Array of Doubled Pairs

Array of Doubled Pairs

What is this problem about?

In the Array of Doubled Pairs interview question, you are given an array of integers of even length. You need to determine if it's possible to reorder the elements into pairs such that for every pair (a, b), b = 2a. This Array of Doubled Pairs coding problem tests your ability to match elements based on a mathematical relationship.

Why is this asked in interviews?

Google uses this to check if a candidate can handle signed numbers and zero effectively. It requires sorting and counting, testing your ability to pick the right starting element for a greedy matching strategy.

Algorithmic pattern used

The Array, Hash Table, Sorting, Greedy interview pattern is the best way to solve this. You count the frequency of each number. Then, you sort the unique numbers by their absolute values. For each number, you greedily try to match it with its double by checking the frequency map.

Example explanation

nums = [4, -2, 2, -4]

1. Counts: {4:1, -2:1, 2:1, -4:1}.
2. Sort by absolute value: [2, -2, 4, -4].
3. Pick 2: Needs a double (4). Both exist. Decrease counts.
4. Pick -2: Needs a double (-4). Both exist. Decrease counts. All elements matched. Result: True.

Common mistakes candidates make

• Sorting Incorrectly: Sorting numerically (e.g., -4, -2, 2, 4) instead of by absolute value. If you pick -4 first, you look for -8, which isn't there, even though -4 is the double of -2.
• Ignoring Zero: Failing to realize that 0 must be paired with another 0.
• Frequency Management: Not correctly updating the map when a pair is found, leading to double-counting.

Interview preparation tip

When a problem requires matching elements in pairs based on a "one is twice the other" or "one is the square of the other" rule, sorting by magnitude is almost always necessary to ensure you process the "base" numbers before their "transformed" counterparts.