7 practice sets · Page 1 of 1
Which of the following lines completes the above code?
find_max(ans[itm - 1][w - wt[itm - 1]] + val[itm - 1], ans[itm - 1][w])
find_max(ans[itm - 1][w - wt[itm - 1]], ans[itm - 1][w])
ans[itm][w] = ans[itm - 1][w];
ans[itm+1][w] = ans[itm - 1][w];
Correct Answer: A — find_max(ans[itm - 1][w - wt[itm - 1]] + val[itm - 1], ans[itm - 1][w])
Explanation:
find_max(ans[itm - 1][w - wt[itm - 1]] + val[itm - 1], ans[itm - 1][w]) completes the above code.
The 0-1 Knapsack problem can be solved using Greedy algorithm.
True
False
Correct Answer: B — False
Explanation:
The Knapsack problem cannot be solved using the greedy algorithm.
What is the time complexity of the brute force algorithm used to solve the Knapsack problem?
O(n)
O(n!)
O(2^{n})
O(n^{3})
Correct Answer: C — O(2^{n})
Explanation:
In the brute force algorithm all the subsets of the items are found and the value of each subset is calculated. The subset of items with the maximum value and a weight less than equal to the maximum allowed weight gives the answer. The time taken to calculate all the subsets is O(2^{n}).
Which of the following problems is equivalent to the 0-1 Knapsack problem?
You are given a bag that can carry a maximum weight of W. You are given N items which have a weight of {w1, w2, w3,...., wn} and a value of {v1, v2, v3,...., vn}. You can break the items into smaller pieces. Choose the items in such a way that you get the maximum value
You are studying for an exam and you have to study N questions. The questions take {t1, t2, t3,...., tn} time(in hours) and carry {m1, m2, m3,...., mn} marks. You can study for a maximum of T hours. You can either study a question or leave it. Choose the questions in such a way that your score is maximized
You are given infinite coins of denominations {v1, v2, v3,....., vn} and a sum S. You have to find the minimum number of coins required to get the sum S
You are given a suitcase that can carry a maximum weight of 15kg. You are given 4 items which have a weight of {10, 20, 15,40} and a value of {1, 2, 3,4}. You can break the items into smaller pieces. Choose the items in such a way that you get the maximum value
Correct Answer: B — You are studying for an exam and you have to study N questions. The questions take {t1, t2, t3,...., tn} time(in hours) and carry {m1, m2, m3,...., mn} marks. You can study for a maximum of T hours. You can either study a question or leave it. Choose the questions in such a way that your score is maximized
Explanation:
In this case, questions are used instead of items. Each question has a score which is same as each item having a value. Also, each question takes a time t which is same as each item having a weight w. You have to maximize the score in time T which is same as maximizing the value using a bag of weight W.
You are given a knapsack that can carry a maximum weight of 60. There are 4 items with weights {20, 30, 40, 70} and values {70, 80, 90, 200}. What is the maximum value of the items you can carry using the knapsack?
160
200
170
90
Correct Answer: A — 160
Explanation:
The maximum value you can get is 160. This can be achieved by choosing the items 1 and 3 that have a total weight of 60.
Which of the following methods can be used to solve the Knapsack problem?
Brute force algorithm
Recursion
Dynamic programming
Brute force, Recursion and Dynamic Programming
Correct Answer: D — Brute force, Recursion and Dynamic Programming
Explanation:
Brute force, Recursion and Dynamic Programming can be used to solve the knapsack problem.
The Knapsack problem is an example of ____________
Greedy algorithm
2D dynamic programming
1D dynamic programming
Divide and conquer
Correct Answer: B — 2D dynamic programming
Explanation:
Knapsack problem is an example of 2D dynamic programming.
