For some calculations, we want an algorithm that accepts only positive integers up to 100. Accept_1to100_Algo INPUT Number IF (0<= Number) AND (Number <= 100) ACCEPT Else REJECT
On what values will this algorithm fail?
The algorithm will fail on the value 0. The requirement is to accept only positive integers up to 100, which means numbers from 1 to 100. However, the condition (0 <= Number) includes 0, which is not a positive integer. Therefore, the algorithm incorrectly accepts 0 when it should reject it.
Can you improve the algorithm?
Yes, the algorithm can be improved. The condition needs to be modified to exclude 0. The improved algorithm is:
Accept_1to100_Algo INPUT Number IF (0 < Number) AND (Number <= 100) ACCEPT Else REJECT
By changing (0 <= Number) to (0 < Number), the algorithm now correctly accepts only positive integers from 1 to 100 and rejects 0 along with all other invalid values.
Explanation
The question tests understanding of algorithm correctness and boundary conditions. The original algorithm uses 'less than or equal to' (<=) which includes 0 in the acceptable range. Since the requirement specifies 'positive integers', 0 must be excluded. Positive integers start from 1, not 0. The improvement changes the comparison operator from <= to <, ensuring only values strictly greater than 0 are accepted.