Solve three algorithmic tasks in Python
Algorithmic Tasks
This problem requires implementing solutions for three distinct algorithmic tasks in Python, each with specific performance constraints.
Task 1: Movie Ratings (Longest Strictly Increasing Subsequence - LIS)
Given an integer array ratings of length n, return:
- The length of the longest strictly increasing subsequence (LIS).
- One valid LIS as a list of 1-based indices.
Explain your Dynamic Programming (DP) formulation (state, transition) and provide code.
Constraints:
1 ≤ n ≤ 200000ratings[i]can be any 32-bit signed integer.
Target Complexity:
O(n log n)timeO(n)memory
Task 2: Array Challenge (Optimize with a Tree Structure)
You are given an integer n and an initial array a[1..n]. You will then receive q operations of two types:
add i x: Add integerxtoa[i].sum l r: Output the sum ofa[l..r], inclusive.
Constraints:
1 ≤ n, q ≤ 200000
A naive O(n) per query solution will time out. Implement an O(log n) per-operation solution using a Fenwick tree (BIT) or a Segment tree.
Task 3: Update Release Scheduler (Sort and Compare Two Lists)
You receive two unsorted lists of integers: releases[0..n-1] (timestamps when builds become available) and windows[0..m-1] (deployment windows).
Produce an array schedule[0..m-1] where schedule[j] is the timestamp of the latest release ≤ windows[j] that has not been assigned to any earlier window. If multiple releases qualify for a window, choose the one with the greatest timestamp. If no release is available for a window, set schedule[j] = -1.
Approach:
- Sort both lists.
- Scan with two pointers.
Target Complexity:
O((n + m) log(n + m))timeO(n + m)extra space aside from outputs.
AI interview prep
Core dilemma
The central engineering challenge is to demonstrate mastery of fundamental algorithms and data structures by selecting and implementing the most efficient solutions for distinct problems under strict time and space complexity constraints. This involves understanding the nuances of dynamic programming, tree-based data structures, and two-pointer techniques, and correctly applying them to achieve optimal performance.
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Unlock the interviewer X-Ray rubric, tradeoff matrix, stress tests, clarifying questions, and key concepts.
Solve three algorithmic tasks in Python
Algorithmic Tasks
This problem requires implementing solutions for three distinct algorithmic tasks in Python, each with specific performance constraints.
Task 1: Movie Ratings (Longest Strictly Increasing Subsequence - LIS)
Given an integer array ratings of length n, return:
- The length of the longest strictly increasing subsequence (LIS).
- One valid LIS as a list of 1-based indices.
Explain your Dynamic Programming (DP) formulation (state, transition) and provide code.
Constraints:
1 ≤ n ≤ 200000ratings[i]can be any 32-bit signed integer.
Target Complexity:
O(n log n)timeO(n)memory
Task 2: Array Challenge (Optimize with a Tree Structure)
You are given an integer n and an initial array a[1..n]. You will then receive q operations of two types:
add i x: Add integerxtoa[i].sum l r: Output the sum ofa[l..r], inclusive.
Constraints:
1 ≤ n, q ≤ 200000
A naive O(n) per query solution will time out. Implement an O(log n) per-operation solution using a Fenwick tree (BIT) or a Segment tree.
Task 3: Update Release Scheduler (Sort and Compare Two Lists)
You receive two unsorted lists of integers: releases[0..n-1] (timestamps when builds become available) and windows[0..m-1] (deployment windows).
Produce an array schedule[0..m-1] where schedule[j] is the timestamp of the latest release ≤ windows[j] that has not been assigned to any earlier window. If multiple releases qualify for a window, choose the one with the greatest timestamp. If no release is available for a window, set schedule[j] = -1.
Approach:
- Sort both lists.
- Scan with two pointers.
Target Complexity:
O((n + m) log(n + m))timeO(n + m)extra space aside from outputs.