2. Consider the following more complex variant of the Tower of Hanoi puzzle. The puzzle has...

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2. Consider the following more complex variant of the Tower of Hanoi puzzle. The puzzle has a row of k pegs, numbered from 1 to k. In a single turn, you are allowed to move the smallest disk on peg i to either peg i-1 or peg i + 1, for any index i; as usual, you are not allowed to place a bigger disk on a smaller disk. Your mission is to move a stack of n disks from peg 1 to peg k. (a) Describe a recursive algorithm for the case k = 3. Exactly how many moves does your algorithm make? (b) Describe a recursive algorithm for the case k = n+1 that requires at most O(n³) moves. [Hint: Use part (a).] (c) Describe a recursive algorithm for the case k = n+1 that requires at most O(n²) moves. [Hint: Don't use part (a).] 2. Consider the following more complex variant of the Tower of Hanoi puzzle. The puzzle has a row of k pegs, numbered from 1 to k. In a single turn, you are allowed to move the smallest disk on peg i to either peg i-1 or peg i + 1, for any index i; as usual, you are not allowed to place a bigger disk on a smaller disk. Your mission is to move a stack of n disks from peg 1 to peg k. (a) Describe a recursive algorithm for the case k = 3. Exactly how many moves does your algorithm make? (b) Describe a recursive algorithm for the case k = n+1 that requires at most O(n³) moves. [Hint: Use part (a).] (c) Describe a recursive algorithm for the case k = n+1 that requires at most O(n²) moves. [Hint: Don't use part (a).]

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a Recursive algorithm for k 3 Heres a recursive algorithm for k 3 1 Base cases If n 0there are no di... View the full answer