LeetCode 1969: Minimum Non-Zero Product of the Array Elements Solution
Master LeetCode problem 1969 (Minimum Non-Zero Product of the Array Elements), a medium challenge, with our optimized solutions in Java, C++, and Python. Explore detailed explanations, test your code in our interactive editor, and prepare for coding interviews.
Problem Explanation
Explanation
To minimize the product of the array elements, we have to consider the binary representations of the numbers from 1 to 2^p - 1. Since we want to minimize the product, we should try to make as many elements in the array equal to 1 as possible. To achieve this, we can perform bitwise swaps between the elements to maximize the number of 1s in the binary representation.
The optimal strategy is to pair up the numbers such that their binary representations are mirror images of each other, i.e., when one number has a 1 at a particular bit position, the other number has a 0 at the same position. By performing swaps between such pairs, we can increase the count of 1s and eventually minimize the product.
The final product will be 2^(2^p - 2) mod (10^9 + 7).
Time complexity: O(log p)
Space complexity: O(1)
Solution Code
class Solution {
public int minNonZeroProduct(int p) {
long mod = 1000000007;
long base = (1L << p) % mod - 1;
long power = (1L << p) - 2;
long result = 1;
result = (result * base) % mod;
result = (result * modPow(base - 1, power, mod)) % mod;
return (int) result;
}
private long modPow(long base, long power, long mod) {
long result = 1;
while (power > 0) {
if (power % 2 == 1) {
result = (result * base) % mod;
}
base = (base * base) % mod;
power /= 2;
}
return result;
}
}Try It Yourself
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