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Formatted question description: https://leetcode.ca/all/1256.html

1256. Encode Number

Level

Medium

Description

Given a non-negative integer num, Return its encoding string.

The encoding is done by converting the integer to a string using a secret function that you should deduce from the following table:

Example 1:

Input: num = 23

Output: “1000”

Example 2:

Input: num = 107

Output: “101100”

Constraints:

• 0 <= num <= 10^9

Solution

If n is 0, then f(n) is "". If 1 <= n < 3, then f(n) is a binary string with length 1. If 3 <= n < 7, then f(n) is a binary string with length 2. If 7 <= n < 15, then `f(n) is a binary string with length 3.

The encoding function is as follows. For the given number num, obtain the number of bits bits for number num + 1, where the number of bits means the number of bits remaining after removing leading zeros, calculate difference as the difference between num + 1 and 2 ^ bits, and return the binary representation of difference.

• Java
• C++

• class Solution {
      public String encode(int num) {
          num++;
          int bits = (int) (Math.log(num) / Math.log(2));
          int difference = num - (int) Math.pow(2, bits);
          String encodeStr = binary(difference, bits);
          return encodeStr;
      }
  
      public String binary(int num, int bits) {
          String str = "";
          for (int i = 0; i < bits; i++) {
              int remainder = num % 2;
              str = remainder + str;
              num /= 2;
          }
          return str;
      }
  }
  

• // OJ: https://leetcode.com/problems/encode-number/
  // Time: O(logN)
  // Space: O(logN)
  class Solution {
  public:
      string encode(int n) {
          ++n;
          string ans;
          int len = log(n);
          while (n) {
              ans += '0' + (n & 1);
              n >>= 1;
          }
          if (ans.size() > len) ans.pop_back();
          return string(rbegin(ans), rend(ans));
      }
  };
  

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