Problem
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.
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 10^9 + 7, the result is 505379714.
Constraints:
1 <= n <= 10^5
Solution (Java)
class Solution {
private static final long MOD = 1000_000_007;
public int concatenatedBinary(int n) {
// calculate the length of binary string
int length = 0;
long sum = 0;
for (int i = 1; i <= n; i++) {
if ((i & i - 1) == 0) {
length++;
}
sum <<= length;
sum += i;
if (sum > MOD) {
sum %= MOD;
}
}
return (int) (sum % MOD);
}
}
Explain:
nope.
Complexity:
- Time complexity : O(n).
- Space complexity : O(n).