17 Good Number
Problem Statement
Write a Recursive Approach to Check if a Given Digit String Represents a Good Number.
A digit string is good if the digits (0-indexed) at even indices are even and the digits at odd indices are prime ((2, 3, 5, or 7).
Examples:
| Sr # | Input | Expected Output | Description |
|---|---|---|---|
| 1 | 02468 | Not Good | Number 6 at index 3 is not a prime number. |
| 2 | 23478 | Good | All digits at even indices are even, and all digits at odd indices are prime. Therefore, the digit string is considered "good". |
| 3 | 224365 | Good | All digits at even indices are even, and all digits at odd indices are prime. Therefore, the digit string is considered "good". |
Try it yourself
Try solving this question here:
🎯 STRICT STANDOUT — Problem cue: Good Number
1. Why
Count good digit strings often reduces to modular fast pow: 5^ceil * 4^floor mod 1e9+7.
2. Big-O (K11)
Fast pow T(e)=T(e/2)+O(1) → Θ(log e) time/stack; iterative pow Θ(1) space3. Pattern + when-NOT
FAST POW / modular counting. When-NOT: tiny n loop; enumerate strings → backtrack.
4. Edge
n=1 small; exp=0 → 1; mod mul every step5. Panel
Q: Why log not linear mul? A: Square and halve exponent.
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