Package g1901_2000.s1969_minimum_non_zero_product_of_the_array_elements

Class Solution

  • public class Solution
extends Object
    1969 - Minimum Non-Zero Product of the Array Elements.

    Medium

    You are given a positive integer p. Consider an array nums ( 1-indexed ) that consists of the integers in the inclusive range [1, 2p - 1] in their binary representations. You are allowed to do the following operation any number of times:

    • Choose two elements x and y from nums.
    • Choose a bit in x and swap it with its corresponding bit in y. Corresponding bit refers to the bit that is in the same position in the other integer.

    For example, if x = 1101 and y = 0011, after swapping the 2nd bit from the right, we have x = 1111 and y = 0001.

    Find the minimum non-zero product of nums after performing the above operation any number of times. Return this product modulo 109 + 7.

    Note: The answer should be the minimum product before the modulo operation is done.

    Example 1:

    Input: p = 1

    Output: 1

    Explanation: nums = [1]. There is only one element, so the product equals that element.

    Example 2:

    Input: p = 2

    Output: 6

    Explanation: nums = [01, 10, 11].

    Any swap would either make the product 0 or stay the same.

    Thus, the array product of 1 * 2 * 3 = 6 is already minimized.

    Example 3:

    Input: p = 3

    Output: 1512

    Explanation: nums = [001, 010, 011, 100, 101, 110, 111]

    • In the first operation we can swap the leftmost bit of the second and fifth elements.

      • The resulting array is [001, 110, 011, 100, 001, 110, 111].

    • In the second operation we can swap the middle bit of the third and fourth elements.

      • The resulting array is [001, 110, 001, 110, 001, 110, 111].

    The array product is 1 * 6 * 1 * 6 * 1 * 6 * 7 = 1512, which is the minimum possible product.

    Constraints:

    • 1 <= p <= 60

    • Constructor Detail

      • Solution

        public Solution()

    • Method Detail

      • minNonZeroProduct

        public int minNonZeroProduct​(int p)