Freaks City

1. Prefix Sum Technique 1.1 One-Dimensional Prefix Sum The prefix sum algorithm is an optimization technique used to calculate the sum of elements within a specific range $[L, R]$ in $O(1)$ time after an $O(N)$ preprocessing step. In a naive approach, calculating range sums repeatedly would result in $O(N \times M)$ complexity for $M$ queries; ...

The objective is to compute the diameter of a given binary tree. In this context, the diameter is defined as the length of the longest path between any two nodes within the structure. This path does not necessarily need to pass through the root node. The length of a path is quantified by the number of edges connecting the nodes. Algorithmic Str ...

Problem Statement Given a sequence \(a_1, a_2, \dots, a_n\), select elements to delete such that the remaining subsequence maximizes the count of indices \(i\) where \(a_i = i\). The goal is to compute this maximum value. Initial Solution and Limitations A dynamic programming approach tracks the longest subsequence satisfying \(a_j = j\) after ...

Score: 260 points | Rank: 3rd T1: 100 points T2: 100 points T3: 60 points T4: 0 points Problem Solutiosn T1 - Sequence Generaiton Standard simulation problem. For each sequence iteration, count consecutive digits from the previous sequence. #include <bits/stdc++.h> using namespace std; string sequence[30]; int main() { int n; ...

Binary Search Applications in Fractional Programming Consider an optimization problem where we seek the maximum average value over subarrays of minimum length. Given array elements $a_1, a_2, ..., a_n$ and minimum length constraint $L$, we want to find: $$\max_{\substack{1 \leq i \leq j \leq n \ j - i + 1 \geq L}} \frac{\sum_{k=i}^{j} a_k}{j - ...

This soluiton addresses the challenge of counting reversible substrings where the reversed version would create a numerically smaller value. DP Strategy The dynamic programming approach builds solutions incrementally by comparing substring pairs: For substrings of length 2, directly compare characters For longer substrings, use previously comp ...

Problem Overview Given a tree with weighted nodes and multiple queries, each query asks for the sum of node weights along the path between two nodes x and y, where the weights fall within a specified range [l, r]. Solution Approach This problem can be efficiently solved using persistent segment trees (also known as chairman trees) combined with ...

Approach Check if all input value are identical. Solution Code #include <iostream> #include <vector> bool checkUniform(const std::vector<int>& values) { for(size_t i = 1; i < values.size(); ++i) { if(values[i] != values[0]) return false; } return true; } int main() { int testCases; std::ci ...

Problem Analysis The challenge involves cutting bamboo stalks of varying heights down to a uniform height of 1 using magical operations. Each spell can simultaneously reduce multiple consecutive bamboo pieces of identical height. When applied to bamboo of height H, the new height becomes ⌊√(⌊H/2⌋ + 1)⌋. The goal is to determine the minimum numb ...