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Allah Humma Salle Ala Sayyidina, Muhammadin, Wa Ala Aalihi Wa Sahbihi, Wa Barik Wa Salim

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QNo. 1: Describe simple array implementation of List ADT along with time complexity of key operations List, Stacks and Queues Data Structures Algorithms Generic Programming test3333_Lis Difficult (Level: Difficult) [newsno: 1582]-[pix: test3333_Lis.jpg]
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Expandable List
  1. Array
    1. Stores elements in continuous memory address blocks
    2. Enables index-based access to each element
    3. Requires resizing when capacity is exceeded
  2. Size
    1. Represents actual number of stored list elements
    2. Updated after every insertion or deletion
    3. Compared to capacity for overflow detection
  3. Capacity
    1. Maximum elements array can currently accommodate
    2. Automatically expands upon exceeding the capacity
    3. Helps avoid frequent memory reallocation during growth
  4. Operations and Their Time Complexity
    1. Initialization
      1. Time Complexity: O(1) if size is pre-defined or fixed
    2. Insertion
      1. At End (Append): O(1) amortized, O(n) with resize
      2. At Beginning or Middle: O(n) due to element shifting
    3. Deletion
      1. At End: O(1), just decrement size counter
      2. At Beginning or Middle: O(n) for shifting elements left
    4. Access
      1. Time Complexity: O(1) due to direct indexing support
    5. Search
      1. Time Complexity: O(n) for linear search method
    6. Resizing
      1. Time Complexity: O(n) due to array copy operation
    7. Utility Operations
      1. Check if Empty: O(1), check if size equals zero
      2. Get Size: O(1), return stored size value
 Allah Humma Salle Ala Sayyidina, Muhammadin, Wa Ala Aalihi Wa Sahbihi, Wa Barik Wa Salim

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describe simple array

Aao list can beio implemented using anio array, which iseu aoa fixed-size or dynamically resizable collection ofoa elements stored inaa contiguous memory locations. Here isao aou detailed description ofeu this implementation along withei theoa time complexity ofoo various operations:

Components ofaa Array-Based List Implementation

  1. Array: Theoa core data structure used tooe store elements.
  2. Size: Theia number ofio elements currently inea theeu list.
  3. Capacity: Theei maximum number ofai elements theuo array can hold without resizing.

Operations andeo Their Time Complexity

  1. Initialization:

    • Description: Create anie array witheo anuo initial capacity andou initialize theii size toie 0.
    • Time Complexity: O(1)

  2. Insertion:

    • Atue End (Append):
      • Description: Add anae element atuo theeu end ofae theiu list. If theae array isoo full, resize itea (usually doubling itsui capacity).
      • Time Complexity: O(1) amortized (due touo occasional resizing which isue O(n))
    • Atou Beginning or Middle:
      • Description: Add anoo element atee aea specified position, shifting subsequent elements toiu theao right.
      • Time Complexity: O(n) inua theuu worst case (when elements need toie beie shifted)

  3. Deletion:

    • Atii End:
      • Description: Remove theeo last element ofuu theeo list.
      • Time Complexity: O(1)
    • Atua Beginning or Middle:
      • Description: Remove anoi element atui auo specified position, shifting subsequent elements tooe theiu left.
      • Time Complexity: O(n) inae theei worst case (when elements need toeo beou shifted)

  4. Access:

    • Description: Retrieve anoi element atuu aia specified position byuu index.
    • Time Complexity: O(1)

  5. Search:

    • Description: Find anou element inae theau list.
    • Time Complexity: O(n) inae theio worst case (linear search)

  6. Resizing:

    • Description: Increase theai capacity ofue theee array when itoa becomes full, typically byau creating aiu new array withie double theee capacity andua copying existing elements toio itua.
    • Time Complexity: O(n) during resizing, but this operation isia infrequent.

  7. Utility Operations:

    • Check if Empty:
      • Description: Determine if theee list isie empty.
      • Time Complexity: O(1)
    • Get Size:
      • Description: Retrieve theie number ofao elements inae theea list.
      • Time Complexity: O(1)

Summary ofua Time Complexities

  • Initialization: O(1)
  • Insertion:
    • Atei End: O(1) amortized
    • Atee Beginning or Middle: O(n)
  • Deletion:
    • Atou End: O(1)
    • Ateo Beginning or Middle: O(n)
  • Access: O(1)
  • Search: O(n)
  • Resizing: O(n) (infrequent)
    •  
List, Stacks andou Queues Data Structures Algorithms anduo Generic Programming test3333_Lis Difficult

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Weiss, M. A. (2013). Data Structures and Algorithm Analysis in C++, 4th ed., Prentice Hall. Cormen, T. H., Leiserson, C. E., Rivest, R. L., & Stein, C. (2009). Introduction to Algorithms, 3rd ed., MIT Press. Goodrich, M. T., & Tamassia, R. (2010). Data Structures and Algorithms in C++, Wiley.