Class StdRandom


  • public final class StdRandom
    extends java.lang.Object
    The StdRandom class provides static methods for generating random number from various discrete and continuous distributions, including Bernoulli, uniform, Gaussian, exponential, pareto, Poisson, and Cauchy. It also provides method for shuffling an array or subarray.

    For additional documentation, see Section 2.2 of Introduction to Programming in Java: An Interdisciplinary Approach by Robert Sedgewick and Kevin Wayne.

    • Method Summary

      All Methods Static Methods Concrete Methods Deprecated Methods 
      Modifier and Type Method Description
      static boolean bernoulli()
      Returns a random boolean from a Bernoulli distribution with success probability 1/2.
      static boolean bernoulli​(double p)
      Returns a random boolean from a Bernoulli distribution with success probability p.
      static double beta​(double alpha, double beta)
      Returns a random real number from a beta distribution with parameters α and β.
      static double cauchy()
      Returns a random real number from the Cauchy distribution.
      static int discrete​(double[] probabilities)
      Returns a random integer from the specified discrete distribution.
      static int discrete​(int[] frequencies)
      Returns a random integer from the specified discrete distribution.
      static double exp​(double lambda)
      Returns a random real number from an exponential distribution with rate λ.
      static double gaussian()
      Returns a random real number from a standard Gaussian distribution.
      static double gaussian​(double mu, double sigma)
      Returns a random real number from a Gaussian distribution with mean μ and standard deviation σ.
      static int geometric​(double p)
      Returns a random integer from a geometric distribution with success probability p.
      static long getSeed()
      Returns the seed of the pseudorandom number generator.
      static double pareto()
      Returns a random real number from the standard Pareto distribution.
      static double pareto​(double alpha)
      Returns a random real number from a Pareto distribution with shape parameter α.
      static int poisson​(double lambda)
      Returns a random integer from a Poisson distribution with mean λ.
      static double random()
      Deprecated.
      Replaced by uniform().
      static void setSeed​(long s)
      Sets the seed of the pseudorandom number generator.
      static void shuffle​(double[] a)
      Rearranges the elements of the specified array in uniformly random order.
      static void shuffle​(double[] a, int lo, int hi)
      Rearranges the elements of the specified subarray in uniformly random order.
      static void shuffle​(int[] a)
      Rearranges the elements of the specified array in uniformly random order.
      static void shuffle​(int[] a, int lo, int hi)
      Rearranges the elements of the specified subarray in uniformly random order.
      static void shuffle​(java.lang.Object[] a)
      Rearranges the elements of the specified array in uniformly random order.
      static void shuffle​(java.lang.Object[] a, int lo, int hi)
      Rearranges the elements of the specified subarray in uniformly random order.
      static double uniform()
      Returns a random real number uniformly in [0, 1).
      static double uniform​(double a, double b)
      Returns a random real number uniformly in [a, b).
      static int uniform​(int n)
      Returns a random integer uniformly in [0, n).
      static int uniform​(int a, int b)
      Returns a random integer uniformly in [a, b).
      • Methods inherited from class java.lang.Object

        clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
    • Method Detail

      • setSeed

        public static void setSeed​(long s)
        Sets the seed of the pseudorandom number generator. This method enables you to produce the same sequence of "random" number for each execution of the program. Ordinarily, you should call this method at most once per program.
        Parameters:
        s - the seed
      • getSeed

        public static long getSeed()
        Returns the seed of the pseudorandom number generator.
        Returns:
        the seed
      • uniform

        public static double uniform()
        Returns a random real number uniformly in [0, 1).
        Returns:
        a random real number uniformly in [0, 1)
      • uniform

        public static int uniform​(int n)
        Returns a random integer uniformly in [0, n).
        Parameters:
        n - number of possible integers
        Returns:
        a random integer uniformly between 0 (inclusive) and N (exclusive)
        Throws:
        java.lang.IllegalArgumentException - if n <= 0
      • random

        @Deprecated
        public static double random()
        Deprecated.
        Replaced by uniform().
        Returns a random real number uniformly in [0, 1).
        Returns:
        a random real number uniformly in [0, 1)
      • uniform

        public static int uniform​(int a,
                                  int b)
        Returns a random integer uniformly in [a, b).
        Parameters:
        a - the left endpoint
        b - the right endpoint
        Returns:
        a random integer uniformly in [a, b)
        Throws:
        java.lang.IllegalArgumentException - if b <= a
        java.lang.IllegalArgumentException - if b - a >= Integer.MAX_VALUE
      • uniform

        public static double uniform​(double a,
                                     double b)
        Returns a random real number uniformly in [a, b).
        Parameters:
        a - the left endpoint
        b - the right endpoint
        Returns:
        a random real number uniformly in [a, b)
        Throws:
        java.lang.IllegalArgumentException - unless a < b
      • bernoulli

        public static boolean bernoulli​(double p)
        Returns a random boolean from a Bernoulli distribution with success probability p.
        Parameters:
        p - the probability of returning true
        Returns:
        true with probability p and false with probability p
        Throws:
        java.lang.IllegalArgumentException - unless p >= 0.0 and p <= 1.0
      • bernoulli

        public static boolean bernoulli()
        Returns a random boolean from a Bernoulli distribution with success probability 1/2.
        Returns:
        true with probability 1/2 and false with probability 1/2
      • gaussian

        public static double gaussian()
        Returns a random real number from a standard Gaussian distribution.
        Returns:
        a random real number from a standard Gaussian distribution (mean 0 and standard deviation 1).
      • gaussian

        public static double gaussian​(double mu,
                                      double sigma)
        Returns a random real number from a Gaussian distribution with mean μ and standard deviation σ.
        Parameters:
        mu - the mean
        sigma - the standard deviation
        Returns:
        a real number distributed according to the Gaussian distribution with mean mu and standard deviation sigma
      • geometric

        public static int geometric​(double p)
        Returns a random integer from a geometric distribution with success probability p.
        Parameters:
        p - the parameter of the geometric distribution
        Returns:
        a random integer from a geometric distribution with success probability p; or Integer.MAX_VALUE if p is (nearly) equal to 1.0.
        Throws:
        java.lang.IllegalArgumentException - unless p >= 0.0 and p <= 1.0
      • poisson

        public static int poisson​(double lambda)
        Returns a random integer from a Poisson distribution with mean λ.
        Parameters:
        lambda - the mean of the Poisson distribution
        Returns:
        a random integer from a Poisson distribution with mean lambda
        Throws:
        java.lang.IllegalArgumentException - unless lambda > 0.0 and not infinite
      • pareto

        public static double pareto()
        Returns a random real number from the standard Pareto distribution.
        Returns:
        a random real number from the standard Pareto distribution
      • pareto

        public static double pareto​(double alpha)
        Returns a random real number from a Pareto distribution with shape parameter α.
        Parameters:
        alpha - shape parameter
        Returns:
        a random real number from a Pareto distribution with shape parameter alpha
        Throws:
        java.lang.IllegalArgumentException - unless alpha > 0.0
      • cauchy

        public static double cauchy()
        Returns a random real number from the Cauchy distribution.
        Returns:
        a random real number from the Cauchy distribution.
      • discrete

        public static int discrete​(double[] probabilities)
        Returns a random integer from the specified discrete distribution.
        Parameters:
        probabilities - the probability of occurrence of each integer
        Returns:
        a random integer from a discrete distribution: i with probability probabilities[i]
        Throws:
        java.lang.NullPointerException - if probabilities is null
        java.lang.IllegalArgumentException - if sum of array entries is not (very nearly) equal to 1.0
        java.lang.IllegalArgumentException - unless probabilities[i] >= 0.0 for each index i
      • discrete

        public static int discrete​(int[] frequencies)
        Returns a random integer from the specified discrete distribution.
        Parameters:
        frequencies - the frequency of occurrence of each integer
        Returns:
        a random integer from a discrete distribution: i with probability proportional to frequencies[i]
        Throws:
        java.lang.NullPointerException - if frequencies is null
        java.lang.IllegalArgumentException - if all array entries are 0
        java.lang.IllegalArgumentException - if frequencies[i] is negative for any index i
        java.lang.IllegalArgumentException - if sum of frequencies exceeds Integer.MAX_VALUE (231 - 1)
      • exp

        public static double exp​(double lambda)
        Returns a random real number from an exponential distribution with rate λ.
        Parameters:
        lambda - the rate of the exponential distribution
        Returns:
        a random real number from an exponential distribution with rate lambda
        Throws:
        java.lang.IllegalArgumentException - unless lambda > 0.0
      • beta

        public static double beta​(double alpha,
                                  double beta)
        Returns a random real number from a beta distribution with parameters α and β. The result is normalized in [-1,1]
        Parameters:
        alpha - the shape parameter α
        beta - the shape parameter β
        Returns:
        a random real number from a beta distribution normalized in [-1,1]
        Throws:
        java.lang.IllegalArgumentException - unless alpha, beta > 0.0
      • shuffle

        public static void shuffle​(java.lang.Object[] a)
        Rearranges the elements of the specified array in uniformly random order.
        Parameters:
        a - the array to shuffle
        Throws:
        java.lang.NullPointerException - if a is null
      • shuffle

        public static void shuffle​(double[] a)
        Rearranges the elements of the specified array in uniformly random order.
        Parameters:
        a - the array to shuffle
        Throws:
        java.lang.NullPointerException - if a is null
      • shuffle

        public static void shuffle​(int[] a)
        Rearranges the elements of the specified array in uniformly random order.
        Parameters:
        a - the array to shuffle
        Throws:
        java.lang.NullPointerException - if a is null
      • shuffle

        public static void shuffle​(java.lang.Object[] a,
                                   int lo,
                                   int hi)
        Rearranges the elements of the specified subarray in uniformly random order.
        Parameters:
        a - the array to shuffle
        lo - the left endpoint (inclusive)
        hi - the right endpoint (inclusive)
        Throws:
        java.lang.NullPointerException - if a is null
        java.lang.IndexOutOfBoundsException - unless (0 <= lo) && (lo <= hi) && (hi < a.length)
      • shuffle

        public static void shuffle​(double[] a,
                                   int lo,
                                   int hi)
        Rearranges the elements of the specified subarray in uniformly random order.
        Parameters:
        a - the array to shuffle
        lo - the left endpoint (inclusive)
        hi - the right endpoint (inclusive)
        Throws:
        java.lang.NullPointerException - if a is null
        java.lang.IndexOutOfBoundsException - unless (0 <= lo) && (lo <= hi) && (hi < a.length)
      • shuffle

        public static void shuffle​(int[] a,
                                   int lo,
                                   int hi)
        Rearranges the elements of the specified subarray in uniformly random order.
        Parameters:
        a - the array to shuffle
        lo - the left endpoint (inclusive)
        hi - the right endpoint (inclusive)
        Throws:
        java.lang.NullPointerException - if a is null
        java.lang.IndexOutOfBoundsException - unless (0 <= lo) && (lo <= hi) && (hi < a.length)