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Makefile
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README.md
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main.c
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min_stack.c
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min_stack.h
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min_stack_test.c
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Learning Profile for Assignment #1 - Question #6 - Computer Science 272: Data Structures and Algorithms

Name: Mo Khan Student ID: 3431709

Problem Statement

Design and implement a MinStack data structure that can store comparable elements and supports the stack operations push(x), pop(), and size(), as well as the min() operation, which returns the minimum value currently stored in the data structure.

All operations should run in constant time.

Description of the Code

To keep track of the min value, I chose to use two Stacks. One stack keeps track of each item that is pushed on. The second stack keeps track of each new minimum value that is pushed on to the stack.

push(), pop() and size() are operate in constant time. However, min operates in constant time until each of the min values have been popped off of the min stack. After that it falls back to a linear time algorithm to determine the next min.

Errors and Warnings

モ make run_test
clang build/min_stack.o build/min_stack_test.o -lcgreen -o build/test
cgreen-runner -c -v build/test
Discovered MinStack:when_a_single_item_is_on_the_stack_it_has_a_size_of_one (CgreenSpec__MinStack__when_a_single_item_is_on_the_stack_it_has_a_size_of_one__)
Discovered MinStack:when_a_single_item_is_on_the_stack_it_is_the_min (CgreenSpec__MinStack__when_a_single_item_is_on_the_stack_it_is_the_min__)
Discovered MinStack:when_a_single_item_is_on_the_stack_when_it_is_popped_off_it_returns_a_min_of_null (CgreenSpec__MinStack__when_a_single_item_is_on_the_stack_when_it_is_popped_off_it_returns_a_min_of_null__)
Discovered MinStack:when_a_single_item_is_on_the_stack_when_it_is_popped_off_it_returns_a_size_of_zero (CgreenSpec__MinStack__when_a_single_item_is_on_the_stack_when_it_is_popped_off_it_returns_a_size_of_zero__)
Discovered MinStack:when_a_single_item_is_on_the_stack_when_it_is_popped_off_it_returns_the_item (CgreenSpec__MinStack__when_a_single_item_is_on_the_stack_when_it_is_popped_off_it_returns_the_item__)
Discovered MinStack:when_empty (CgreenSpec__MinStack__when_empty__)
Discovered MinStack:when_empty_it_has_a_min_of_null (CgreenSpec__MinStack__when_empty_it_has_a_min_of_null__)
Discovered MinStack:when_empty_it_has_a_size_of_zero (CgreenSpec__MinStack__when_empty_it_has_a_size_of_zero__)
Discovered MinStack:when_pushing_a_single_integer (CgreenSpec__MinStack__when_pushing_a_single_integer__)
Discovered MinStack:when_pushing_duplicate_values_on_to_the_stack (CgreenSpec__MinStack__when_pushing_duplicate_values_on_to_the_stack__)
Discovered MinStack:when_pushing_multiple_integers_out_of_order (CgreenSpec__MinStack__when_pushing_multiple_integers_out_of_order__)
Discovered 11 test(s)
Opening [build/test] to run all 11 discovered tests ...
Running "test" (11 tests)...
  "MinStack": 39 passes in 7ms.
Completed "test": 39 passes in 7ms.

Sample Input and Output

モ make run
clang    -c -o build/main.o main.c
clang build/min_stack.o build/main.o -o build/program
./build/program
=== COMP-272 - Assignment 1 - Question 6 ===
Pushing:
==========
Push: 7, Min: 7
	[7]
Push: 24, Min: 7
	[24][7]
Push: 23, Min: 7
	[23][24][7]
Push: 8, Min: 7
	[8][23][24][7]
Push: 5, Min: 5
	[5][8][23][24][7]
Push: 22, Min: 5
	[22][5][8][23][24][7]
Push: 19, Min: 5
	[19][22][5][8][23][24][7]
Push: 3, Min: 3
	[3][19][22][5][8][23][24][7]
Push: 23, Min: 3
	[23][3][19][22][5][8][23][24][7]
Push: 9, Min: 3
	[9][23][3][19][22][5][8][23][24][7]
Push: 15, Min: 3
	[15][9][23][3][19][22][5][8][23][24][7]
Push: 15, Min: 3
	[15][15][9][23][3][19][22][5][8][23][24][7]
Push: 17, Min: 3
	[17][15][15][9][23][3][19][22][5][8][23][24][7]
Push: 17, Min: 3
	[17][17][15][15][9][23][3][19][22][5][8][23][24][7]
Push: 12, Min: 3
	[12][17][17][15][15][9][23][3][19][22][5][8][23][24][7]
Push: 3, Min: 3
	[3][12][17][17][15][15][9][23][3][19][22][5][8][23][24][7]
Push: 2, Min: 2
	[2][3][12][17][17][15][15][9][23][3][19][22][5][8][23][24][7]
Push: 4, Min: 2
	[4][2][3][12][17][17][15][15][9][23][3][19][22][5][8][23][24][7]
Push: 15, Min: 2
	[15][4][2][3][12][17][17][15][15][9][23][3][19][22][5][8][23][24][7]
Push: 12, Min: 2
	[12][15][4][2][3][12][17][17][15][15][9][23][3][19][22][5][8][23][24][7]
Push: 3, Min: 2
	[3][12][15][4][2][3][12][17][17][15][15][9][23][3][19][22][5][8][23][24][7]
Push: 19, Min: 2
	[19][3][12][15][4][2][3][12][17][17][15][15][9][23][3][19][22][5][8][23][24][7]
Push: 9, Min: 2
	[9][19][3][12][15][4][2][3][12][17][17][15][15][9][23][3][19][22][5][8][23][24][7]
Push: 7, Min: 2
	[7][9][19][3][12][15][4][2][3][12][17][17][15][15][9][23][3][19][22][5][8][23][24][7]
Push: 10, Min: 2
	[10][7][9][19][3][12][15][4][2][3][12][17][17][15][15][9][23][3][19][22][5][8][23][24][7]
Popping:
==========
	[10][7][9][19][3][12][15][4][2][3][12][17][17][15][15][9][23][3][19][22][5][8][23][24][7]
Pop: 10, Min: 2
	[7][9][19][3][12][15][4][2][3][12][17][17][15][15][9][23][3][19][22][5][8][23][24][7]
Pop: 7, Min: 2
	[9][19][3][12][15][4][2][3][12][17][17][15][15][9][23][3][19][22][5][8][23][24][7]
Pop: 9, Min: 2
	[19][3][12][15][4][2][3][12][17][17][15][15][9][23][3][19][22][5][8][23][24][7]
Pop: 19, Min: 2
	[3][12][15][4][2][3][12][17][17][15][15][9][23][3][19][22][5][8][23][24][7]
Pop: 3, Min: 2
	[12][15][4][2][3][12][17][17][15][15][9][23][3][19][22][5][8][23][24][7]
Pop: 12, Min: 2
	[15][4][2][3][12][17][17][15][15][9][23][3][19][22][5][8][23][24][7]
Pop: 15, Min: 2
	[4][2][3][12][17][17][15][15][9][23][3][19][22][5][8][23][24][7]
Pop: 4, Min: 2
	[2][3][12][17][17][15][15][9][23][3][19][22][5][8][23][24][7]
Pop: 2, Min: 3
	[3][12][17][17][15][15][9][23][3][19][22][5][8][23][24][7]
Pop: 3, Min: 5
	[12][17][17][15][15][9][23][3][19][22][5][8][23][24][7]
Pop: 12, Min: 5
	[17][17][15][15][9][23][3][19][22][5][8][23][24][7]
Pop: 17, Min: 5
	[17][15][15][9][23][3][19][22][5][8][23][24][7]
Pop: 17, Min: 5
	[15][15][9][23][3][19][22][5][8][23][24][7]
Pop: 15, Min: 5
	[15][9][23][3][19][22][5][8][23][24][7]
Pop: 15, Min: 5
	[9][23][3][19][22][5][8][23][24][7]
Pop: 9, Min: 5
	[23][3][19][22][5][8][23][24][7]
Pop: 23, Min: 5
	[3][19][22][5][8][23][24][7]
Pop: 3, Min: 5
	[19][22][5][8][23][24][7]
Pop: 19, Min: 5
	[22][5][8][23][24][7]
Pop: 22, Min: 5
	[5][8][23][24][7]
Pop: 5, Min: 7
	[8][23][24][7]
Pop: 8, Min: 7
	[23][24][7]
Pop: 23, Min: 7
	[24][7]
Pop: 24, Min: 7
	[7]
Pop: 7, Min: 0

Bye

Discussion

I struggled to find a good algorithm that would guarantee a constant time implementation of min().

The worst case scenario for this implementation is when the min value is pushed on to the stack right in the center. Half of the pops will would yield a constant time implementation of min() and the other half would yield a linear time implementation of min().