CompSci 165 Project #1
SEARCHING

due April 13 (W week 3)

Requirements

• Write a system of routines that will do the following.
  1. Implement three search algorithms (A):
     • Binary Search
     • Interpolation Search
     • Hybrid Interpolation/Binary Search

  2. Generate 1000 random distinct integer search values (V) in [0, 8000].

  3. For each of the following 2 values of N (10⁴ and 10⁶),
     use my FILLIN procedure to generate 10 random sorted sequences (S)
     of N floating point numbers having values in [0.0, N).

  4. For each sequence S, for each search value V, for each search algorithm A:
     Use A to search S for the smallest element having value greater than V.
     The algorithm returns the value of that element (successful search),
     or -1.0 if no such element exists (unsuccessful search).

  5. For each value of N, for each algorithm A,
     • determine the observed
       • worst-case
       • best-case
       • average-case
       • sample standard deviation
       of the number of probes required.
     • determine the observed average values of the
       • search integers that result in successful searches
       • returned values from successful searches
     • determine the observed average
       • CPU time required for a search
     (7 numbers for each of 2 values of N for each of 3 algorithms)

  6. Display the determined 42 values in a reader-friendly format.

• Analyze your empirical observations and compare them with your theoretical expectations. 
  Compare and contrast the number of probes and CPU time. 
  Explain any anomalous observations.

• To allow easier correctness checking, provide a usage option that prints, in a user-friendly format,
  the result of a single search for a value v in a randomly generated (via FILLIN) array (S)
  of 100 double floats in the interval [0,100].   The value v is an integer randomly picked in [0,80].

  Print:
    (1) the random value v that your program used
    (2) either (a) the value of the element that resulted, if the search is successful
               or (b) -1, if the search is unsuccessful.
    (3) the 100 double float values of the S array you used

Definitions

• The average (or mean) of a set of n samples is their sum divided by n.

• The deviation of a sample is the difference of that sample from the mean.

• The root-mean-square (rms) deviation is the square root of the average of the squares of the deviations.

• The sample standard deviation is similar to the rms deviation,
  but the sum of the squared deviations is divided by n-1 instead of n. 
  This is often calculated using the formula:
  An alternate, equally valid, formula is s = square root of { (x-x)²   /   (n-1) }

Usage

• To generate random floating point values in the range [0,1), use my dshrandom() routine.

• Initialize random number generator with input seed by:           dshrandom( input )

• Obtain a random real value in the range [0, BIG) by:           BIG*dshrandom( 0 )

• Obtain a random integer value in the range [0, BIG-1] by:       Floor{   BIG*dshrandom( 0 )   }

• To fill in elements X[a] to X[b] in vector X with increasing real values
  strictly in the range [low, high), use my FILLIN procedure:           FILLIN(X,a,b,low,high)
  But be careful that the variable types are correct.