【演算法】亂序檢查

Richaaaard發表於2015-06-15
演算法

亂序檢查。通過實驗檢查表中的亂序程式碼是否能夠產生預期的效果。編寫一個程式

ShuffleTest，接受命令列引數M和N，將大小為M的陣列打亂N次且在每次打亂之前都將陣列

重新初始化為a[i] = i。列印一個MxM的表格，對於所有的列j，行i表示的是i在打亂後

落到j的位置的次數。陣列中的所有元素的值都應該接近於N/M。

亂序程式碼：（StdRandom來自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;
        }
    }

實驗程式碼：

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] + "\t");
                }
                StdOut.print("\n");
            }
        }
    }
    
    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] + "\t");
                }
                StdOut.print("\n");
            }
        }
        
        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();
    }
}

 

實驗結果：

 Please input M:
10
Please input N:
1000

i\j 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

i\j 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

結果分析：
當M<N時，陣列中的所有元素的值都應該接近於N/M。但當M>N時，無法得出結論。

糟糕的打亂。假設在我們的亂序程式碼中你選擇的是一個0到N-1而非i到N-1之間的隨機整數。

證明得到的結果並非均勻的分佈在N!種可能性之間。用亂序檢查的測試檢驗這個版本。

實驗結果：

Please input M:
10
Please input N:
1000

i\j 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

i\j 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

 

參考資料：

演算法 第四版  謝路雲 譯 Algorithms Fourth Edition [美] Robert Sedgewick, Kevin Wayne著

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

原始碼下載連結：

 http://pan.baidu.com/s/1pJ0xicF

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