README_EN.md

1680. Concatenation of Consecutive Binary Numbers

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Description

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

Solutions

Python3

class Solution:
    def concatenatedBinary(self, n: int) -> int:
        mod = 10**9 + 7
        ans = shift = 0
        for i in range(1, n + 1):
            if (i & (i - 1)) == 0:
                shift += 1
            ans = ((ans << shift) + i) % mod
        return ans

Java

class Solution {
    private static final int MOD = (int) 1e9 + 7;

    public int concatenatedBinary(int n) {
        long ans = 0;
        int shift = 0;
        for (int i = 1; i <= n; ++i) {
            if ((i & (i - 1)) == 0) {
                ++shift;
            }
            ans = ((ans << shift) + i) % MOD;
        }
        return (int) ans;
    }
}

C++

class Solution {
public:
    const int mod = 1e9 + 7;

    int concatenatedBinary(int n) {
        long ans = 0;
        int shift = 0;
        for (int i = 1; i <= n; ++i) {
            if ((i & (i - 1)) == 0) {
                ++shift;
            }
            ans = ((ans << shift) + i) % mod;
        }
        return ans;
    }
};

Go

func concatenatedBinary(n int) int {
	var ans, shift int
	const mod int = 1e9 + 7
	for i := 1; i <= n; i++ {
		if i&(i-1) == 0 {
			shift++
		}
		ans = ((ans << shift) + i) % mod
	}
	return ans
}

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