Description
Insertion Sort vs. Selection Sort
Implement Insertion Sort (as discussed in class) and Selection Sort (as described below). You can use
one of the following programming languages: C/C++, Java or Python.
Selection Sort
Selection Sort is the following algorithm. Given an array A[1 . . . n] you first find the smallest element
in A and exchange it with A[1]. Then find the second smallest element in A and exchange it with A[2].
Continue this for the first n − 1 elements of A (See CLRS Exercise 2.2-2).
Input/Output:
Your input will be a sequence of n numbers x1, x2, . . . , xn given in an input file in this order. Each number will
be an integer between 1 and n. The output should be a file containing these integers sorted in non-decreasing
order.
For each of the first 4 input types below you should plot the running time of each algorithm for inputs
of size n = 5000, 10000, 15000, . . . up to 30000. Plot both algorithms on the same chart so that it is easy
to compare. For the last input type (small random inputs) see instructions below. When measuring the
running time you should only measure the time of sorting, not the time spent generating the data.
Input/Plot 1: Large random inputs. Generate each xi to be a uniformly random integer between
1 and n. On random inputs that you generate: For each data point take the average of 3 runs (each time
generating a new random input).
Input/Plot 2: Non-decreasing inputs. Generate each xi to be a uniformly random integer between
1 and n and sort the resulting sequence in non-decreasing order (x1 ≤ x2 ≤ . . . ≤ xn). Then run each of the
sorting algorithms again and measure its performance.
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Input/Plot 3: Non-increasing inputs. Generate each xi to be a uniformly random integer between
1 and n and sort the resulting sequence in non-increasing order (x1 ≥ x2 ≥ . . . ≥ xn). Then run each of the
sorting algorithms again and measure its performance.
Input/Plot 4: Noisy non-decreasing inputs. Generate input in two steps:
1. Generate input as in Plot 2.
2. Repeat the following 50 times: Pick two random integers i and j and exchange xi and xj .
For each data point take the average of 3 runs (each time generating a new random input).
Input 5: Small random inputs. Generate 100,000 inputs as in Input/Plot 1 for n = 50. Measure
the overall runtime of sorting these inputs. There is no plot for this type of input, just compare the two
resulting runtimes.
Write-up
Explain your choices: Explain any platform/language choices that you made for your code and plots.
How did you create and store the data you used to make the plots. Did you run into any difficulties or made
any interesting observations?
Conclusions: Both of these algorithms have asymptotic quadratic running time (O(n
2
)). Does the first
plot reflect this? How do the two algorithms compare in terms of the running time? How about the second
plot? Do you think this one is quadratic? Why do you think it looks the way it does? How does the third
plot compare to the first and second? What about the fourth plot? Would you use these algorithms for real
data and if so why?
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