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count to 0 to store the number of valid paths.h to store the frequency of prefix sums.preorder(node, curr_sum) that takes the current node and the current prefix sum as arguments.preorder, add the value of the current node to curr_sum.curr_sum equals the target sum, increment count by 1.count by the frequency of curr_sum - targetSum from the hashmap.curr_sum in the hashmap by 1.preorder for the left and right children of the current node with the updated curr_sum.curr_sum in the hashmap by 1 to avoid counting paths from parallel subtrees.count after the traversal is complete.