CS2700 - Programming and Data Structures

Meetings  

• Theme 1 : Program Correctness - 6 meetings

  • Meeting 01 : Mon, Jul 30, 10:00 am-10:50 am

  Challenges in programming. Ideas and Tools developed so far through CS1100 and CS1200. <br> Program Correctness. Efficiency, Time and Space. Need of organizing the data for efficiency. Some example situations.

  References
  Exercises
  Reading

  Challenges in programming. Ideas and Tools developed so far through CS1100 and CS1200.
  Program Correctness. Efficiency, Time and Space. Need of organizing the data for efficiency. Some example situations.
  

  References

  :

  None

  • Meeting 02 : Tue, Jul 31, 09:00 am-09:50 am

  (TA Introduction & Grouping) <br> Program Correctness. The overall idea. Input and output specification. Breaking into small components. Pre-conditions and Post-conditions. Hoare triplets. Composition Axiom. Strengthening the pre-conditions. Weakening the post-conditions. Examples.

  References
  Exercises
  Reading

  (TA Introduction & Grouping)
  Program Correctness. The overall idea. Input and output specification. Breaking into small components. Pre-conditions and Post-conditions. Hoare triplets. Composition Axiom. Strengthening the pre-conditions. Weakening the post-conditions. Examples.
  

  References

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  None

  • Meeting 03 : Wed, Aug 01, 08:00 am-08:50 am

  Assignment axiom. - the Hoare triplet for the assignment Statement. Example. The if-then-else axiom. The "absolute value" example. Outline of a proof.

  References
  Exercises
  Reading

  Assignment axiom. - the Hoare triplet for the assignment Statement. Example. The if-then-else axiom. The "absolute value" example. Outline of a proof.
  

  References

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  None

  • Meeting 04 : Fri, Aug 03, 01:00 pm-01:50 pm

  The components of a correctness proof of a program. Example of "Computing the absolute value". The full formal proof of correctness. Handling while loops. Loop invariants. The loop Axiom. Writing down the correctness proof.

  References
  Exercises
  Reading

  The components of a correctness proof of a program. Example of "Computing the absolute value". The full formal proof of correctness. Handling while loops. Loop invariants. The loop Axiom. Writing down the correctness proof.
  

  References

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  None

  • Meeting 05 : Mon, Aug 06, 10:00 am-10:50 am

  Two more examples of proving correctness of loops. Trying out a loop invariant and strengthening it. Effects in program design. Exercises.

  References
  Exercises
  Reading

  Two more examples of proving correctness of loops. Trying out a loop invariant and strengthening it. Effects in program design. Exercises.
  

  References

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  None

  • Meeting 06 : Tue, Aug 07, 09:00 am-09:50 am

  Correctness of recursive functions. Why use induction. The factorial function. Proving the Hoare triplet property inductively. Two parameter recursion. Euclid's algorithm. Exercise.

  References
  Exercises
  Reading

  Correctness of recursive functions. Why use induction. The factorial function. Proving the Hoare triplet property inductively. Two parameter recursion. Euclid's algorithm. Exercise.
  

  References

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  None

• Theme 2 : Basics of Asymptotic Analysis - 6 meetings

  • Meeting 07 : Fri, Aug 10, 01:00 pm-01:50 pm

  Comparing two algorithms solving the same problem. <br> Counting what? Running Time? Seconds? Dependence on hardware.<br> Counting in terms of what? Input size. Different behaviours. Notion of worst case analysis.<br> Dependence on the input size n. Different run-time functions. Substituting numbers for a fixed processor speed to get a sense. We care about the "growth rate".

  References
  Exercises
  Reading

  Comparing two algorithms solving the same problem.
  Counting what? Running Time? Seconds? Dependence on hardware.
  Counting in terms of what? Input size. Different behaviours. Notion of worst case analysis.
  Dependence on the input size n. Different run-time functions. Substituting numbers for a fixed processor speed to get a sense. We care about the "growth rate".
  

  References

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  None

  • Meeting 08 : Mon, Aug 13, 10:00 am-10:50 am

  Ignoring of constant factors. Ignoring "small" finite inputs. Arriving at the definition of Big-Oh comparison of running times. Examples.

  References
  Exercises
  Reading

  Ignoring of constant factors. Ignoring "small" finite inputs. Arriving at the definition of Big-Oh comparison of running times. Examples.
  

  References

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  None

  • Meeting 09 : Tue, Aug 14, 09:00 am-09:50 am

  The definition of Big-Omega. Theta notation. Properties of the big-Oh notations.

  References
  Exercises
  Reading

  The definition of Big-Omega. Theta notation. Properties of the big-Oh notations.
  

  References

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  None

  • Meeting 10 : Mon, Aug 20, 10:00 am-10:50 am

  Common functions that appear as the run time and their asymptotic behaviours. Polynomials, Exponentials. Logarithms.

  References
  Exercises
  Reading

  Common functions that appear as the run time and their asymptotic behaviours. Polynomials, Exponentials. Logarithms.
  

  References

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  None

  • Meeting 11 : Tue, Aug 21, 09:00 am-09:50 am

  How do we write the run time expression for programs. Sequencing rule. Nested Loops. If then else. Recursion. Recurrence relations. Solution of recurrence relations. The recurrence and the solution.

  References
  Exercises
  Reading

  How do we write the run time expression for programs. Sequencing rule. Nested Loops. If then else. Recursion. Recurrence relations. Solution of recurrence relations. The recurrence and the solution.
  

  References

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  None

  • Meeting 12 : Fri, Aug 24, 01:00 pm-01:50 pm

  Recursion and fibonacci recurrence. Analysis. Algorithm Designer's thought process. Algorithm, Correctness, Analysis, Upper bounds and Lower Bounds for the problem.<br> Example : Maximum subarray problem. O(n^3) algorithm. Omega(n) lower bound. The gap between them and the quest.

  References
  Exercises
  Reading

  Recursion and fibonacci recurrence. Analysis. Algorithm Designer's thought process. Algorithm, Correctness, Analysis, Upper bounds and Lower Bounds for the problem.
  Example : Maximum subarray problem. O(n^3) algorithm. Omega(n) lower bound. The gap between them and the quest.
  

  References

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  None

• Theme 3 : Arrays : Sorting, Searching. - 7 meetings

  • Meeting 13 : Mon, Aug 27, 10:00 am-10:50 am

  Comparison Sorting Model. Insertion sort. Easy Upper and lower bounds for sorting. Lower Bounds for Sorting.

  References
  Exercises
  Reading

  Comparison Sorting Model. Insertion sort. Easy Upper and lower bounds for sorting. Lower Bounds for Sorting.
  

  References

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  None

  • Meeting 14 : Tue, Aug 28, 09:00 am-09:50 am

  Merge Sort, Analysis of Merge Sort. Guess and verify. Examples. Substitute and expand/simplify. Sorting problem review. Upper bounds and lower Bounds. Argument that any comparison sort must take at least Omega(n log n) comparisons.

  References
  Exercises
  Reading

  Merge Sort, Analysis of Merge Sort. Guess and verify. Examples. Substitute and expand/simplify. Sorting problem review. Upper bounds and lower Bounds. Argument that any comparison sort must take at least Omega(n log n) comparisons.
  

  References

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  None

  • Meeting 15 : Wed, Aug 29, 08:00 am-08:50 am

  In-place sorting. Quicksort. Pivot and partition algorithms. Recursive subproblems. Examples.

  References
  Exercises
  Reading

  In-place sorting. Quicksort. Pivot and partition algorithms. Recursive subproblems. Examples.
  

  References

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  None

  • Meeting 16 : Fri, Aug 31, 01:00 pm-01:50 pm

  DoT 01

  References
  Exercises
  Reading

  DoT 01
  

  References

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  None

  • Meeting 17 : Mon, Sep 03, 10:00 am-10:50 am

  Analysis of Quicksort. Worst case and best case recurrences. Limitations of worst cases analysis. Average case analysis of algorithms. Intuition for average case analysis for Quicksort. Average case analysis for Insertion Sort. Connection between comparisons and inversions. Average number of inversions in a permutation on n elements.

  References
  Exercises
  Reading

  Analysis of Quicksort. Worst case and best case recurrences. Limitations of worst cases analysis. Average case analysis of algorithms. Intuition for average case analysis for Quicksort. Average case analysis for Insertion Sort. Connection between comparisons and inversions. Average number of inversions in a permutation on n elements.
  

  References

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  None

  • Meeting 18 : Tue, Sep 04, 09:00 am-09:50 am

  Exact computation of average number of inversions in a permutation of n-elements. Average case analysis of insertion sort. <br>Sorting Roundup. Stability in sorting algorithms. Stable implementations of Merge Sort. Stability analysis of standard implementations of Selection Sort, Insertion Sort, Merge Sort, Quick Sort.

  References
  Exercises
  Reading

  Exact computation of average number of inversions in a permutation of n-elements. Average case analysis of insertion sort.
  Sorting Roundup. Stability in sorting algorithms. Stable implementations of Merge Sort. Stability analysis of standard implementations of Selection Sort, Insertion Sort, Merge Sort, Quick Sort.
  

  References

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  None

  • Meeting 19 : Fri, Sep 07, 01:00 pm-01:50 pm

  Sorting in linear time. Counting Sort. Analysis. Radix Sort. Advantages and Disadvantages.

  References
  Exercises
  Reading

  Sorting in linear time. Counting Sort. Analysis. Radix Sort. Advantages and Disadvantages.
  

  References

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  None

• Theme 4 : List ADT - 4 meetings

  • Meeting 20 : Mon, Sep 10, 10:00 am-10:50 am

  Abstract Data Types. The list ADT. Implementation of List ADT with Arrays. Insertion and Deletion. Finding an element. Accessing the k-th element. Time complexity analysis.

  References	Section 3.2 in [MAW 2007] Textbook.
  Exercises
  Reading

  Abstract Data Types. The list ADT. Implementation of List ADT with Arrays. Insertion and Deletion. Finding an element. Accessing the k-th element. Time complexity analysis.
  

  References

  :

  Section 3.2 in [MAW 2007] Textbook.

  • Meeting 21 : Tue, Sep 11, 09:00 am-09:50 am

  Limitation of array based implementation. Ideas of the vector class. Discussion of non-continguous memory locations for lists. Implementation of List ADT with Linked Lists. Vector class in C++.

  References	Section 3.2 in [MAW 2007] Textbook.
  Exercises
  Reading

  Limitation of array based implementation. Ideas of the vector class. Discussion of non-continguous memory locations for lists. Implementation of List ADT with Linked Lists. Vector class in C++.
  

  References

  :

  Section 3.2 in [MAW 2007] Textbook.

  • Meeting 22 : Tue, Sep 11, 02:00 pm-02:50 pm

  Implementation of List ADT with linked lists. Insertion under various cases, Doubly linked lists,Circular Linked Lists. Advantages and Disadvantages.

  References	Section 3.2 in [MAW 2007] Textbook.
  Exercises
  Reading

  Implementation of List ADT with linked lists. Insertion under various cases, Doubly linked lists,Circular Linked Lists. Advantages and Disadvantages.
  

  References

  :

  Section 3.2 in [MAW 2007] Textbook.

  • Meeting 23 : Wed, Sep 12, 08:00 am-08:50 am

  Deletion operation in lists. Find operation in lists. Algorithm for reversing in linked lists.

  References	Section 3.2 in [MAW 2007] Textbook.
  Exercises
  Reading

  Deletion operation in lists. Find operation in lists. Algorithm for reversing in linked lists.
  

  References

  :

  Section 3.2 in [MAW 2007] Textbook.

• Theme 5 : Stacks & Queues ADTs - 6 meetings

  • Meeting 24 : Mon, Sep 17, 01:00 pm-01:50 pm

  Checking Balanced Paranthesis. Simple algorithms. Motivation for the stack ADT. Implementation of Stack ADT using arrays. Analysis of the cost.

  References	Section 3.6 in [MAW 2007] Textbook.
  Exercises
  Reading

  Checking Balanced Paranthesis. Simple algorithms. Motivation for the stack ADT. Implementation of Stack ADT using arrays. Analysis of the cost.
  

  References

  :

  Section 3.6 in [MAW 2007] Textbook.

  • Meeting 25 : Tue, Sep 18, 09:00 am-09:50 am

  Implementation of a stack using linked list. Application 1 : Checking if an expression is balanced in terms of paranethesisation.

  References	Section 3.6 in [MAW 2007] Textbook.
  Exercises
  Reading

  Implementation of a stack using linked list. Application 1 : Checking if an expression is balanced in terms of paranethesisation.
  

  References

  :

  Section 3.6 in [MAW 2007] Textbook.

  • Meeting 26 : Wed, Sep 19, 08:00 am-08:50 am

  Application of Stack 2 : Evaluation of Postfix expressions. Algorithm using a stack.

  References	Section 3.6 in [MAW 2007] Textbook.
  Exercises
  Reading

  Application of Stack 2 : Evaluation of Postfix expressions. Algorithm using a stack.
  

  References

  :

  Section 3.6 in [MAW 2007] Textbook.

  • Meeting 27 : Mon, Sep 24, 10:00 am-10:50 am

  Application of Stack 3 : Converting Infix to Postfix expressions.

  References	Section 3.6 in [MAW 2007] Textbook.
  Exercises
  Reading

  Application of Stack 3 : Converting Infix to Postfix expressions.
  

  References

  :

  Section 3.6 in [MAW 2007] Textbook.

  • Meeting 28 : Tue, Sep 25, 09:00 am-09:50 am

  Queue ADT. Array Implementation. Difficulties. Circular Queue. Analysis. Implementation using Linked Lists.

  References	Section 3.7 in [MAW 2007] Textbook.
  Exercises
  Reading

  Queue ADT. Array Implementation. Difficulties. Circular Queue. Analysis. Implementation using Linked Lists.
  

  References

  :

  Section 3.7 in [MAW 2007] Textbook.

  • Meeting 29 : Wed, Sep 26, 08:00 am-08:50 am

  SQ1. Implementing Queues with linked lists. Implementation of Queues using two stacks.

  References	Class notes.
  Exercises
  Reading

  SQ1. Implementing Queues with linked lists. Implementation of Queues using two stacks.
  

  References

  :

  Class notes.

• Theme 6 : Tree ADT (Trees & Traversals) - 4 meetings

  • Meeting 30 : Fri, Sep 28, 01:00 pm-01:50 pm

  Introduction & Motivation to Trees. Definitions. Representations of trees using linked lists. Directory Tree structure. Motivation for traversals. Pre-order and post-order.

  References	Section 4.1 in [MAW 2007] Textbook.
  Exercises
  Reading

  Introduction & Motivation to Trees. Definitions. Representations of trees using linked lists. Directory Tree structure. Motivation for traversals. Pre-order and post-order.
  

  References

  :

  Section 4.1 in [MAW 2007] Textbook.

  • Meeting 31 : Mon, Oct 01, 10:00 am-10:50 am

  Pre-order Traversal, Post Order Traversals. Algorithms for pre-order traversal. Recursive and Non-recursive versions (using one stack).

  References	Section 4 in [MAW 2007] Textbook. For non-recursive implementation, please refer to class notes.
  Exercises
  Reading

  Pre-order Traversal, Post Order Traversals. Algorithms for pre-order traversal. Recursive and Non-recursive versions (using one stack).
  

  References

  :

  Section 4 in [MAW 2007] Textbook. For non-recursive implementation, please refer to class notes.

  • Meeting 32 : Wed, Oct 03, 08:00 am-08:50 am

  Binary trees. Expression trees. In-order, pre-order, post-order traversals on binary trees. Using them to generate post/pre/infix notation. <br> Building the expression tree from postfix expressions.

  References	Section 4.2 in [MAW 2007] Textbook.
  Exercises
  Reading

  Binary trees. Expression trees. In-order, pre-order, post-order traversals on binary trees. Using them to generate post/pre/infix notation.
  Building the expression tree from postfix expressions.
  

  References

  :

  Section 4.2 in [MAW 2007] Textbook.

  • Meeting 33 : Thu, Oct 04, 02:00 pm-02:50 pm

  Level order Traversal. Non-recursive implementation using a queue. Does combination of in-order, pre-order, post-order, and level-order uniquely fix the tree. Constructing the binary tree given in-order and pre-order traversal.

  References	Link to <a href="https://www.cmi.ac.in/~madhavan/courses/programming06/lecture12-21sep2006.txt">Notes by Madhavan Mukund</a> (psuedo-code there is written in Haskell, you can ignore that).
  Exercises	Write down algorithms for constructing the binary tree given (1) in-order and post-order traversal (2)in-order and level-order traversal.
  Reading

  Level order Traversal. Non-recursive implementation using a queue. Does combination of in-order, pre-order, post-order, and level-order uniquely fix the tree. Constructing the binary tree given in-order and pre-order traversal.
  

  References	:	Link to Notes by Madhavan Mukund (psuedo-code there is written in Haskell, you can ignore that).
  Exercises	:	Write down algorithms for constructing the binary tree given (1) in-order and post-order traversal (2)in-order and level-order traversal.

• Theme 7 : Dictionary ADT - I (Binary Search Trees) - 6 meetings

  • Meeting 34 : Mon, Oct 08, 10:00 am-10:50 am

  Binary search trees property of binary trees with keys in each node. Application in maintaining list of "comparable" data. Findmin. Insertion. Recursive version of insert operation.

  References	Section 4.3 in [MAW 2007] Textbook.
  Exercises
  Reading

  Binary search trees property of binary trees with keys in each node. Application in maintaining list of "comparable" data. Findmin. Insertion. Recursive version of insert operation.
  

  References

  :

  Section 4.3 in [MAW 2007] Textbook.

  • Meeting 35 : Tue, Oct 09, 09:00 am-09:50 am

  Delete operation on BSTs. Examples. Pseudocode. "Pass-by-reference trick". An application - recursive make-emtpy routine.

  References	Section 4.3 in [MAW 2007] Textbook.
  Exercises
  Reading

  Delete operation on BSTs. Examples. Pseudocode. "Pass-by-reference trick". An application - recursive make-emtpy routine.
  

  References

  :

  Section 4.3 in [MAW 2007] Textbook.

  • Meeting 36 : Wed, Oct 10, 08:00 am-08:50 am

  Analysis of BSTs. Effect of order of insertion on tree depth. Average depth. examples. Insertion order.

  References	Class notes. Lecture content not directly from any source.
  Exercises
  Reading

  Analysis of BSTs. Effect of order of insertion on tree depth. Average depth. examples. Insertion order.
  

  References

  :

  Class notes. Lecture content not directly from any source.

  • Meeting 37 : Fri, Oct 12, 01:00 pm-01:50 pm

  Average depth of BSTs obtained from a randomly chosen insertion order is O(log n). The need for balancing. A few attempts to define balancedness.

  References	<a href="http://lcm.csa.iisc.ernet.in/dsa/node92.html">Notes from the web</a>
  Exercises
  Reading

  Average depth of BSTs obtained from a randomly chosen insertion order is O(log n). The need for balancing. A few attempts to define balancedness.
  

  References

  :

  Notes from the web

  • Meeting 38 : Mon, Oct 15, 10:00 am-10:50 am

  AVL Trees. Basic and case analysis of height imbalances. Insertion. Single Rotation case.

  References
  Exercises
  Reading

  AVL Trees. Basic and case analysis of height imbalances. Insertion. Single Rotation case.
  

  References

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  None

  • Meeting 39 : Tue, Oct 16, 09:00 am-09:50 am

  Double rotation case. Recursive implementation of single rotation. Delete in AVL trees. Depth upper bounds for AVL trees. Cost of AVL tree operations.

  References
  Exercises
  Reading

  Double rotation case. Recursive implementation of single rotation. Delete in AVL trees. Depth upper bounds for AVL trees. Cost of AVL tree operations.
  

  References

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  None

• Theme 8 : Priority Queue ADT (Heaps) - 2 meetings

  • Meeting 40 : Mon, Oct 22, 10:00 am-10:50 am

  Priority Queue ADT. Motivation. An implementation idea using Binary trees. Binary heaps, Min-Heaps, Max-Heaps, Array representation. Inserting into a max-heap. Build Heap.

  References
  Exercises
  Reading

  Priority Queue ADT. Motivation. An implementation idea using Binary trees. Binary heaps, Min-Heaps, Max-Heaps, Array representation. Inserting into a max-heap. Build Heap.
  

  References

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  None

  • Meeting 41 : Tue, Oct 23, 09:00 am-09:50 am

  A recursive Buildheap. O(n) analysis. Delete-Max using BuildHeap, Heapsort and the analysis. In-place nature.

  References
  Exercises
  Reading

  A recursive Buildheap. O(n) analysis. Delete-Max using BuildHeap, Heapsort and the analysis. In-place nature.
  

  References

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  None

• Theme 9 : Dictionary ADT - II (Hashing) - 6 meetings

  • Meeting 42 : Wed, Oct 24, 08:00 am-08:50 am

  Dictionary ADT. Direct Addressing. Hashing, Collision. Handling Collision.

  References
  Exercises
  Reading

  Dictionary ADT. Direct Addressing. Hashing, Collision. Handling Collision.
  

  References

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  None

  • Meeting 43 : Fri, Oct 26, 01:00 pm-01:50 pm

  Chaining. Implementation of Chaining. Analysis of average insert, search and delete time in Chaining.

  References
  Exercises
  Reading

  Chaining. Implementation of Chaining. Analysis of average insert, search and delete time in Chaining.
  

  References

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  None

  • Meeting 44 : Mon, Oct 29, 10:00 am-10:50 am

  Open Addressing. Linear Probing. Quadratic Probing. Implementation details.

  References
  Exercises
  Reading

  Open Addressing. Linear Probing. Quadratic Probing. Implementation details.
  

  References

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  None

  • Meeting 45 : Tue, Oct 30, 09:00 am-09:50 am

  Surprise Quiz 2. <br><br> Proof that Quadratic Probing actually works if hashtable is of size prime.

  References
  Exercises
  Reading

  Surprise Quiz 2.
  
  Proof that Quadratic Probing actually works if hashtable is of size prime.
  

  References

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  None

  • Meeting 46 : Wed, Oct 31, 08:00 am-08:50 am

  Hash Functions. Adversarial argument. Randomization. Universal Hashing. Requirements from the family.

  References
  Exercises
  Reading

  Hash Functions. Adversarial argument. Randomization. Universal Hashing. Requirements from the family.
  

  References

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  None

  • Meeting 47 : Fri, Nov 02, 01:00 pm-01:50 pm

  Algebraic structures at help. Constructing a universal hash family.

  References
  Exercises
  Reading

  Algebraic structures at help. Constructing a universal hash family.
  

  References

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  None

• Theme 10 : Graph ADT (Traversals, Components and Beyond) - 5 meetings

  • Meeting 48 : Mon, Nov 05, 10:00 am-10:50 am

  Graphs. Modelling real world problems. Representations. Adjacency Matrix and Adjacency List. Reachability Problem. Printing the path. Breadth First Search.

  References
  Exercises
  Reading

  Graphs. Modelling real world problems. Representations. Adjacency Matrix and Adjacency List. Reachability Problem. Printing the path. Breadth First Search.
  

  References

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  None

  • Meeting 49 : Wed, Nov 07, 08:00 am-08:50 am

  Anaysis of BFS. Correctness of BFS. Shortest Path Computation. Depth first search.

  References
  Exercises
  Reading

  Anaysis of BFS. Correctness of BFS. Shortest Path Computation. Depth first search.
  

  References

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  None

  • Meeting 50 : Fri, Nov 09, 01:00 pm-01:50 pm

  Maintaining the connected components in a graph. Union-Find Data Structure. The requirements and an application. Implementation of Union-Find using arrays. Analysis of the implementation. Runtime bounds.

  References
  Exercises
  Reading

  Maintaining the connected components in a graph. Union-Find Data Structure. The requirements and an application. Implementation of Union-Find using arrays. Analysis of the implementation. Runtime bounds.
  

  References

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  None

  • Meeting 51 : Mon, Nov 12, 10:00 am-10:50 am

  Amortized Analysis in Data Structures. Example.

  References
  Exercises
  Reading

  Amortized Analysis in Data Structures. Example.
  

  References

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  None

  • Meeting 52 : Tue, Nov 13, 09:00 am-09:50 am

  Beyond the basic data structures - a discussion on what we did not cover in the course. Research frontiers and pointers.

  References
  Exercises
  Reading

  Beyond the basic data structures - a discussion on what we did not cover in the course. Research frontiers and pointers.
  

  References

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  None

• Evaluation Meetings - 3 meetings

  • Meeting 53 : Wed, Sep 05, 08:00 am-08:50 am

  Quiz - 1

  References
  Exercises
  Reading

  Quiz - 1
  

  References

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  None

  • Meeting 54 : Fri, Oct 05, 01:00 pm-01:50 pm

  Short Exam 1

  References
  Exercises
  Reading

  Short Exam 1
  

  References

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  None

  • Meeting 55 : Wed, Oct 17, 08:00 am-08:50 am

  Quiz - 2

  References
  Exercises
  Reading

  Quiz - 2
  

  References

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  None