Encode Number

Encode Number - Problem

Given a non-negative integer num, return its encoding string. The encoding follows a pattern where each number maps to a binary-like representation.

The encoding pattern can be deduced from these examples:

0 → "" (empty string)
1 → "0"
2 → "1"
3 → "00"
4 → "01"
5 → "10"
6 → "11"

Your task is to find the pattern and implement the encoding function.

Input & Output

Example 1 — Small Number

$ Input: num = 5

› Output: "10"

💡 Note: Number 5 belongs to group 2 (range 3-6), at position 1 within the group. Position 1 in 2-bit binary is "10".

Example 2 — Edge Case Zero

$ Input: num = 0

› Output: ""

💡 Note: Zero maps to empty string according to the encoding pattern.

Example 3 — Group Boundary

$ Input: num = 3

› Output: "00"

💡 Note: Number 3 is the first in group 2, at position 0. Position 0 in 2-bit binary is "00".

Constraints

0 ≤ num ≤ 10⁹

Visualization

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Asked in

G Google 25 f Facebook 18 M Microsoft 15

The key insight is recognizing that numbers are grouped by powers of 2, where group k contains 2^k numbers encoded with k-bit binary representations. The optimal approach uses mathematical calculation to directly find the group and position. Time: O(log n), Space: O(1)

Common Approaches

Approach	Time	Space	Notes
✓ Brute Force Pattern Recognition	O(n)	O(n)	Generate all encodings from 0 to num by finding the pattern
Mathematical Pattern Recognition	O(log n)	O(1)	Directly calculate encoding using mathematical formula

Brute Force Pattern Recognition — Algorithm Steps

Analyze the given examples to find the pattern
Build encoding for each number from 0 to num
Return the encoding for the target number

Visualization

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Step-by-Step Walkthrough

Pattern Analysis

Identify groups: 0→"", 1-2→single bit, 3-6→double bit

Sequential Build

Generate encoding for each number from 0 to target

Result

Return encoding at target index

Code -

solution.c — C

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

char* solution(int num) {
    if (num == 0) {
        char* result = malloc(1);
        result[0] = '\0';
        return result;
    }
    
    // Find which group this number belongs to
    int group = 1;
    while (((1 << group) - 1) + (1 << group) <= num) {
        group++;
    }
    
    // Position within the group
    int pos = num - ((1 << group) - 1);
    
    // Generate binary representation with 'group' bits
    char* encoding = malloc(group + 1);
    for (int j = 0; j < group; j++) {
        encoding[j] = ((pos >> (group - 1 - j)) & 1) ? '1' : '0';
    }
    encoding[group] = '\0';
    
    return encoding;
}

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

Time & Space Complexity

Time Complexity

⏱️

O(n)

Need to generate encodings for all numbers from 0 to num

✓ Linear Growth

Space Complexity

O(n)

Store encodings for all numbers in a list or array

⚡ Linearithmic Space

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Related Problems

Common Approaches

Brute Force Pattern Recognition — Algorithm Steps

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Code -

Time & Space Complexity

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