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Algorithm Design Techniques | Dynamic Programming

Define Rn to be the maximum amount earned by cutting a rod of length n meters into one or more pieces of integer length and selling them. For i > 0, let p[i] denotes the selling price of a rod whose length is i meters. Consider the array of prices: p[1] = 1, p[2] = 5, p[3] = 8, p[4] = 9, p[5] = 10, p[6] = 17, p[7] = 18 Which of the following statements is/are correct about R7?
Which of the following is a correct time complexity to solve the 0/1 knapsack problem where n and w represents the number of items and capacity of knapsack respectively?
Consider product of three matrices M1, M2 and M3 having w rows and x columns, x rows and y columns, and y rows and z columns. Under what condition will it take less time to compute the product as (M1M2)M3 than to compute M1 (M2M3)?
A 0-1 knapsack problem has four items and knapsack capacity 11. The weight and profit of each item is given in below table. Pi (Rs.) 50 30 32 27    W = 11  Wi (Kg) 5 6 4 3 Which of the following greedy strategy gives the maximum profit?
Assume that multiplying a matrix G1 of dimension ? × ? with another matrix G2 of dimension ? × ? requires ??? scalar multiplications. Computing the product of n matrices G1G2G3…Gn can be done by parenthesizing in different ways. Define Gi Gi+1 as an explicitly computed pair for a given paranthesization if they are directly multiplied. For example, in the matrix multiplication chain G1G2G3G4G5G6 using parenthesization (G1(G2G3))(G4(G5G6)), G2G3 and G5G6 are the only explicitly computed pairs.Consider a matrix multiplication chain F1F2F3F4F5, where matrices F1, F2, F3, F4 and F5 are of dimensions 2 × 25, 25 × 3, 3 × 16, 16 × 1 and 1 × 1000, respectively. In the parenthesization of F1F2F3F4F5 that minimizes the total number of scalar multiplications, the explicitly computed pairs is/are
Which of the following is the longest common subsequence of the sequences <h, i, n, d, u, i, s, t, a, n> and <i, n, d, i, a, n>?
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