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##### ###### ##### ### # # ### # # ###### ## ## ## ## ## ## ## # # # # # ## ##### #### ##### # # # # # # # #### ## # ## ## ## ## # # # # # ## ## # ###### ## ### # ### # ######
Count as you go
Maintain a running prefix sum and a hash map of prefix sum frequencies:
Initialize: , , hash map with (empty prefix).
For each element, add it to .
Add to (number of valid subarrays ending here).
Increment by .
Return . The hash map tracks "how many times has each prefix sum occurred?" Time: . Space: .
