Five patterns to remember:
Precompute once, query many times. Prefix sums trade setup for queries.
Range sum = difference of two prefix values. The formula is universal.
HashMap + prefix sums solves "count subarrays with property X" problems.
Prefix and suffix together handle "all except current" scenarios.
2D prefix sums use inclusion-exclusion for rectangle queries. These patterns appear everywhere: subarray sums, grids, string problems. The core idea stays the same.