Rising labels: Positive proof strip
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Inputs
readings is a list of integers (numbers with no decimal part). It may be empty, and numbers may repeat unless task 1 says otherwise.
Your tasks
- Create a list
risingLengths. A subsequence keeps numbers in their original order but may skip some numbers. For each position inreadings, find the longest strictly increasing subsequence that ends at that position. Strictly increasing means each next number must be larger; equal numbers do not count as an increase. Record the length, not the chosen numbers. Put one length per position inrisingLengths. - Create a list
positiveValuesthat keeps only the numbers inrisingLengthsthat are greater than 0, in the same order. - Complete
risingLabelsPositiveProofStripso it returnspositiveValues. Return it, do not print it.
Example
If readings is [7, 7, -2, 11, 4], then risingLengths is [1, 1, 1, 2, 2] and risingLabelsPositiveProofStrip returns [1, 1, 1, 2, 2].
Rules
- Keep repeated numbers.
- If
risingLengthsis empty, return [].
Test data
TEST DATA 1: readings is [8, 0, 8, 3, -12].
TEST DATA 2: readings is [2, 2, -6, 2].
Examples
Input: readings = [8,0,8,3,-12] Output: [1,1,2,2,1]
risingLengths is [1, 1, 2, 2, 1]. Keep only numbers greater than 0, without changing their order. Return [1, 1, 2, 2, 1].
Input: readings = [2,2,-6,2] Output: [1,1,1,2]
risingLengths is [1, 1, 1, 2]. Keep only numbers greater than 0, without changing their order. Return [1, 1, 1, 2].
Input: readings = [] Output: []
risingLengths is []. Keep only numbers greater than 0, without changing their order. Return [].
Input limits
- 0 <= input size <= 64.
- Answers fit in a signed 32-bit integer: -2,147,483,648 through 2,147,483,647.
- Input numbers have no decimal part. They range from -1,000,000 to 1,000,000. Follow any extra input rules in task 1.
Efficiency goal
Big-O describes how the work or memory needed grows as the input gets larger.
Efficiency goal: time O(n log n); extra memory, including the helper list, O(n). n is the input length. These labels describe how work and memory grow with the input.
Practice focus
Build risingLengths first, then return exactly what the tasks ask for. Follow the order, keep repeated values when the rule says so, and check the empty case.