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Problem · Dynamic Programming

Count Bitonic Subsequences

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● Hard

AtlassianINTERNFULLTIMEOA

Problem statement

Count non-empty subsequences that strictly increase to an interior peak and then strictly decrease. Both the increasing and decreasing parts must contain at least one step. Return the count modulo 10^9 + 7.

Function

countBitonicSubsequences(arr: int[]) → int

Examples

Example 1

arr = [1,2,3,2,1]return = 11

Eleven index-distinct subsequences have a strict rise followed by a strict fall.

Example 2

arr = [1,2,3,1]return = 4

The valid subsequences are [1,2,1], [1,3,1], [2,3,1], and [1,2,3,1].

Constraints

1 <= arr.length <= 100000
1 <= arr[i] <= 200