Following is an algorithm to classify numbers as “Single Digit”, “Double Digit” or “Big”. Classify_Numbers_Algo INPUT Number IF Number < 9 “Single Digit” Else If Number < 99 “Double Digit” Else “Big” Verify for (5, 9, 47, 99, 100 200) and correct the algorithm if required
Verification of Algorithm:
For Number = 5: Is 5 < 9? Yes. Output: "Single Digit". This is correct as 5 is a single digit number.
For Number = 9: Is 9 < 9? No. Else If 9 < 99? Yes. Output: "Double Digit". This is incorrect because 9 is a single digit number, not double digit.
For Number = 47: Is 47 < 9? No. Else If 47 < 99? Yes. Output: "Double Digit". This is correct as 47 is a double digit number.
For Number = 99: Is 99 < 9? No. Else If 99 < 99? No. Else: "Big". This is incorrect because 99 is a double digit number, not "Big".
For Number = 100: Is 100 < 9? No. Else If 100 < 99? No. Else: "Big". This is correct.
For Number = 200: Is 200 < 9? No. Else If 200 < 99? No. Else: "Big". This is correct.
Corrected Algorithm:
Classify_Numbers_Algo INPUT Number IF Number <= 9 "Single Digit" Else If Number <= 99 "Double Digit" Else "Big"
The algorithm needs correction because the conditions use "<" (less than) instead of "<=" (less than or equal to). Numbers 9 and 99 are boundary values that are misclassified. Using "<=" ensures that single digit numbers (0-9) and double digit numbers (10-99) are correctly identified.
Explanation
The algorithm has logical errors in the boundary conditions. The condition 'Number < 9' excludes 9 from being classified as 'Single Digit', and 'Number < 99' excludes 99 from being classified as 'Double Digit'. The corrected algorithm uses '<=' to include these boundary values properly.
Solution Steps
Step 1: Test each input value (5, 9, 47, 99, 100, 200) through the algorithm
Step 2: Identify that 9 is wrongly classified as 'Double Digit' instead of 'Single Digit'
Step 3: Identify that 99 is wrongly classified as 'Big' instead of 'Double Digit'
Step 4: Correct the conditions by changing '<' to '<=' for proper boundary handling