Freaks City

Challenging problems require innovative approaches to solve efficiently. Short Colorful Strip Given that n equals m, the final configuration must be a permutation of n. Key observations: When coloring an interval, the smallest color within that interval is always colored first. The coloring operation requires all points in the covered interval ...

Maximizing Collected Value from Falling Objects Given n falling objects on a 2D plane, each with a falling speed and initial height, starting from position (x0, 0). When directly aligned with an object, it can be collected instantly, yielding a value equal to its current height divided by 1000. The objective is to maximize the total collected v ...

The elimination rule—removing consecutive identical elements when their count reaches a threshold $k$—suggests an interval dynamic programming approach. A two-dimensional DP state is insufficient because it cannot capture how the leftmost element in a segment is eventually removed. To resolve this, we introduce a third dimension that tracks how ...

Progress: Dynamic Programming - Linear DP, Knapsack, Interval DP Merging Palindromic Substrings Tags: Interval DP Foundation - Longest Palindromic Substring Problem: Given a string (S), find the length of its longest palindromic substring. Approach: A longer palindrome can always be constructed by adding identical characters to both ends of a s ...