Package g1901_2000.s1969_minimum_non_zero_product_of_the_array_elements

Class Solution

java.lang.Object
g1901_2000.s1969_minimum_non_zero_product_of_the_array_elements.Solution
public class Solution extends java.lang.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 Summary

    Constructors
    Constructor
    Description
    Solution()
     

  • Method Summary

    Modifier and Type
    Method
    Description
    int
    minNonZeroProduct(int p)
     

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Constructor Details

    • Solution

      public Solution()

  • Method Details

    • minNonZeroProduct

      public int minNonZeroProduct(int p)