GATE CS 2005 Q5 — Arrays, Stacks and Queues

To find the most efficient way to store the frequencies, we analyze the range of scores we need to track:

• The input scores are integers in the range $[0, 100]$.
• We only need to print the frequency of each score above $50$.
• The scores strictly greater than $50$ are: $$\{51, 52, 53, \dots, 100\}$$

The total number of distinct scores in this range is: $$100 - 51 + 1 = 50$$

We can map these $50$ possible scores to an array of size $50$ (with indices $0$ to $49$), where index $i$ stores the frequency of the score $51 + i$. This provides $O(1)$ direct access time and uses the minimum possible memory.

Therefore, an array of $50$ numbers is the best way to store the frequencies.