Freaks City

Plane Closest Pair A standard approach utilizes divide and conquer strategies. Sort all points by their x-corodinate recursively split the set into two halves. After solving subproblems, examine points near the dividing line that could potentially form a shorter pair then the current minimum found. const int MAX_PTS = 250005; struct Point { ...

Problem A Each meal costs 800 yen. For every 15 meals purchased, a refund of 200 yen is issued. Given $ x $, the total number of meals consumed, compute the net expenditure. The formula is: $$ 800x - \left\lfloor \frac{x}{15} \right\rfloor \cdot 200 $$ Problem B After $ N $ workouts, where initial strength is 1 and each $ i $-th workout multipl ...

Core Ideas of Dynamic Programming Dynamic programming (DP) requires moving beyond memorized templates. The essence is decomposing a problem into overlapping subproblems, defining states, and establishing transition equations. Three fundamental steps drive most DP solutions: State definition (what each dp entry represents) Table filling and tra ...

Li Chao Segment Tree Problem: Maintain a collection S of linear functions with the following operations: Insert a linear function f(x) = kx + b over a range [l, r] Query maxf∈S f(x) for a given x The naive approach decomposes a linear function's range into O(log n) segment tree nodes and stores all functions at each node. However, this can le ...

Problem Statement A train has n compartments numbered from 1 to n. Each compartment requires a set of items, where item numbers range from 1 to m. A vendor named Alice is assigned to any continuous sequence of compartments to sell goods. For any such sequence, she must prepare all items required by those compartments and create a unique chant f ...

Problem A: Maximum Value Boundary Analysis In this problem, we need to calculate the sum of counts $f(k)$ for pairs $(i, j)$ that satisfy specific boundary conditions related to two arrays $A$ and $B$. Let $f(k)$ represent the number of valid pairs where the second index $j$ equals $k$. We define $last\_k$ as the index where the maximum value o ...

Improving C++ I/O Performance In C++, there are two primary methods for input and output operations: the C-style functions (scanf and printf) and the C++ stream-based methods (cin and cout). When using the universal header file <iostream>, these approaches can be used interchangeably. Although C++ inherits similarities from C, the stream- ...

In a tree-structured neighborhood where the root represents the delivery station, a courier must visit all requested delivery nodes at least once. The goal is to compute, after each new delivery request, the shortest total distance required to deliver all orders so far—without needing to return to the root. The key insight is that traversing al ...

Problem Statement Given three positive integers $n$, $x$, and $y$, we need to find the maximum size of a set $S$ satisfying: $S \subseteq {1, 2, \ldots, n}$ For any $a \in S$ and $b \in S$, $|a - b| \neq x$ and $|a - b| \neq y$ Output the maximum possible cardinality of $S$. Constraints: $1 \leq n \leq 10^9$, $1 \leq x, y \leq 22$ Observation ...

This article addresses the problem of identifying and counting specific 4-tuples based on a given set of 3-tuples. Given a collection of M three-element tuples (a, b, c), the objective is to determine the total number of distinct 4-element tuples (x, y, z, w) that satisfy the following conditions: (x, y, z) is one of the input 3-tuples. The 3- ...