Freaks City

Directory Preprocessing LCA External Function Version Preprocessing void solve() { int n, k; cin >> n >> k; vector<vector<int>> adj(n + 1); for (int i = 1; i <= n - 1; ++i) { int x, y; cin >> x >> y; adj[x].push_back(y); adj[y].push_back(x); } vecto ...

343. Integer Break Problem Link: LeetCode 343 - Integer Break Given an integer n, break it into at least two positive integers, where the sum equals n. Return the maximum product possible from these integers. Example: Input: 2 Output: 1 Explanation: 2 = 1 + 1, 1 × 1 = 1 Apprroach This is a classic dynamic programming problem that can be solv ...

Tree to Prufer Sequence Find the leaf node with the smallest label, and add its parent to the sequence. Delete that leaf node. Repeat the above operations until a sequence of length (n-2) is obtained. The reverse process reconstructs the tree. A Prufer sequence establishes a bijection between the spanning trees of a complete graph with (n) ve ...

Tree Definiiton and Characteristics A tree is a data structure with n (n ≥ 0) finite nodes in a hierarchical relationship. Called a "tree" as it resembles an upside - down tree (root up, leaves down). Key traits: A node may have 0+ child nodes. The root node has no parent. Every non - root node has exactly one parent. Except the root ...

Given a tree with n nodes (≤ 10⁶) and weighted edges, define Min(x, y) as the minimum edge weight along the unique path between nodes x and y. The goal is to compute: max_{r=1}^n Σ_{v ≠ r} Min(r, v) A naive approach would compute the sum for each root r by traversing all paths, yielding O(n²) complexity — infeasible for large n. Instead, revers ...

Weighted Independent Set with Point Updates on a Tree Consider a rooted tree where every node carries a weight. We must support point-weight modifications and after each change report the maximum-weight independent set of the entire tree. Node count and operation count are up to (10^5), weights are bounded in absolute value by (10^2). Standard ...

A - Three Pairwise Maximums Given three pairwise maximum values, determine if they can be derived from three positive integers. The solutoin involves sorting the input values and verifying consistency conditions. #include <iostream> #include <algorithm> using namespace std; void solve() { int nums[3]; cin >> nums[0] & ...

Introduction During the summer vacation, I systematically studied various operations on trees through Teacher Tuo's sharing and discovered many useful techniques, which I now summarize. Teacher Tuo is amazing! One Problem Type: Batch processing queries of the form f(dep(lca(x,y))), where f(x) is a function of x. Approach: First perform tree ...

Recovering a Swapped Binary Search Tree A binary search tree (BST) has two of its nodes swapped by mistake. The task is to restore the tree to its correct BST form without altering its structure. The challenge is to achieve this with constant space complexity (O(1) space), avoiding the use of a full in-order traversal list. Approach The key obs ...

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 ...