Freaks City

Problem 1: Equalizing Elements via Modulo Problem Statement Given an array of integers, determine if it is possible to make all elements equal by repeatedly applying a modulo operation with an integer $x \ge 2$. In each step, every element $a_i$ is replaced by $a_i \bmod x$. Analysis The core constraint lies in the behavior of small numbers und ...

Problem Overview Given a positive integer array nums and m queries, each query asks for the minimum number of operations to transform all elements in nums to a target value q. One operation allows incrementing or decrementing a single element by 1. The array resets to its original state after each query. Solution Approach For each target value, ...

Binary Search Implemantation Patterns Two common binary search variations address different optimization scenarios: Maximizing Minimum Value #include <iostream> #include <vector> #include <algorithm> using namespace std; bool validateMin(vector<long>& positions, long min_gap, int removals) { long prev = 0; i ...

Problem Statement: Given positive integers $n$, $m$, and $m$ triplets $(l_i, r_i, c_i)$, we have an array $a_{1..n}$ initialized with zeros. For each operation $i = 1, ..., m$, perform the following steps: Choose any integer $k \in [0, c_i]$. Add $k$ to all elements $a_j$ where $j \in [l_i, r_i]$. Add $c_i - k$ to all elements $a_j$ where $j \ ...

The problem involves finding the longest common substring between two strings composed solely of lowercase letters. The string lengths can reach up to 250,000. The solution uses binary search combined with hashing techniques to efficiently determine the maximum length of the shared substring. Let's denote the two input strings as $ s_1 $ and $ ...

Problem Overview Given an empty array a, perform n operations of two types: Type 1: Append a number x (1 ≤ x ≤ n) to the array. Type 2: Replicate the current array x times (1 ≤ x ≤ 10^9) and append the copies. After all operations, q queries ask for the value at position k (1-indexed). Constraints: n, q ≤ 10^5, and 1 ≤ k ≤ min(10^18, final_ar ...

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 - ...

Binary Search Fundamentals Problem Statement Given a sorted array of n integers in ascending order and a target value, implement a function that searches for the target in the array. Return the index if the target exists, otherwise return -1. Constraints: All elements in the array are unique n ranges from [1, 10000] Each element falls within [ ...

Binary Search Implementation Element Removal Optimization Sorted Squares Generation Spiral Matrix Construction Binary Search Implementation Binary seearch implementation requires careful consideration of boundary conditions: Loop condition: left < right vs left <= right Right boundary update: right = middle vs right = middle ...

Problem Analysis and Solution Given two arrays, the goal is to pair elements from each array to maximize the sum of their products. Since positive multiplied by positive yields positive, and negative multiplied by negative also yields positive, we can seperate both arrays into positive and negative components. The optimal strategy is to pair la ...