Match the following with respect to algorithm paradigms:

 

List - I

 

List - II

(a)

The 8-Queen’s problem

(i)

Dynamic programming

(b)

Single-Source shortest paths

(ii)

Divide and conquer

(c)

STRASSEN’s Matrix multiplication

(iii)

Greedy approach

(d)

Optimal binary search trees

(iv)

Backtracking

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  1. (a) - (iv), (b) - (i), (c) - (iii), (d) - (ii)
  2. (a) - (iv), (b) - (iii), (c) - (i), (d) - (ii)
  3. (a) - (iii), (b) - (iv), (c) - (ii), (d) - (i)
  4. (a) - (iv), (b) - (iii), (c) - (ii), (d) - (i)

Answer (Detailed Solution Below)

Option 4 : (a) - (iv), (b) - (iii), (c) - (ii), (d) - (i)
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Detailed Solution

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8 - queen’s problem:

  • In this, 8 queens are placed on a 8 × 8 chessboard such that none of them can take same place.
  • It is the backtracking approach. In backtracking approach, all the possible configurations are checked and check whether result is obtained or not.
  •  A queen can only be attacked if it is in the same row or column or diagonal of another queen.

 

Single source shortest path:

  • It is used to find the shortest path starting from a source to the all other vertices.
  • It is based on greedy approach.
  • Example of single source shortest path algorithm is Dijkstra’s algorithm which initially consider all the distance to infinity and distance to source is 0.

 

Strassen’s matrix multiplication:

  • It is a method used for matrix multiplication. It uses divide and conquer approach to multiply the matrices.
  • Time consumption is improved by using Strassen’s method as compared to standard multiplication method.
  • It is faster than standard method. Strassen’s multiplication can be performed only on square matrices.

 

Optimal binary search tree:

  • It is also known as weight balanced binary tree. In optimal binary search tree, dummy key is added in the tree by first constructing a binary search tree.
  • It is based on dynamic programming approach. Total cost must be as small as possible.
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