Tail calls and pruning

Questions 1 to 5 of 8

1. 1. True or false, and why: in this function, the recursive call is in tail position. ``cpp int countUp(int n) { if (n == 0) return 0; return 1 + countUp(n - 1); } ``

   True, because the call is returned directly from the return statement.False, because 1 is added after the call returns, so the function still has work to do.
2. 2. True or false, and why: a tail-recursive factorial with 10,000,000 calls runs without a crash when built with plain g++ -std=c++20 -Wall, which uses no -O flag.

   False, because a -O0 build keeps every call frame, so the program runs out of stack and exits with code 139.True, because the call is in tail position, so the frame is reused.
3. 3. True or false, and why: rewriting a tail-recursive function as a loop gives the same answer when the loop reassigns every parameter that the recursive call changed.

   True, because the loop repeats the same steps with the same values that the recursion would pass along.False, because a loop always gives a different result from the recursion it replaces.
4. 4. The factorial accumulator is written factAcc(n, acc). Which starting value must be passed as acc in the first call, factAcc(5, ?)?

   015120
5. 5. The suffix check in the pruned sum search is written as if (sum + suffix[i] < target) break;. Why is it < and not <=?

   Because <= makes the loop run one step more, but the answers stay the same.Because the suffix sums are always bigger than the target, so <= never triggers.Because a sum equal to the target is still a valid answer, and <= would cut that branch off.Because <= stops the check from using break, so the loop keeps going.