Program to Find Out the Occurrence of a Digit from a Given Range in Python

When working with digit counting problems, we need to find how many times a specific digit appears in a range of numbers. This problem asks us to count occurrences of digit d in all numbers from 1 to n.

For example, if n = 45 and d = 5, we need to count digit 5 in numbers: [5, 15, 25, 35, 45], giving us a total count of 5.

Using Recursive Approach

The recursive solution breaks down the problem by processing digits systematically ?

class Solution:
    def solve(self, n, d):
        if n < 0:
            return 0
        
        k = n // 10 - 1
        ans = self.solve(k, d) * 10 + k + 1
        
        if d == 0:
            ans -= 1
            
        m = n // 10 * 10
        while m <= n:
            ans += str(m).count(str(d))
            m += 1
            
        return ans

# Test the solution
solution = Solution()
result = solution.solve(45, 5)
print(f"Digit 5 appears {result} times in range 1 to 45")

Digit 5 appears 5 times in range 1 to 45

Using Simple Iterative Approach

A more straightforward method iterates through all numbers and counts digit occurrences ?

def count_digit_occurrences(n, d):
    count = 0
    for i in range(1, n + 1):
        count += str(i).count(str(d))
    return count

# Test with different examples
print(f"Digit 5 in range 1-45: {count_digit_occurrences(45, 5)}")
print(f"Digit 1 in range 1-100: {count_digit_occurrences(100, 1)}")
print(f"Digit 0 in range 1-20: {count_digit_occurrences(20, 0)}")

Digit 5 in range 1-45: 5
Digit 1 in range 1-100: 21
Digit 0 in range 1-20: 2

How the Recursive Algorithm Works

The recursive approach uses these key steps:

• Base case: If n < 0, return 0
• Recursive calculation: Count occurrences in smaller ranges
• Special handling: Adjust count for digit 0 (no leading zeros)
• Final range: Count occurrences in remaining numbers

Comparison

Practical Example

Let's trace through the numbers containing digit 5 in range 1-45 ?

def find_numbers_with_digit(n, d):
    numbers = []
    for i in range(1, n + 1):
        if str(d) in str(i):
            numbers.append(i)
    return numbers

# Find all numbers containing digit 5
numbers_with_5 = find_numbers_with_digit(45, 5)
print(f"Numbers containing digit 5: {numbers_with_5}")
print(f"Total count: {len(numbers_with_5)}")

Numbers containing digit 5: [5, 15, 25, 35, 45]
Total count: 5

Conclusion

Use the iterative approach for simple cases and better readability. The recursive method is more efficient for large ranges but requires careful handling of edge cases like digit 0.