Find The K-th Lucky Number

Find The K-th Lucky Number - Problem

In a mystical world of numbers, 4 and 7 are considered lucky digits. A number is called lucky if it contains only these lucky digits (4 and 7).

Your task is to find the k-th lucky number in ascending order. For example:

1st lucky number: "4"
2nd lucky number: "7"
3rd lucky number: "44"
4th lucky number: "47"
5th lucky number: "74"
6th lucky number: "77"

Goal: Given an integer k, return the k-th lucky number as a string.

Input & Output

example_1.py — Python

$ Input: k = 1

› Output: "4"

💡 Note: The 1st lucky number is "4" (the smallest number containing only digits 4 and 7)

example_2.py — Python

$ Input: k = 5

› Output: "74"

💡 Note: Lucky numbers in order: 1st="4", 2nd="7", 3rd="44", 4th="47", 5th="74"

example_3.py — Python

$ Input: k = 10

› Output: "474"

💡 Note: The 10th lucky number falls in the 3-digit level: "444", "447", "474", "477", "744", "747", "774", "777" where "474" is the 10th overall

Constraints

1 ≤ k ≤ 10⁹
The answer will fit in a 32-bit integer when converted to number
Lucky numbers contain only digits 4 and 7

Visualization

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Understanding the Visualization

Tree Structure

Level 1 has 2 numbers (4,7), Level 2 has 4 numbers (44,47,74,77), etc.

Level Detection

Calculate which level contains the k-th number using powers of 2

Position Mapping

Convert the position within level to binary representation

Binary to Lucky

Map each binary bit: 0→'4', 1→'7' to construct the result

Key Takeaway

🎯 Key Insight: Lucky numbers form a complete binary tree where each level doubles the count. Using binary representation allows direct computation in O(log k) time.

Asked in

G Google 45 a Amazon 35 f Facebook 28 ⊞ Microsoft 22

The optimal solution uses binary tree representation where each lucky number corresponds to a path from root to node. By treating positions as binary numbers and mapping 0→4, 1→7, we can directly compute the k-th lucky number in O(log k) time without generating intermediate numbers.

Common Approaches

Approach	Time	Space	Notes
✓ Binary Representation (Optimal)	O(log k)	O(log k)	Convert k to binary representation and map 0→4, 1→7 based on tree structure
Brute Force (Generate All Lucky Numbers)	O(k)	O(k)	Generate lucky numbers one by one until we reach the k-th number

Binary Representation (Optimal) — Algorithm Steps

Find the level (length) of the k-th lucky number using powers of 2
Calculate the position within that level
Convert the position to binary representation
Map each binary digit: 0 → '4', 1 → '7'
Construct and return the resulting lucky number

Visualization

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Step-by-Step Walkthrough

Tree Structure

Each level l contains 2^l numbers

Find Level

Determine which level contains the k-th number

Calculate Position

Find position within that level

Binary Mapping

Convert position to binary, map 0→4, 1→7

Code -

solution.c — C

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

char* findKthLucky(int k) {
    // Find the level (length of the k-th lucky number)
    int level = 1;
    int total = 0;
    
    while (total + (1 << level) < k) {
        total += (1 << level);
        level++;
    }
    
    // Position within the current level (0-indexed)
    int pos = k - total - 1;
    
    // Convert position to binary and map to lucky digits
    char* result = (char*)malloc((level + 1) * sizeof(char));
    
    for (int i = level - 1; i >= 0; i--) {
        if (pos & (1 << i)) {
            result[level - 1 - i] = '7';
        } else {
            result[level - 1 - i] = '4';
        }
    }
    
    result[level] = '\0';
    return result;
}

int main() {
    int k;
    scanf("%d", &k);
    printf("%s\n", findKthLucky(k));
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(log k)

We only need to find the level (O(log k)) and convert position to binary (O(log k))

⚡ Linearithmic

Space Complexity

O(log k)

Space for the result string which has length proportional to log k

✓ Linear Space

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Medium Frequency

~15 min Avg. Time

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Smart Actions

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