.getA();
                shuffle(a);
                for (int k = 0; k < a.length; k++) {
                    int i = a[k];
                    int j = k;
                    matrix[i][j] += 1;
                }
                
            }
        }
        
        public void print() {
            for (int i = 0; i < M; i++) {
                for (int j = 0; j < M; j++) {
                    StdOut.print(matrix[i][j] + "	");
                }
                StdOut.print("
");
            }
        }
        
        public static void shuffle(int[] a) {
            int N = a.length;
            for (int i = 0; i < N; i++) {
                int r = StdRandom.uniform(N-i);     // between 0 and N-1
                int temp = a[i];
                a[i] = a[r];
                a[r] = temp;
            }
        }
    }

    public static void main(String[] args) {
        StdOut.println("Please input M: ");
        int M = StdIn.readInt();
        StdOut.println("Please input N: ");
        int N = StdIn.readInt();
        StdOut.println("Random Check: ");
        RandomChecker rc = new RandomChecker(M, N);
        rc.execute();
        rc.print();
        
        StdOut.println("Bad Random: ");
        BadRandomChecker br = new BadRandomChecker(M, N);
        br.execute();
        br.print();
    }
}

实验结果：

 Please input M:
10
Please input N:
1000

ij	1	2	3	4	5	6	7	8	9	10
1	108	106	95	102	98	85	104	101	112	89
2	102	102	96	99	113	84	88	105	102	109
3	101	99	84	92	103	104	96	118	100	103
4	107	104	112	88	96	104	101	98	84	106
5	76	104	111	102	97	113	101	93	110	93
6	107	103	91	121	96	123	86	103	87	83
7	98	103	94	98	94	109	116	89	98	101
8	97	79	91	102	94	97	105	99	107	129
9	98	104	102	116	93	107	105	97	90	88
10	106	96	124	80	116	74	98	97	110	99

Please input M:
5
Please input N:
100

ij	1	2	3	4	5
1	13	17	22	20	28
2	27	15	25	19	14
3	15	23	22	23	17
4	19	26	18	17	20
5	26	19	13	21	21

结果分析：
当M<N时，数组中的所有元素的值都应该接近于N/M。但当M>N时，无法得出结论。

糟糕的打乱。假设在我们的乱序代码中你选择的是一个0到N-1而非i到N-1之间的随机整数。

证明得到的结果并非均匀的分布在N!种可能性之间。用乱序检查的测试检验这个版本。

实验结果：

Please input M:
10
Please input N:
1000

ij	1	2	3	4	5	6	7	8	9	10
1	95	101	131	89	103	83	114	96	93	95
2	0	107	112	100	116	128	118	111	100	108
3	0	62	98	119	134	118	146	136	132	55
4	0	54	100	118	136	180	136	139	95	42
5	0	47	82	154	146	188	187	97	72	27
6	0	32	75	161	228	110	147	136	64	47
7	0	54	139	213	43	77	60	211	151	52
8	0	148	252	23	48	66	50	23	260	130
9	0	395	6	15	32	33	31	38	17	433
10	905	0	5	8	14	17	11	13	16	11

Please input M:
5
Please input N:
100

ij	1	2	3	4	5
1	18	18	23	17	24
2	0	22	29	32	17
3	0	15	31	40	14
4	0	44	10	8	38
5	82	1	7	3	7

参考资料：

算法 第四版  谢路云 译 Algorithms Fourth Edition [美] Robert Sedgewick, Kevin Wayne著

http://algs4.cs.princeton.edu/home/

源码下载链接：

 http://pan.baidu.com/s/1pJ0xicF