Question

1. Minimization and Maximization Problems

Which of the following best describes the role of the greedy approach in minimization (min) and maximization (max) optimization problems?

A) The greedy approach never works for min or max problems

B) The greedy approach never works for min problems but may work for max problems

C) The greedy approach never works for max problems but may work for min problems

D) The greedy approach may work for min and max problems

E) The greedy approach always works for min problems and may work for max problems

F) The greedy approach always works for max problems and may work for min problems

G) The greedy approach always works for min and max problems

2. Greedy Algorithm Examples

Which algorithms use the greedy strategy?

Multiple answers:You can select more than one option

A) Median-of-Medians with Quick Select

B) Prim's Minimum Spanning Tree algorithm

C) Kruskal's Minimum Spanning Tree algorithm

D) Cocktail-Shaker Sort

E) Huffman Coding

F) Dijkstra's Single-Source-Shortest-Path algorithm

3. Coin Change Problem

Which function should be used to determine how many coins of denomination d should be used to make change for the remaining value v, assuming that the higher denominations of coins have already been tried and exhausted?

A) v - d (subtraction)

B) v x d (multiplication)

C) v / d (fractional division)

D) v // d (integer division)

E) v % d (modulo)

F) v ^ d (exponentiation)

4. Coin Change Algorithm - Time Complexity

Which best describes the worst case time complexity of the Coin Change Algorithm as originally implemented and after the suggested improvement? Let n be the amount for which we are trying to make change, and let d be the number of denominations of coins.

A) O(n^d) staying at O(n^d)

B) O(n^d) reducing to O(n)

C) O(n^d) reducing to O(d)

D) O(n x d) staying at O(n x d)

E) O(n x d) reducing to O(n)

F) O(n x d) reducing to O(d)

G) O(n / d) staying at O(n / d)

H) O(n / d) increasing to O(n)

I) O(n / d) increasing to O(d)

Please, include a short explanation with the answer.

Answer 1

1) Minimization and Maximization Problems-
D) The greedy approach may work for min and max problems
This is because sometimes greedy approach works and when it fails dynamic programming is used for optimization.

2) Greedy Algorithm Examples-
B) Prim's Minimum Spanning Tree algorithm
C) Kruskal's Minimum Spanning Tree algorithm
D) Cocktail-Shaker Sort
E) Huffman Coding
F) Dijkstra's Single-Source-Shortest-Path algorithm
A) Median-of-Medians with Quick Select is a divide and conquer algorithm.

3) Coin Change Problem-
D) v // d (integer division)​​​​​​​ must be used to find the no. of coins of denomination d that should be used to make change for the remaining value v.

4) Coin Change Algorithm - Time Complexity-
D) O(n x d) staying at O(n x d)​​​​​​​ achived using dynamic programming.


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