Prefix sums are precomputed sums of array elements from the start to each index. They simplify range sum queries and are useful in problems with repeated sum calculations.

Prefix sums are a powerful technique used in competitive programming to quickly calculate the sum of elements in a range. A prefix sum array stores the cumulative sum of elements from the start of the array up to each index, allowing range sum queries to be answered in constant time. For example, in an array of integers, the sum of elements from index i to j can be calculated using the prefix sum array without recalculating from scratch, significantly reducing the time complexity from O(n) to O(1) for each query. Prefix sums are particularly useful in problems involving repeated sum calculations, such as finding subarray sums or solving range queries efficiently. They can also be adapted for 2D arrays in grid problems, allowing for fast calculations of submatrix sums. Understanding and applying prefix sums is essential for solving a variety of array and range-based problems efficiently in competitive programming.