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Problem 300: Longest Increasing Subsequence Given an integer array, determine the length of the longest strictly increasing subsequence. A subsequence is derived by deleting zero or more elements without changing the order of remainign elements. Example: - Input: [10, 9, 2, 5, 3, 7, 101, 18] - Output: 4 - Explanation: The longest increasing sub ...

Overview Linear dynamic programming is one of the most fundamental types of DP problems. Instead of a lengthy introduction, the key is to solve many problems to develop intuition. Basic Steps State Definition: Define dp[i] as the optimal solution (maximum, minimum, count of ways, etc.) for the first i elements. State Transition: Derive the cur ...

Longest Increasing Subsequence (LIS) Problem: Given an unsorted array, find the length of the longest increasing subsequence. Dynamic Programming Approach: Define DP array: Let lis[i] represent the length of the longest increasing subsequence ending at index i. Transition: For each i, iterate through all j < i, and if nums[i] > nums[j], ...

Longest Encreasing Subsequence The problem can be solved using a greedy approach by maintaining a sequence that represents the smallest possible tail value for all increasing subsequences of each length. The key insight is that for any increasing subsequence, if we encounter a number that's smaller than the current tail of our sequence, we can ...