##### ###### ##### ### # # ### # # ###### ## ## ## ## ## ## ## # # # # # ## ##### #### ##### # # # # # # # #### ## # ## ## ## ## # # # # # ## ## # ###### ## ### # ### # ######
##### ###### ##### ### # # ### # # ###### ## ## ## ## ## ## ## # # # # # ## ##### #### ##### # # # # # # # #### ## # ## ## ## ## # # # # # ## ## # ###### ## ### # ### # ######
The trap
Checking all subarrays and their sums takes . With prefix sums, sum computation is , but still pairs.
Example: . Checking all subarray pairs is too slow.
Prefix sums + merge sort: count pairs of prefix sums where . During merge, both halves are sorted. Two pointers count valid pairs. .
