Freaks City

Problem Statement Given a positive integer n, determine the smallest number of perfect squares that sum to n. A perfect square is an integer equal to the square of another integer — for example, 1, 4, 9, and 16 are perfect squares; 3 and 11 are not. Naive Recursiev Approach A top-down recursive solution defines minSquares(x) as the minimum coun ...

Problem Statement Given an integer array fee where fee[i] represents the cost to step onto the ith stair. After paying this fee, you may advance either one or two steps upward. You can begin climbing from either stair 0 or stair 1 without incurring any initial expense. Calcluate and return the minimum cost required to reach beyond the final sta ...

Given a sequence of integers of length n, the objective is to identify a contiguous subarray that yields the maximum possible sum. This is a fundamental problem in computer science, solvable through several distinct algorithmic approaches. Dynamic Programming The optimal substructure for this problem can be defined by letting f(i) represent the ...

To determine which edges can lie on a shortest path from source S to target T in a directed graph, compute shortest distances from S to all nodes. Then, perform a reverse BFS starting from T on the transposed graph. For each dequeued node cur and its neighbor nex in the transposed graph, if Dist[nex] == Dist[cur] - weight(cur->nex) holds, th ...

Problem Description There are n students seeking consultation from a teacher simultaneously. Each student has estimated their consultation time requirements. The teacher can arrange the consultation order, with students entering the teacher's office sequentially. The consultation process for each student consists of: Entering the office - stud ...

Bitmask Dynamic Programming (Bitmask DP) is a technique used to solve problems where the state of a system can be represented by a small set of binary flags. By using an integer's bits to store boolean information—where each bit corresponds to a specific element's status—we can compactly represent and manipulate complex configurations. Core Con ...

Binary search is a fundamental algorithm with applications in various computational problems. The key considerations when implementing binary search include identifying the search target, determining search boundaries, and designing the validation function. Music Notes Timing Analysis Determine the number of songs played within a given time fra ...

To solve the support vector machine (SVM) primal and dual problems using the CVX toolbox, we need to formulate and optimize the corresponding mathematical models. 1. Primal Problem of SVM (Hard Margin) Objective Function: [\min_{w,b} \frac{1}{2} |w|^2 ]Constraints: [y_i (w^T x_i + b) \geq 1 \quad \forall i ]``` % Generate linearly separable dat ...

Performance Optimization Strategies Skip Parsing with noParse When third-party libraries like jQuery or Lodash—known to have no internal dependencies—are included in a project, parsing them during bundling is unnecessary. The noParse option instructs Webpack to skip parsing these files, improving build speed. module: { noParse: /jquery|lodash ...

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 ...