Practice: Program Decomposition

Eight problems to split into functions. Before you type, write down which helpers you need and what each one takes and returns — then main almost writes itself.

• Prime Predicate: up to 2·10⁴ numbers of up to 10⁹, some negative. The d * d <= n loop is fast enough; trying every d up to n is not.
• GCD Prime Check: two helpers, and one call inside the other — isPrime(gcd(a, b)). Remember that 1 is not prime.
• Primes with Digit Sum Divisible by 3: when no number qualifies, print only the 0 line.
• Perfect, Abundant, or Deficient: the proper divisors are all the divisors except n itself. Add them up with divisor pairs, and take care when d and n / d are the same number. The number 1 has no proper divisors.
• Most Frequent Character: count the letters in an array of 26. On a tie the smallest letter wins, so go from a to z and replace the best only when a count is strictly bigger.
• Palindrome 2 asks for two things at once: one of the two strings is a palindrome, and one of the two joined strings, s + t or t + s, is a palindrome too. One isPalindrome, four calls.
• Operation Dispatcher: one function that gets the command as a string and the two numbers, and returns the result. The products fit in a long long.
• Rotate Matrix: the grid can be 500 × 500, a quarter of a million numbers — keep the fast-IO lines. Work out where the element of row i, column j of the answer comes from on a 2 × 2 and a 3 × 3 example first. When n = 0, print nothing.