A program P reads in 500 integers in the range [0..100] representing the…

Answer: Use an array of 50 integers, one counter for each score from 51 through 100.

• Create an array named frequencies with 50 elements and initialize all elements to 0.

• For each of the 500 input scores s: if s > 50 then increment frequencies[s - 51].

• After processing, frequencies[i] contains the count of score (i + 51). Print each score (i + 51) with its corresponding frequencies[i].

Why this is best:

• Uses minimal fixed space (50 counters) because only scores 51–100 need tracking.

• Updates are constant time (O(1)) per score; overall time is O(500) for the inputs.

• Avoids unnecessary memory use compared to larger arrays sized for unrelated ranges or per-student storage.

Implementation note: If you instead needed frequencies for the entire 0–100 range, use an array of 101 counters and index directly by the score value.