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Minimum NonZero Product of the Array Elements solution leetcode

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You are given a positive integer p
. Consider an array nums
(1indexed) that consists of the integers in the inclusive range [1, 2^{p}  1]
in their binary representations. You are allowed to do the following operation any number of times:
 Choose two elements
x
andy
fromnums
.  Choose a bit in
x
and swap it with its corresponding bit iny
. 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 2^{nd}
bit from the right, we have x = 1111
and y = 0001
.
Find the minimum nonzero product of nums
after performing the above operation any number of times. Return this product modulo 10^{9} + 7
.
Note: The answer should be the minimum product before the modulo operation is done. Minimum NonZero Product of the Array Elements solution leetcode
Example 1:
Input: p = 1 Output: 1 Explanation: nums = [1]. There is only one element, so the product equals that element.
Example 2: Minimum NonZero Product of the Array Elements solution leetcode
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: Minimum NonZero Product of the Array Elements solution leetcode
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

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