g1601_1700.s1680_concatenation_of_consecutive_binary_numbers.Solution Maven / Gradle / Ivy

Go to download

Show more of this group Show more artifacts with this name
Show all versions of leetcode-in-java21 Show documentation

Java-based LeetCode algorithm problem solutions, regularly updated

There is a newer version: 1.38

package g1601_1700.s1680_concatenation_of_consecutive_binary_numbers;

// #Medium #Math #Bit_Manipulation #Simulation
// #2022_04_15_Time_70_ms_(95.05%)_Space_39.2_MB_(98.02%)

/**
 * 1680 - Concatenation of Consecutive Binary Numbers\.
 *
 * Medium
 *
 * 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
**/
public 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);
    }
}