Freaks City

1. Binary Tree Categories Full Binary Tree: A binary tree where all nodes have either 0 or 2 children, and all leaf nodes are at the same level. For depth k, the tree contains (2^k - 1) nodes. Complete Binary Tree: A binary tree where all levels except possibly the last are completely filled, and all nodes are as far left as possible. Binary Se ...

Given two sorted integer arrays nums1 and nums2 in non-decreasing order, with lengths m and n respectively, merge them into nums1 while maintaining sorted order. Implementation Code function merge(nums1, m, nums2, n) { let i = nums1.length - 1; m--; n--; while(n >= 0) { while(m >= 0 && nums1[m] > nums2[n ...

Probabilistic Path Enumeration in Directed Acyclic Graphs Given a directed acyclic graph (DAG) consisting of $V$ vertices and $E$ edges, each edge $e_k$ possesses an independent activation probability $p_k$. The objective is to compute the expected number of functional paths originating from vertex $0$ and terminating at vertex $V-1$. A path is ...

Competition Overview The problem difficulty is generally estimated as F < A = J = I < L = G = E < C = K = H. The contest featured a mix of standard algorithms and optimization problems. Below is the detailed analysis and solution for each problem. Problem F: Prefix Sum Threshold Problem Statement:Given an initial score of 1500 and a sequence o ...

Given an m x n board of characters and a list of strings words, return all words on the board. Each word must be constructed from letters of sequentially adjacent cells, where adjacent cells are horizontally or vertically neighboring. The same letter cell may not be used more than once in a word. 1. Trie with DFS Build a trie from the given wor ...

Stack and Queue in C++ STL The C++ Standard Library provides implementations of both stack and queue data structures. These are fundamental containers that follow specific access orders—LIFO (Last In, First Out) for stacks and FIFO (First In, First Out) for queues. Stack Interface push(element): Inserts an element at the top pop(): Removes the ...

Given a string, identify the length of its longest contiguous substring containing no duplicate cahracters. Example 1: Input: "abcabcbb" Output: 3 Explanation: The longest substring without repeating characters is "abc", which has a length of 3. Example 2: Input: "bbbbb" Output: 1 Explanation: The longest substrin ...

Array Algorithms Binary Search Fundamentals Binary search operates on sorted sequences with distinct elements. The algorithm halves the search space repeatedly until locating the target or exhausting the range. Critical Implementation Details: Midpoint Calculation: Use mid = lo + (hi - lo) // 2 instead of (lo + hi) // 2 to prevent integer ove ...

Goldbach's Conjecture states that every even integer greater than or equal to 4 can be represented as the sum of two prime numbers. For a given even number $n$, we need to calculate the number of unique pairs $(p_1, p_2)$ such that $p_1 + p_2 = n$ and both $p_1, p_2$ are prime numbers. Algorithmic Strategy The maximum value for $n$ is $2^{15}$ ...

Problem A: Equilibrium Distribution The objective requires calculating the maximum uniform amount two participants can receive by redistributing three initial piles. The mathematical foundation relies on summing all available items across the piles and performing integer division by two. Since any remainder must remain undistributed to satisfy ...