Princeton University algorithm course algorithm part I week 3 sorting algorithm complexity sorting complexity

Computational Complexity: used to study the algorithm efficiency framework for solving specific problems x

Model of computation: allowed operations (allowable operations)

Cost Model: Operation counts)

Upper Bound (Upper Bound): maximum cost

Lower Bound (Lower Bound): Minimum Cost

Optimal Algorithm: The most probable cost algorithm (algorithm with best possible cost guarantee for X)

 

Example: Sorting

Computing Model: Decision Tree)

The height of the decision tree determines the time consumed.

Cost Model: Compares)

Upper Bound: The merge order is nlgn.

Lower Bound: nlgn

Optimal Algorithm: Merge Sorting (the upper time bound of mergesort reaches the lower time bound of the sorting algorithm, but mergesort consumes too much memory)

 

Factors Affecting sorting complexity

• Start order of input
  
  • If the input is more ordered, we may not need to compare the nlgn times (in the case of sequential order, insert sort only needs to compare N-1 times)
• Repeated Element
  • If the input contains repeated elements, we may not need to compare the nlgn times (3-way quicksort ))
• Digital properties of keys: We can use digital/feature comparison (digit/character compares) instead of key compares to compare numbers and strings.

Princeton University algorithm course algorithm part I week 3 sorting algorithm complexity sorting complexity