Data Structures Algorithms-II MCQs

Page No. 106

Which of the following methods can be used to solve the Knapsack problem?


aBrute force algorithm

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bRecursion

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cDynamic programming

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dBrute force, Recursion and Dynamic Programming

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The Knapsack problem is an example of ____________


aGreedy algorithm

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b 2D dynamic programming

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c1D dynamic programming

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dDivide and conquer

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Consider the brute force implementation in which we find all the possible ways of multiplying the given set of n matrices. What is the time complexity of this implementation?


aO(n!)

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bO(n3)

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cO(n2)

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dExponential

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View Answer Exponential

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?


a6050

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b7500

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c7750

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d12000

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View Answer 7750

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?


a18000

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b12000

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c24000

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d32000

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View Answer 18000

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?


a10*20

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b20*30

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c10*30

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d10*20*30

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View Answer 10*20*30

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?


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

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

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

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

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


aDynamic programming

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bBrute force

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cRecursion

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dDynamic Programming, Brute force, Recursion

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Which of the following is the longest common subsequence between the strings “hbcfgmnapq” and “cbhgrsfnmq” ?


ahgmq

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bcfnq

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cbfmq

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dfgmna

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View Answer fgmna

What is the time complexity of the brute force algorithm used to find the longest common subsequence?


aO(n)

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bO(n2)

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cO(n3)

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dO(2n)

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View Answer O(2n)

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