Concatenation of Consecutive Binary Numbers
Problem Statement - link #
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 10^9 + 7.
Examples #
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 <= 10^5
Solutions #
class Solution {
public:
int m = 1e9 + 7 ;
int con(int i){
int res = 0;
while(i){
i >>= 1;
res++;
}
return res;
}
int concatenatedBinary(int n) {
long res = 0;
for(int i = 1; i < n+1; i++){
res <<= con(i);
res |= i;
res %= m;
}
return res;
}
};