Lessons from Subarray Sum

What did you learn?

$1.$ Prefix sum + hash map is a powerful combination for subarray problems with exact sum constraints.

$2.$ Initialize the hash map with $\{0: 1\}$ to handle subarrays starting at index $0$.

$3.$ This pattern works because you're doing "complement lookup" on prefix sums, just like two-sum on values. This technique solves many variations: subarrays divisible by $k$, subarrays with equal $0$s and $1$s, and more.