Freaks City

Preparation Strategy Prior to a major algorithm competition, it is beneficial to maintain momentum by solving medium-difficulty problems within a time limit. This approach helps reinforce template usage and sharpens intuition without exhausting mental resources. The following selection covers common patterns including simulation, sorting, strin ...

Algorithmic Analysis The core requirement involves accumulating the totals of every contiguous segment of length $m$ within a sequence of $n$ integers. A straightforward nested loop approach computes each window independently, yielding $O(n \cdot m)$ operations. With constraints reaching $10^6$, this quadratic scaling triggers timeout errors. L ...

Problem A: Graph Coloring We are given an integer n and need to color the integers from 1 to n. The constraint is that for any two integers i and j where i < j, if their difference j - i is a prime number, they must have differant colors. The goal is to use the minimum number of colors possible and provide a valid coloring scheme. For n > ...

The solution to the first problem hinges on a capacity threshold observation regarding subtrees relative to a target node. If the aggregate capacity of all subtrees excluding the target exceeds a specific bound, the second player can guarantee allocating at least half of the operations outside the target subtree. This lower bound is tight when ...

Given an array of n elements arr_1, arr_2, ..., arr_n, support q operations: Type 1: Update arr_x = value Type 2: Query maximum subarray sum in range [l, r] Information to Maintain To solve this problem using divide and conquer, we need to determine what information can be merged to compute the required result. The maximum subarray sum in a r ...

In the "Bao Le Me" food delivery system, there are N restaurents numbeerd from 1 to N. Each restaurant has a priority value that starts at 0 at time 0. For every time unit: If a restaurant receives no orders, its priority decreases by 1, but never goes below 0. If it receives one or more orders, its priority increases by 2 per order. ...

Problem A: 24-Hour Time Calculation Given the current time $A$ and a duration $B$ in hours, the task is to determine the start time of an event using a 24-hour clock format. Since the clock cycles every 24 hours, the solution involves a simple modular arithmetic operation. The resulting time is calculated as $(A + B) \pmod{24}$. #include < ...

The objective is to evaluate the following double summation for a sequence $A$ of length $N$: $$ \sum_{L=0}^{N-1} \sum_{R=L}^{N-1} \left( \max_{k \in [L, R]} A[k] - \min_{k \in [L, R]} A[k] \right) $$ A brute-force enumeration of all contiguous segments results in quadratic or cubic complexity, which is insufficient for large inputs. Two linear ...

Sorting Algorithms Quick Sort (Manual Implementation) #include <bits/stdc++.h> using namespace std; typedef long long ll; const int MAXN = 100010; ll arr[MAXN]; int n; void quickPartition(int left, int right) { if (left >= right) return; int pivotIdx = (left + right) / 2; ll pivotVal = arr[pivotIdx]; int i = left ...

Problem A: Array Segment Reversal Given an array of integers from 1 to n, reverse a specified segment between indices l and r. #include <iostream> #include <algorithm> using namespace std; int main() { int n, l, r; cin >> n >> l >> r; int arr[n+1]; for(int i=1; i<=n; i++) arr[i] = i; reverse ...