Freaks City

Resource Redistribution with Asymmetric Operations Given a sequence (a) of length (n) and two positive integers (x, y) where (y \le x). You may repeatedly pick two elements and transfer resources: subtract (x) from one and add (y) to the other, provided the first remains non‑negative. Determine the maximum possible value of any element after op ...

Given an integer array nums, find and return the maximum sum of elements that is divisible by three. Examples Example 1: Input: nums = [3,6,5,1,8] Output: 18 Explanation: Choose numbers 3, 6, 1, and 8. Their sum is 18 (the maximum sum divisible by three). Example 2: Input: nums = [4] Output: 0 Explanation: 4 is not divisible by 3, so no number ...

Factorization into Factorial Divisors Given integers (n) and (m) where (1 \le m \le n!) and (n \le 20), decompose (m) into a sum of at most (n) divisors of (n!). A solution is guaranteed to exist. Define a sequence (d_i = \frac{n!}{i!}) for (i) from 1 to (n). By iterating downwards from (i=n) to (1) and greedily subtracting the largest possible ...

Problem 1: Dumpling Purchase Optimization The problem reduces to a daily deciison: buy dumplings at the current price or rely on an earlier purchase plus storage cost. The total expense for day i if we buy on day j ≤ i is price[j] + c*(i - j). This can be rewritten as (price[j] - c*j) + c*i. Thus we can maintain the minimum value of price[j] - ...

Problem A - 4 Question With (n) horizontal lines and (m) vertical lines drawn on a plane, how many axis-aligned rectangles are formed that contain no interior lines? Solution Consider each dimension independent. Along any straight line, (n) distinct points partition the line into (n - 1) segments. These segments serve as the edges of our rectan ...

Consider a sequence $A = (a_1, a_2, \dots, a_n)$. We want to partition $A$ into contiguous subsequences, and then arrange these subsequences to form a new sequence $f_1, f_2, \dots, f_k$. Each contiguous subsequence $f_1, \dots, f_p$ must satisfy either $f_1 \le f_2 \le \dots \le f_p$ or $f_1 \ge f_2 \ge \dots \ge f_p$. The cost associated with ...

A. Word Rearrangement This is a straightforward problem requiring only basic input/output handling. w1, w2 = input().split() print(w2) print(w1) B. Cooking Tangyuan The key idea is to simulate the process of using packages to fulfill cooking rounds. Each package contributes a fixed number of tangyuan, and excess can carry over. n, x, k = map(i ...

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 ...

Greedy Algorithm: Minimum Cameras to Monitor a Binary Tree Given a binary tree, we need to place cameras on nodes such that every node in the tree is monitored. A camera placed on a node monitors itself, its parenet, and its immediate children. Determine the minimum number of cameras required. Approach We can solve this problem using a greedy a ...

Core Core Data Structures Structure Purpose LiveIntervals Stores live ranges for every virtual register LiveRegMatrix Tracks physical-to-virtual mappings and interference PriorityQueue Heap-based queue ordered by Priority VirtRegMap Final virtual → physical assignment EvictAdvisor Decides whether evicting an existing allocation i ...