Similar RGB Color

RGB colors can be represented in two formats:

Full format: #AABBCC where each color component (Red, Green, Blue) uses 2 hexadecimal digits
Shorthand format: #ABC where each color component uses 1 repeated hexadecimal digit (equivalent to #AABBCC)

For example, #15c is shorthand for #1155cc, and #f0a represents #ff00aa.

Your task: Given a color in full format #ABCDEF, find the most similar color that can be represented in shorthand format.

Similarity formula: The similarity between two colors #ABCDEF and #UVWXYZ is calculated as:
-(AB - UV)² - (CD - WX)² - (EF - YZ)²

The higher this value (closer to 0), the more similar the colors are. Return any shorthand color with the highest similarity.

Input & Output

example_1.py — Basic Case

$ Input: "#09f166"

› Output: "#11ee66"

💡 Note: The closest shorthand color to #09f166 is #1e6, which expands to #11ee66. This minimizes the total squared difference across all RGB components.

example_2.py — Perfect Match

$ Input: "#aabbcc"

› Output: "#abc"

💡 Note: #aabbcc is already in shorthand format as #abc, so the similarity is 0 (perfect match).

example_3.py — High Contrast

$ Input: "#ffffff"

› Output: "#fff"

💡 Note: The pure white color #ffffff has a perfect shorthand representation #fff.

Visualization

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Understanding the Visualization

Parse Target Color

Extract RGB values from the input hex color

Generate All Shorthand Colors

Create all 16³ = 4096 possible shorthand combinations

Calculate Similarities

Compute similarity score using squared difference formula

Return Best Match

Select the shorthand color with highest similarity score

Key Takeaway

🎯 Key Insight: With only 4,096 possible shorthand colors, exhaustive search is both simple and optimal, running in constant time!

Time & Space Complexity

Time Complexity

⏱️

O(1)

Always checks exactly 4096 combinations (16³), which is constant

✓ Linear Growth

Space Complexity

O(1)

Only uses a few variables to store the best color and similarity

✓ Linear Space

Constraints

color is a valid RGB color in the format #ABCDEF
Color string length is exactly 7 characters (including #)
All hex digits are lowercase letters a-f or digits 0-9
Guaranteed unique solution or multiple valid answers accepted

Asked in

G Google 15 Ae Adobe 12 f Meta 8 Apple 5

The optimal approach is to enumerate all possible shorthand colors (4096 total) and find the one with maximum similarity. Since the search space is small and fixed, this brute force method runs in O(1) constant time and is actually the most efficient solution.

Common Approaches

Approach	Time	Space	Notes
✓ Enumerate All Shorthand Colors	O(1)	O(1)	Check all 4096 possible shorthand colors to find the most similar one

Enumerate All Shorthand Colors — Algorithm Steps

Extract RGB components from input color
Iterate through all hex digits (0-F) for each color component
For each combination, create shorthand color and convert to full format
Calculate similarity using the negative squared difference formula
Keep track of the color with maximum similarity
Return the most similar shorthand color

Visualization

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Step-by-Step Walkthrough

Parse Input

Extract R=171, G=187, B=204 from #ABBCCC

Generate Candidates

Create all 4096 shorthand colors (16³ combinations)

Calculate Similarity

For each candidate, compute similarity score

Find Maximum

Return the shorthand color with highest similarity

Code -

solution.c — C

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

int hexToInt(char c) {
    if (c >= '0' && c <= '9') return c - '0';
    if (c >= 'a' && c <= 'f') return c - 'a' + 10;
    if (c >= 'A' && c <= 'F') return c - 'A' + 10;
    return 0;
}

char* similarRGB(char* color) {
    static char result[8];
    
    // Extract RGB components
    int r = hexToInt(color[1]) * 16 + hexToInt(color[2]);
    int g = hexToInt(color[3]) * 16 + hexToInt(color[4]);
    int b = hexToInt(color[5]) * 16 + hexToInt(color[6]);
    
    int bestSimilarity = INT_MIN;
    char hexChars[] = "0123456789abcdef";
    
    // Try all possible shorthand colors
    for (int i = 0; i < 16; i++) {
        for (int j = 0; j < 16; j++) {
            for (int k = 0; k < 16; k++) {
                // Convert shorthand to full format
                int rShort = i * 17; // i*16 + i = i*17
                int gShort = j * 17;
                int bShort = k * 17;
                
                // Calculate similarity
                int sim = -(r - rShort) * (r - rShort) - 
                         (g - gShort) * (g - gShort) - 
                         (b - bShort) * (b - bShort);
                
                if (sim > bestSimilarity) {
                    bestSimilarity = sim;
                    sprintf(result, "#%c%c%c", hexChars[i], hexChars[j], hexChars[k]);
                }
            }
        }
    }
    
    return result;
}

int main() {
    char input[20];
    fgets(input, sizeof(input), stdin);
    
    // Remove quotes and newline
    char* start = strchr(input, '#');
    char* end = strchr(start, '"');
    if (end) *end = '\0';
    
    char* result = similarRGB(start);
    printf("\"%s\"", result);
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(1)

Always checks exactly 4096 combinations (16³), which is constant

✓ Linear Growth

Space Complexity

O(1)

Only uses a few variables to store the best color and similarity

✓ Linear Space

Constraints

color is a valid RGB color in the format #ABCDEF
Color string length is exactly 7 characters (including #)
All hex digits are lowercase letters a-f or digits 0-9
Guaranteed unique solution or multiple valid answers accepted

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