Number of Ways to Split Array

Number of Ways to Split Array

What is this problem about?

The Number of Ways to Split Array problem asks you to count the number of valid split points in an array where the sum of the prefix (left part) is ≥ sum of the suffix (right part). Both parts must be non-empty. This coding problem uses a single prefix sum pass with running totals.

Why is this asked in interviews?

Microsoft, Meta, Nvidia, Amazon, Google, and Bloomberg ask this as a straightforward prefix sum problem. It validates that candidates can maintain running prefix sums without sorting or nested loops. The array and prefix sum interview pattern is directly demonstrated.

Algorithmic pattern used

Prefix sum single pass. Compute total sum. For each split position i (from 0 to n-2): prefix_sum += arr[i]; suffix_sum = total - prefix_sum. If prefix_sum >= suffix_sum, increment count. Return count.

Example explanation

arr=[10,4,-8,7]. Total=13.

• Split at 0: prefix=10, suffix=3. 10≥3 ✓. Count=1.
• Split at 1: prefix=14, suffix=-1. 14≥-1 ✓. Count=2.
• Split at 2: prefix=6, suffix=7. 6≥7? No. Answer = 2.

Common mistakes candidates make

• Recomputing prefix and suffix sums from scratch per split point.
• Including i=n-1 as a split (suffix would be empty).
• Using integer overflow for large arrays (use long/int64).
• Confusing prefix_sum ≥ suffix_sum with prefix_sum > suffix_sum.

Interview preparation tip

Prefix sum problems should always use a single running variable updated incrementally, not recomputed from scratch. The pattern: precompute total sum, then maintain prefix += arr[i] and compare prefix with total - prefix per split point. This O(n) approach is both optimal and easy to explain. Practice verifying boundary conditions: split at position 0 (left has 1 element) and position n-2 (right has 1 element) are the valid extremes.