Browse topic-based Data Structure And Algorithm practice sets.
302 practice sets · Page 10 of 16
If an optimal solution can be created for a problem by constructing optimal solutions for its subproblems, the problem possesses ____________ property.
Overlapping subproblems
Optimal substructure
Memoization
Greedy
Correct Answer: B — Optimal substructure
Explanation:
Optimal substructure is the property in which an optimal solution is found for the problem by constructing optimal solutions for the subproblems.
Which of the following is/are property/properties of a dynamic programming problem?
Optimal substructure
Overlapping subproblems
Greedy approach
Both optimal substructure and overlapping subproblems
Correct Answer: D — Both optimal substructure and overlapping subproblems
Explanation:
A problem that can be solved using dynamic programming possesses overlapping subproblems as well as optimal substructure properties.
Which of the following lines should be added to complete the above code?
arr[num_of_dice][S]
arr[dice][sm]
arr[dice][S]
arr[S][dice]
Correct Answer: A — arr[num_of_dice][S]
Explanation:
The line arr[num_of_dice][S] completes the above code.
There are 10 dice having 5 faces. The faces are numbered from 1 to 5. What is the number of ways in which a sum of 4 can be achieved?
0
2
4
8
Correct Answer: A — 0
Explanation:
Since there are 10 dice and the minimum value each die can take is 1, the minimum possible sum is 10. Hence, a sum of 4 cannot be achieved.
There are n dice with f faces. The faces are numbered from 1 to f. What is the maximum possible sum that can be obtained when the n dice are rolled together?
1
f*f
n*n
n*f
Correct Answer: D — n*f
Explanation:
The sum will be maximum when all the faces show a value f. The sum in this case will be n*f.
There are n dice with f faces. The faces are numbered from 1 to f. What is the minimum possible sum that can be obtained when the n dice are rolled together?
1
f
n
n*f
Correct Answer: C — n
Explanation:
The sum will be minimum when all the faces show a value 1. The sum in this case will be n.
You have 2 dice each of them having 6 faces numbered from 1 to 6. What is the number of ways in which a sum of 11 can be achieved?
0
1
2
3
Correct Answer: C — 2
Explanation:
The sum of 11 can be achieved when the dice show {6, 5} or {5, 6}.
You have 3 dice each having 6 faces. What is the number of permutations that can be obtained when you roll the 3 dice together?
27
36
216
81
Correct Answer: C — 216
Explanation:
The total number of permutations that can be obtained is 6 * 6 * 6 = 216.
You have n dice each having f faces. What is the number of permutations that can be obtained when you roll the n dice together?
nnn...f times
fff...n times
nnn...n times
fff...f times
Correct Answer: B — fff...n times
Explanation:
Each die can take f values and there are n dice. So, the total number of permutations is fff...n times.
You are given n dice each having f faces. You have to find the number of ways in which a sum of S can be achieved. This is the dice throw problem. Which of the following methods can be used to solve the dice throw problem?
Brute force
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 dice throw problem.
Which of the following lines should be added to complete the "if(op[pos] == '|')" part of the code?
False[row][col] += True[row][pos] * False[pos+1][col]; True[row][col] += t_row_pos * t_pos_col + False[row][pos] * False[pos+1][col];
False[row][col] += False[row][pos] * True[pos+1][col]; True[row][col] += t_row_pos * t_pos_col - True[row][pos] * True[pos+1][col];
False[row][col] += True[row][pos] * True[pos+1][col]; True[row][col] += t_row_pos * t_pos_col + True[row][pos] * True[pos+1][col];
False[row][col] += False[row][pos] * False[pos+1][col]; True[row][col] += t_row_pos * t_pos_col - False[row][pos] * False[pos+1][col];
Correct Answer: D — False[row][col] += False[row][pos] * False[pos+1][col]; True[row][col] += t_row_pos * t_pos_col - False[row][pos] * False[pos+1][col];
Explanation:
The following lines should be added:
False[row][col] += False[row][pos] * False[pos+1][col];
True[row][col] += t_row_pos * t_pos_col + False[row][pos] * False[pos+1][col];
What is the maximum number of ways in which a boolean expression with n + 1 terms can be parenthesized, such that the output is true?
nth catalan number
n factorial
n cube
n square
Correct Answer: A — nth catalan number
Explanation:
The number of ways will be maximum when all the possible parenthesizations result in a true value. The number of possible parenthesizations is given by the nth catalan number.
Which of the following gives the total number of ways of parenthesizing an expression with n + 1 terms?
n factorial
n square
n cube
nth catalan number
Correct Answer: D — nth catalan number
Explanation:
The nth Catalan number gives the total number of ways of parenthesizing an expression with n + 1 terms.
Consider the expression T | F ∧ T. In how many ways can the expression be parenthesized so that the output is F (false)?
0
1
2
3
Correct Answer: B — 1
Explanation:
The expression can be parenthesized as (T | F) ∧ T, so that the output is F (false).
Consider the expression T & F ∧ T. What is the number of ways in which the expression can be parenthesized so that the output is T (true)?
0
1
2
3
Correct Answer: C — 2
Explanation:
The expression can be parenthesized as (T & F) ∧ T or T & (F ∧ T), so that the output is T.
Consider the expression T & F | T. What is the number of ways in which the expression can be parenthesized so that the output is T (true)?
0
1
2
3
Correct Answer: C — 2
Explanation:
The expression can be parenthesized as T & (F | T) and (T & F) | T so that the output is T.
You are given a boolean expression which consists of operators &, | and ∧ (AND, OR and XOR) and symbols T or F (true or false). You have to find the number of ways in which the symbols can be parenthesized so that the expression evaluates to true. This is the boolean parenthesization problem. Which of the following methods can be used to solve the problem?
Dynamic programming
Recursion
Brute force
Dynamic programming, Recursion and Brute force
Correct Answer: D — Dynamic programming, Recursion and Brute force
Explanation:
Dynamic programming, Recursion and Brute force can be used to solve the Boolean parenthesization problem.
You are given infinite coins of denominations 3, 5, 7. Which of the following sum CANNOT be achieved using these coins?
15
16
17
4
Correct Answer: D — 4
Explanation:
Sums can be achieved as follows:
15 = {5,5,5}
16 = {3,3,5,5}
17 = {3,7,7}
we can't achieve for sum=4 because our available denominations are 3,5,7 and sum of any two denominations is greater than 4.
You are given infinite coins of denominations 5, 7, 9. Which of the following sum CANNOT be achieved using these coins?
50
21
13
23
Correct Answer: C — 13
Explanation:
One way to achieve a sum of 50 is to use ten coins of 5. A sum of 21 can be achieved by using three coins of 7. One way to achieve a sum of 23 is to use two coins of 7 and one coin of 9. A sum of 13 cannot be achieved.
You are given infinite coins of denominations 1, 3, 4. What is the minimum number of coins required to achieve a sum of 7?
1
2
3
4
Correct Answer: B — 2
Explanation:
A sum of 7 can be achieved by using a minimum of two coins {3,4}.
