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5.8
   Loi de Benford - Corrigé
Niveau 1
  
 
Fichiers:
   Benford.java     

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class Benford {

    /* METHODES UTILTAIRES FOURNIES*/
    // affichage  d'un tableau d'entiers
    public static void print(int[] tab) {
        for (int i = 0; i < tab.length; ++i) {
            System.out.print(tab[i] + " ");
        }
        System.out.println();
    }

    // affichage  d'un tableau de doubles
    public static void print(double[] tab) {
        for (int i = 0; i < tab.length; ++i) {
            System.out.print(tab[i] + " ");
        }
        System.out.println();
    }

    public static void main(String[] args) {

        int[] frequencies = new int[9];
        double[] numbers = new double[25];

        //  TEST 1.1
        System.out.println("Test 1.1 : ");
        fillWithSquare(numbers);
        print(numbers);
        System.out.println();
        // FIN TEST 1.1 

        //TEST 1.2
        System.out.println("Test 1.2 : ");
        System.out.println(extractMaxDigit(0));
        System.out.println(extractMaxDigit(632));
        System.out.println(extractMaxDigit(-221));
        System.out.println(extractMaxDigit(-554.15));
        System.out.println(extractMaxDigit(0.00421));
        System.out.println();
        // FIN TEST 1.2

        //  TEST 1.3
        System.out.println("Test 1.3 : ");
        analyze(numbers, frequencies);
        print(frequencies);
        System.out.println();
        // FIN TEST 1.3

        // TEST 1.4
        System.out.println("Test 1.4 : ");
        // NE DECOMMENTEZ CETTE PARTIE
        // QUE SI VOUS N'AVEZ PAS REUSSI LA PARTIE PRECEDENTE
        // int tab = {7, 4, 3,  5,  2,  2, 0, 1, 1}
        //frequencies  = tab;
        testBenford(frequencies, numbers.length);
        // FIN TEST 1.4
    }

    public static int extractMaxDigit(double number) {
        if (number == 0) {
            return 0;
        } else if (number < 0) {
            number = -number;
        }

        while (number < 1) {
            number *= 10;
        }

        while (number >= 10) {
            number /= 10;
        }

        return (int)number;
    }

    public static void fillWithSquare(double[] numbers) {
        for (int i = 0, j = 0; i < numbers.length; ++i) {
            j = i + 1;
            numbers[i] = j * j / 100.0;
        }
    }

    public static void analyze(double[] numbers, int[] frequencies) {
        for (int i = 0; i < numbers.length; ++i) {
            int j = extractMaxDigit(numbers[i]);
            ++frequencies[j-1];
        }
    }

    public static void testBenford(int[] frequencies, int size) {
        System.out.println("Comparaison des frequences avec les predictions de la loi de Benford :");
        for (int i = 0; i < 9; ++i){
            System.out.print( (i+1) + " : " + 100*(frequencies[i]/(double)size) + "%, ");
            System.out.println( "Benford : "  + Math.log10(1 + 1.0/(i+1))*100 + "%");
        }
    }
}

 

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