Freaks City

Longest Increasing Subsequence (LIS) Problem: Given an unsorted array, find the length of the longest increasing subsequence. Dynamic Programming Approach: Define DP array: Let lis[i] represent the length of the longest increasing subsequence ending at index i. Transition: For each i, iterate through all j < i, and if nums[i] > nums[j], ...

Dynamic programming (DP) is an optimization paradigm that solves complex problems by decomposing them into overlapping subproblems whose solutions are cached to avoid recomputation. It relies on two key properties: optimal substructure and overlapping subprobelms. Optimal substructure means an optimal solution can be built from optimal solution ...

A: Basic Arithmetic and Output Given integers a, b, c, d, compute (a + b) * (c - d) and output the result followed by the string "Takahashi". int a = input(), b = input(), c = input(), d = input(); cout << (a + b) * (c - d) << endl; cout << "Takahashi" << endl; Time complexity: O(1) B: Finding Corne ...

Problem Description We're playing a number guessing game with the following rules: I pick a number between 1 and n. You guess which number I picked. Each time you guess wrong, I tell you whether my number is higher or lower. When you guess a number x and it's wrong, you pay $x. You win when you guess the correct number. Given n ≥ 1, determine ...

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 ...

In this problem, there are n questions with given point values and m special questions that allow doubling the current score instead of earning their base points. The goal is to arrange the order of answering all questions so that the final score is maximized. Each question i has a fixed value val[i]. Among them, m indices correspond to doublin ...

Counting GCD Pairs in Dynamic Multisets Maintain a multiset of positive integers with insertion and deletion operations. For each query, count unordered pairs (i, j) where i ≠ j and gcd(i, j) = k. Constraints: n, V ≤ 10^5. Conisder the change in answer count: $$\sum_{i=1}^{V}c_i[\gcd(i,x)=k]$$ Let x' = x/k: $$\sum_{i=1}^{\lfloor V/k \rfloor}c_{ ...

Maximizing Minimum Distance Between ElementsGiven an array of unique positions and a number of items to place, the goal is to position the items such that the minimum absolute difference between any two items' positions is maximized.Example 1:Input: positions = [1,2,3,4,7], items = 3Output: 3Explanation: Placing items at positions 1, 4, and 7 y ...

Given a directed graph with nodes labeled 0 through n-1, where edge are colored either red or blue and may include self-loops and parallel edges. Each [i, j] pair in red_edges represents a red directed edge from node i to node j. Similarly, each [i, j] pair in blue_edges represents a blue directed edge from node i to node j. Compute an array re ...

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 ...