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## Data Structure Questions and Answers-Matrix-chain Multiplication

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Question 1 |

Which of the following methods can be used to solve the matrix chain multiplication problem?

Dynamic programming | |

Brute force | |

Recursion | |

All of the mentioned |

**Aptitude test Questions answers**

Question 1 Explanation:

All of the mentioned methods can be used to solve the matrix chain multiplication problem.

Question 2 |

Which of the following is the recurrence relation for the matrix chain multiplication problem where mat[i-1] * mat[i] gives the dimension of the ith matrix?

dp[i, j] = 1 if i=j dp[i, j] = min{dp[i, k] + dp[k+1, j]} | |

dp[i, j] = 0 if i=j dp[i, j] = min{dp[i, k] + dp[k+1, j]} | |

dp[i, j] = 1 if i=j dp[i, j] = min{dp[i, k] + dp[k+1, j]} + mat[i-1]*mat[k]*mat[j]. | |

dp[i, j] = 0 if i=j dp[i, j] = min{dp[i, k] + dp[k+1, j]} + mat[i-1]*mat[k]*mat[j]. |

**Management Questions answers**

Question 2 Explanation:

The recurrence relation is given by:

dp[i, j] = 0 if i=j

dp[i, j] = min{dp[i, k] + dp[k+1, j]} + mat[i-1]*mat[k]*mat[j].

Question 3 |

Consider the two matrices P and Q which are 10 x 20 and 20 x 30 matrices respectively. What is the number of multiplications required to multiply the two matrices?

10*20 | |

20*30 | |

10*30 | |

10*20*30 |

**Bank exam Questions answers**

Question 3 Explanation:

The number of multiplications required is 10*20*30.

Question 4 |

Consider the matrices P, Q and R which are 10 x 20, 20 x 30 and 30 x 40 matrices respectively. What is the minimum number of multiplications required to multiply the three matrices?

18000 | |

12000 | |

24000 | |

32000 |

**English literature Questions answers**

Question 4 Explanation:

The minimum number of multiplications are 18000. This is the case when the matrices are parenthesized as (P*Q)*R.

Question 5 |

Consider the matrices P, Q, R and S which are 20 x 15, 15 x 30, 30 x 5 and 5 x 40 matrices respectively. What is the minimum number of multiplications required to multiply the four matrices?

6050 | |

7500 | |

7750 | |

12000 |

**Education Questions answers**

Question 5 Explanation:

The minimum number of multiplications required is 7750.

There are 5 questions to complete.