Freaks City

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 ...

Problem Statement Given a sequence of length n: S1, S2, S3, ..., Sn, process T queries. Each query provides four integers l, r, a, b. For all indices i ∈ [l, r], answer two questions: Count of positions where Si ∈ [a, b] Number of distinct values among Si that satisfy Si ∈ [a, b] Constraints: n ≤ 10^5, T ≤ 10^6 Analysis of Failed Approaches A ...

The objective is to modify an integer array by removing all instances of a specific value directly within the original memory space. The function must return the new length of the array after removal. Constraints and Mechanics The solution must adhere to strict space complexity requirements: O(1) Extra Space: No additional arrays or data struc ...

Multiple Choice Questions Computer algorithms refer to: A. Calculation methods B. Problem-solving steps C. Sorting methods D. Scheduling methods Answer: B Comparde to linked lists, sequential lists: A. Allow easier random access B. Have more scatterde physical storage C. Enable simpler insertions/deletions D. Better fit linear logical structur ...

A segment tree supports efficient range updates and queries over an array. The following implementation uses an explicit tree structure with lazy propagation. Node Representation Each node stores its interval boundaries, the aggregated sum, and a pending lazy value that needs to be propagated to its childran before any further traversal. static ...

A linked list is a linear data structure where elements, called nodes, are connected via pointers. Each node contains two parts: a data field and a pointer field that references the next node in the seqeunce. The last node's pointer is null, indicating the end of the list. The first node is known as the head. Types of Linked Lists Singly Linked ...

Sequential List Operations Sequential lists support fundamental operations including insertion, deletion, modification, and traversal. These operations form the basis for understanding more complex data structures. Structure Definition typedef int SLDataType; typedef struct SeqList { SLDataType* arr; // Storage array int capacity; ...

A list in Python is an ordered collection of elements enclosed in square brackets [ ]. Lists are mutable, meaning you can modify their contents after creation. Accessing List Elements To access elements in a list, use their index position starting from 0. Python lists are zero-indexed, so the first element is at index 0, the second at index 1, ...

Link-Cut Trees (LCT) represent an advanced data structure specifically designed to handle dynamic tree problems efficient. By utilizing prefered path decomposition and Splay trees, LCT maintains and manipulates tree structures with logarithmic amortized time complexity for most operations. Core Concepts Preferred Path Decomposition For a given ...

Mathematical Algorithms Fast Exponentiation Reduces the time complexity of computing powers to logarithmic time by leveraging binary decomposition of the exponent. long long binary_pow(long long base, long long exp, long long mod) { long long res = 1; base %= mod; while (exp > 0) { if (exp & 1) res = (res * base) % mo ...