Practice: Several Calls

Five problems where a function calls itself more than once: the largest number by halves, the Tower of Hanoi, counting ways to climb, binary strings under a rule, and lucky numbers.

• Write the base cases first — and check whether you need two (done and went too far).
• For the maximum, split [l, r] in two and take the bigger of the two answers.
• The Tower of Hanoi prints up to a million moves. Print the count first — 2ⁿ − 1, found by doubling 1 n times and taking away 1 — and use "\n" with the fast-IO lines.
• For the binary strings, try 0 before 1 and the order comes out right by itself.
• For lucky numbers, build every number made of 4s and 7s up to n, and check each one.