Скачать или смотреть GFG POD: Count Numbers Containing Specific Digits

🎯 Count n-Digit Numbers Containing At Least One Given Digit | C++ Combinatorics Solution

In this video, we tackle a combinatorics-based counting problem in C++. Given an integer n and a list of digits arr, the goal is to count how many n-digit numbers contain at least one digit from the list.

🧩 Problem Statement
You are given:

An integer n – the number of digits

A vector arr containing allowed digits

Your task is to determine how many n-digit numbers (with no leading zero) contain at least one digit from arr.

✅ Approach Breakdown
We use the complement principle:

Total valid n-digit numbers = 9 × 10^(n − 1)
(First digit can’t be 0)

Count numbers that don’t contain any digits from arr:

Skip all digits in arr

Handle first digit separately if 0 is not present

Final Answer = Total − Count of numbers without arr digits

💡 Key Highlights
Handles edge cases like presence of 0 in arr

Efficient and runs in constant time for any input

Explains both logic and implementation clearly

Uses basic combinatorics and number theory

🛠️ Code Concepts Used
Power function to compute digit combinations

Conditional logic for first-digit constraints

Clean and readable C++ implementation

🧠 Time Complexity: O(m) or O(1) (since m ≤ 10)
👨‍💻 Language: C++

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