In the following, every capital letter represents some hexadecimal digit from 0 to f.

The red-green-blue color "#AABBCC" can be written as "#ABC" in shorthand.  For example, "#15c" is shorthand for the color "#1155cc".

Now, say the similarity between two colors "#ABCDEF" and "#UVWXYZ" is -(AB - UV)^2 - (CD - WX)^2 - (EF - YZ)^2.

Given the color "#ABCDEF", return a 7 character color that is most similar to #ABCDEF, and has a shorthand (that is, it can be represented as some "#XYZ"

Example 1:
Input: color = "#09f166"
Output: "#11ee66"
Explanation:  
The similarity is -(0x09 - 0x11)^2 -(0xf1 - 0xee)^2 - (0x66 - 0x66)^2 = -64 -9 -0 = -73.
This is the highest among any shorthand color.

Note:

• color is a string of length 7.
• color is a valid RGB color: for i > 0, color[i] is a hexadecimal digit from 0 to f
• Any answer which has the same (highest) similarity as the best answer will be accepted.
• All inputs and outputs should use lowercase letters, and the output is 7 characters.

Solution: Brute Force

R, G, B are independent, find the closest color for each channel separately.

Time complexity: O(3 * 16)

Space complexity: O(1)

// Author: Huahua
// Running time: 7 ms
class Solution {
public:
  string similarRGB(string color) {
    const string hex{"0123456789abcdef"};
    vector<int> rgb(3, 0);
    for (int i = 0; i < 3; ++i)
      rgb[i] = hex.find(color[2 * i + 1]) * 16 + hex.find(color[2 * i + 2]);
    
    string ans(7, '#');    
    for (int i = 0; i < 3; ++i) {
      int best = INT_MAX;
      for (int j = 0; j < 16; ++j) {
        int diff = abs(j * 16 + j - rgb[i]);
        if (diff >= best) continue;
        best = diff;
        ans[2 * i + 1] = ans[2 * i + 2] = hex[j];
      }
    }
    return ans;
  }
};

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