#### Approach #1: Sliding Window [Accepted]

Intuition and Algorithm

Every (continuous) increasing subsequence is disjoint, and the boundary of each such subsequence occurs whenever nums[i-1] >= nums[i]. When it does, it marks the start of a new increasing subsequence at nums[i], and we store such i in the variable anchor.

For example, if nums = [7, 8, 9, 1, 2, 3], then anchor starts at 0 (nums[anchor] = 7) and gets set again to anchor = 3 (nums[anchor] = 1). Regardless of the value of anchor, we record a candidate answer of i - anchor + 1, the length of the subarray nums[anchor], nums[anchor+1], ..., nums[i]; and our answer gets updated appropriately.

Complexity Analysis

• Time Complexity: , where is the length of nums. We perform one loop through nums.

• Space Complexity: , the space used by anchor and ans.

Analysis written by: @awice.