GATE CS 2015 Set 2 Q.46 (CS Q.36): Dynamic Programming

Given below are some algorithms, and some algorithm design paradigms.

List-I

List-II
i. Divide and Conquer
ii. Dynamic Programming
iii. Greedy design
iv. Depth-first search
v. Breadth-first search

Match the above algorithms on the left to the corresponding design paradigm they follow.

1-i, 2-iii, 3-i, 4-v

1-iii, 2-i, 3-i, 4-v

1-iii, 2-ii, 3-i, 4-iv

1-ii, 2-iii, 3-i, 4-v

Official answer and solution

Solution

Match classic algorithms with their primary design paradigms.

Examine the algorithmic design paradigms:

Dijkstra's Shortest Path: Repeatedly chooses the unvisited vertex with the minimum tentative distance $\implies$ Greedy design (iii).
Floyd-Warshall algorithm: Computes all-pairs shortest paths via optimal subproblems $d_{ij}^{(k)} = \min(d_{ij}^{(k-1)}, d_{ik}^{(k-1)} + d_{kj}^{(k-1)})$ $\implies$ Dynamic Programming (ii).
Binary search on a sorted array: Recursively partitions the search range in half $\implies$ Divide and Conquer (i).
Backtracking search on a graph: Explores possible candidate solutions depth-first, undoing moves upon reaching dead ends $\implies$ Depth-first search (iv).

The correct alignment is: 1-iii, 2-ii, 3-i, 4-iv (option C).

Final answer

Common trap

Classifying Dijkstra's algorithm as dynamic programming rather than greedy.

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