Numbers With Repeated Digits

Numbers With Repeated Digits - Problem

Given an integer n, return the number of positive integers in the range [1, n] that have at least one repeated digit.

For example, if n = 100, numbers like 11, 22, 33, 44, 55, 66, 77, 88, 99, 100 all have repeated digits.

Input & Output

Example 1 — Small Number

$ Input: n = 20

› Output: 1

💡 Note: Only number 11 has repeated digits in range [1, 20]

Example 2 — Medium Number

$ Input: n = 100

› Output: 10

💡 Note: Numbers 11, 22, 33, 44, 55, 66, 77, 88, 99, 100 all have repeated digits

Example 3 — Single Digit

$ Input: n = 5

› Output: 0

💡 Note: Numbers 1, 2, 3, 4, 5 all have unique digits (single digit numbers)

Constraints

1 ≤ n ≤ 10⁹

Visualization

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Asked in

G Google 15 a Amazon 8 M Microsoft 5

The key insight is that it's easier to count numbers without repeated digits using combinatorics, then subtract from total n. Best approach uses mathematical permutations to count unique digit numbers efficiently. Time: O(d²), Space: O(d) where d is number of digits.

Common Approaches

✓ Brute Force

⏱️ Time: O(n × d) Space: O(d)

For every number from 1 to n, convert it to string and check if any digit appears more than once. Count all numbers that have at least one repeated digit.

Mathematical Approach

⏱️ Time: O(d²) Space: O(d)

Instead of counting numbers with repeated digits directly, count numbers without repeated digits using combinatorics, then subtract from total count n. This is much more efficient.

Brute Force — Algorithm Steps

Step 1: Iterate through all numbers from 1 to n
Step 2: For each number, check if it has repeated digits
Step 3: Count numbers with repeated digits

Visualization

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Step-by-Step Walkthrough

Check Each Number

Go through 1, 2, 3, ..., n

Detect Duplicates

For each number, check if any digit repeats

Count Results

Sum up all numbers with repeated digits

Code -

solution.c — C

#include <stdio.h>
#include <stdbool.h>
#include <string.h>

bool hasRepeatedDigits(int num) {
    char s[20];
    sprintf(s, "%d", num);
    int len = strlen(s);
    
    for (int i = 0; i < len; i++) {
        for (int j = i + 1; j < len; j++) {
            if (s[i] == s[j]) {
                return true;
            }
        }
    }
    return false;
}

int solution(int n) {
    int count = 0;
    for (int i = 1; i <= n; i++) {
        if (hasRepeatedDigits(i)) {
            count++;
        }
    }
    return count;
}

int main() {
    int n;
    scanf("%d", &n);
    int result = solution(n);
    printf("%d\n", result);
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n × d)

Check each of n numbers, each with d digits to verify

✓ Linear Growth

Space Complexity

O(d)

Space to store digit frequency for each number

✓ Linear Space

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Input & Output

Constraints

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Related Problems

Common Approaches

Brute Force — Algorithm Steps

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Code -

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