Following is an algorithm to classify numbers as “Single Digit”, “Double Digit” or “Big”.
Classify_Numbers_Algo
INPUT Number
IF Number

Question

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

Accepted Answer

> [!TLDR] > Testing the boundary values exposes the bug: with `Number < 9` and `Number < 99`, the inputs 9 and 99 are misclassified — the conditions must be `<= 9` and `<= 99`. **The idea (verification and boundary testing).** An algorithm is *verified* by dry-running it on test data — and the most revealing test values are the **boundaries** between categories. Here the categories are single digit (1–9), double digit (10–99) and big (100+), so the values 9 and 99 sit exactly on the edges — and that is precisely where the given algorithm breaks. (The list "(5, 9, 47, 99, 100 200)" is read as the six values 5, 9, 47, 99, 100, 200 — the missing comma is a book misprint.) **Dry run of the algorithm as printed** | Number | IF Number < 9 | Else IF Number < 99 | Output | Expected | Verdict | |---|---|---|---|---|---| | 5 | 5 < 9 → true | — | Single Digit | Single Digit | ✔ | | 9 | 9 < 9 → **false** | 9 < 99 → true | Double Digit | Single Digit | ✘ | | 47 | false | 47 < 99 → true | Double Digit | Double Digit | ✔ | | 99 | false | 99 < 99 → **false** | Big | Double Digit | ✘ | | 100 | false | false | Big | Big | ✔ | | 200 | false | false | Big | Big | ✔ | Four of six pass; the two boundary values **9** and **99** fail because strict `<` excludes the boundary itself. **Corrected algorithm** ``` Classify_Numbers_Algo (corrected) INPUT Number IF Number <= 9 "Single Digit" Else If Number <= 99 "Double Digit" Else "Big" ``` **Python verification of the corrected version** ```python for Number in [5, 9, 47, 99, 100, 200]: …

Number	Number < 9?	Number < 99?	Printed	Correct?
5	yes	—	Single Digit	✓
9	no	yes	Double Digit	✗ (9 is single digit)
47	no	yes	Double Digit	✓
99	no	no	Big	✗ (99 is double digit)
100	no	no	Big	✓
200	no	no	Big	✓

Q.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

Concept understanding — Piecewise Billing Calculation

Piecewise Billing Calculation

The Intuition: Why "Piecewise"?

The Precise Statement

A Concrete Example: Electricity Bill

Number	IF Number < 9	Else IF Number < 99	Output	Expected	Verdict
5	5 < 9 → true	—	Single Digit	Single Digit	✓
9	9 < 9 → false	9 < 99 → true	Double Digit	Single Digit	✗
47	false	47 < 99 → true	Double Digit	Double Digit	✓
99	false	99 < 99 → false	Big	Double Digit	✗
100	false	false	Big	Big	✓
200	false	false	Big	Big	✓

Q.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

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Q.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

Unlock everything free for 14 days