Q. Given an array, check if the array can be divided into two subsets such that the sum of elements of the two subsets is equal. This is the balanced partition problem. Which of the following methods can be used to solve the balanced partition problem?

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Q. In which of the following cases, it is not possible to have two subsets with equal sum?

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Q. What is the time complexity of the brute force algorithm used to solve the balanced partition problem?

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Q. Consider a variation of the balanced partition problem in which we find two subsets such that |S1 – S2| is minimum. Consider the array {1, 2, 3, 4, 5}. Which of the following pairs of subsets is an optimal solution for the above problem?

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Q. What is the sum of each of the balanced partitions for the array {5, 6, 7, 10, 3, 1}?

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Q. 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?

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Q. 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?

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Q. 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?

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Q. 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?

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Q. 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?

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Q. 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?

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Q. 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?

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Q. What is time complexity of the above dynamic programming implementation of the dice throw problem where f is the number of faces, n is the number of dice and s is the sum to be found?

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Q. What is space complexity of the above dynamic programming implementation of the dice throw problem where f is the number of faces, n is the number of dice and s is the sum to be found?

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Q. 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?

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Q. 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)?

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Q. 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)?

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Q. Consider the expression T | F ∧ T. In how many ways can the expression be parenthesized so that the output is F (false)?

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Q. Which of the following gives the total number of ways of parenthesizing an expression with n + 1 terms?

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Q. 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?

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