Equal Sum Arrays With Minimum Number of Operations

Equal Sum Arrays With Minimum Number of Operations

What is this problem about?

The Equal Sum Arrays With Minimum Number of Operations coding problem gives you two arrays of integers, each containing values between 1 and 6 (simulating dice rolls). You want to make the sum of both arrays equal by changing the values of the elements. Each change counts as one operation. You need to find the minimum number of operations to achieve an equal sum, or return -1 if it's impossible.

Why is this asked in interviews?

This is a classic greedy interview pattern problem asked by companies like American Express. It tests a candidate's ability to identify the most impactful change at each step. It evaluates how you handle array sums and whether you can optimize the process by always picking the element that provides the largest possible reduction in the difference between the two sums.

Algorithmic pattern used

The problem is solved using a Greedy strategy with Frequency Counting.

1. Calculate the sums of both arrays. Let the difference be diff.
2. To reduce diff, you can either:
   • Increase an element in the smaller sum array (max gain: 6 - current_value).
   • Decrease an element in the larger sum array (max gain: current_value - 1).
3. Collect all possible "gains" from both arrays and sort them in descending order (or use a frequency array for O(1) access).
4. greedily pick the largest gains until diff <= 0.

Example explanation

nums1 = [1, 2, 3, 4, 5, 6] (Sum 21), nums2 = [1, 1, 2, 2, 2, 2] (Sum 10). diff = 11.

• Max gains from nums1 (decrease): [5, 4, 3, 2, 1, 0].
• Max gains from nums2 (increase): [5, 5, 4, 4, 4, 4]. Combined Gains: [5, 5, 5, 4, 4, 4, 4, 4, 3, 2, 1].

1. Pick 5: diff = 11 - 5 = 6.
2. Pick 5: diff = 6 - 5 = 1.
3. Pick 5: diff = 1 - 5 = -4. (Equal sum reached!). Result: 3 operations.

Common mistakes candidates make

• Not Checking Impossible Case: Forgetting that if the sum of 1s in the larger array is still greater than the sum of 6s in the smaller array, it's impossible.
• Sorting every time: Trying to re-sort the arrays after every change instead of using a pre-calculated list of possible gains.
• Incorrect Gain Calculation: Confusing the roles of the two arrays (increasing vs. decreasing).

Interview preparation tip

Whenever a problem asks for the "minimum number of operations" to reach a target value using a set of changes, always look for a greedy approach where you prioritize the most significant change first.