Largest Number At Least Twice of Others

Problem Description

You are given an integer array nums where the largest integer is unique. Determine whether the largest element in the array is at least twice as much as every other number in the array. If it is, return the index of the largest element, or return -1 otherwise.

Key Insights

• The largest element in the array is guaranteed to be unique.
• To determine if the largest number is at least twice as large as every other number, we can simply compare it to each of the other elements.
• The problem can be solved in a single pass through the array to find the largest number and its index.

Space and Time Complexity

Time Complexity: O(n)
Space Complexity: O(1)

Solution

To solve this problem, we will:

1. Iterate through the array to find the maximum number and its index.
2. During the same iteration, check if the maximum number is at least twice as large as all other numbers.
3. If it satisfies the condition for all elements, return the index; otherwise, return -1.

We will use a single loop to achieve this, ensuring that we only traverse the array once, making our solution efficient.

Code Solutions