Limits, overflow and modulo

Questions 1 to 5 of 8

1. 1. An AI writes int total = 0; and adds n values, each up to 10^9, with n up to 200,000. Local tests with 5 numbers pass. The judge says wrong answer on a large test. What is the most likely cause?

   The loop bound should be n - 1cin cannot read values above 1000The output needs endl at the endThe sum can reach about 2 × 10^14, which is above the int limit of about 2.1 × 10^9, so the sum wraps
2. 2. The problem has n up to 200,000. An AI proposes checking every pair with two nested loops. Which judgement is right?

   Fine, because the loops are simple and a faster reader will fix the restFine, because 10^8 steps per second means it finishes in under a secondToo slow: about 4 × 10^10 steps, roughly 400 times the planning budget of about 10^8, so the method must changeFine, as long as the answer is printed only at the end
3. 3. Which line can overflow, and what fixes it? ``cpp int w = 100000, h = 100000; long long area = (long long)(w * h); ``

   w and h must be unsignedNothing: long long area holds any productThe product w * h is computed in int before the cast. Write (long long)w * h, so the cast comes firstarea must be int, so that the cast matches
4. 4. Binary search uses int mid = (lo + hi) / 2; with lo = 1500000000 and hi = 2000000000. The result is negative. Which replacement is correct?

   (double)(lo + hi) / 2lo + (hi - lo) / 2(lo + hi) / 2 with int changed to short(hi + lo) / 2 with the two names swapped
5. 5. What do these print? -7 % 3 in C++ with long long, and -7 % 3 in Python 3?

   -1 in C++ and -1 in Python2 in C++ and 2 in Python-1 in C++ and 2 in Python2 in C++ and -1 in Python