This Algorithms Final Exam Study Guide assesses understanding of heap properties, sorting algorithms, and hash tables. It tests knowledge crucial for efficient data manipulation and problem-solving in computer science.
True
False
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Ω(o)
W(g(n))
θ(n)
θ(1)
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True
False
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True
False
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True
False
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False
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False
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O
Ω
O
θ
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True
False
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False
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Globally, locally
Top-down, bottom-up
Locally, globally
Bottom-up, top-down
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True
False
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False
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False
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False
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True
False
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True
False
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True
False
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True
False
True
False
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Best case running time for Quicksort
Worst-case running time for Quicksort
Best-case running time for Heapsort
Worst-case running time for Heapsort
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True
False
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False
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Overlapping subproblems
Topological sort
Memoization
Dynamic recursion
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It may have one or more cycles.
It has |V| -1 edges.
It is not necessarily unique.
The sum of weights of the edges is minimal.
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False
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False
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Doubling the recursive calls
Transforming recursive calls to a loop
Solving the same subproblem multiple times
Solving larger subproblems first, followed by smaller subproblems
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The worst case search time
The space remaining in the hash table
The number of expected elements at any slot
The number of probes for insertion
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θ(n^3)
O(n^3)
O(n lg n)
Ω(2^n)
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T(n-1) + θ(n)
θ(n^2)
2T(n/2) + θ(1)
O(n)
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True
False
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2
25
4
15
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It is an optimization problem.
The problem can be solved recursively.
The problem does not have a brute force solution.
The subproblems for the solution overlap.
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Universal hashing
Double hashing
Quadratic probing
Linear probing
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True
False
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False
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Recursion
Divide
Combine
Base case
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Dynamic programming
Binary sort
Depth-first search
Rotation
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|V| and |E^2|
In E and |V|
|E| and |V^2|
|V| and |E| + |V|
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F1
F2
F3
F4
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θ(n)
O(1)
O(α)
θ(n^2)
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The root is red.
The root and leaves are black.
All simple paths from a node to the leaves contain the same number of red and black nodes.
A red node can have only one black child.
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