27. Concatenation of Consecutive Binary Numbers.cpp

/*
Concatenation of Consecutive Binary Numbers
===========================================

Given an integer n, return the decimal value of the binary string formed by concatenating the binary representations of 1 to n in order, modulo 109 + 7.

Example 1:
Input: n = 1
Output: 1
Explanation: "1" in binary corresponds to the decimal value 1. 

Example 2:
Input: n = 3
Output: 27
Explanation: In binary, 1, 2, and 3 corresponds to "1", "10", and "11".
After concatenating them, we have "11011", which corresponds to the decimal value 27.

Example 3:
Input: n = 12
Output: 505379714
Explanation: The concatenation results in "1101110010111011110001001101010111100".
The decimal value of that is 118505380540.
After modulo 109 + 7, the result is 505379714.

Constraints:
1 <= n <= 105

Hint #1  
Express the nth number value in a recursion formula and think about how we can do a fast evaluation.
*/

class Solution
{
  string binary(int num)
  {
    string ans;
    while (num)
    {
      ans += (num % 2) + '0';
      num /= 2;
    }
    return ans;
  }

public:
  int concatenatedBinary(int n)
  {
    int MOD = pow(10, 9) + 7;
    long long ans = 0;
    for (int i = 1; i <= n; ++i)
      ans = (ans * (int)pow(2, binary(i).length()) + i) % MOD;
    return ans;
  }
};