Prefix Sum Fundamentals The prefix sum technique converts range sum queries from O(n) per query to O(1) by preprocessing the array once. Given an array of n integers and m queries asking for the sum of elements between indices l and r (inclusive), the naive approach processes each query by iterating...
Longest Increasing Subsequence To determine the length of the longest strictly increasing subsequence, dynamic programming is applied where dp[i] represents the length of the longest subsequence ending at index i. class Solution { public: int lengthOfLIS(vector<int>& sequence) { int size =...
The foundation of efficient search operations relies on the divide-and-conquer principle applied to monotonic or structured datasets. The standard implementation maintains two pointers, typically left and right, converging toward a target state. To prevant infinite loops and ansure precise boundary...
When processing sorted arrays where elements may appear multiple times, enforcing a maximum occurrence limit requires a two-pointer technique. The objective is to compact the sequence so that no value repeats more than twicee, achieving this modification within the original memory bounds with out au...
Canvas Painting The problem involves finding the maximum number of effective operations to reduce distinct colors. With n initial colors, each operation can reduce one color by making two positions share the same color. The answer is n minus the maximum effective operations. Algorithm: Group paintin...
Data Structures Fundamentals Data structures provide the foundation for algorithm implemantation, offering various ways to organize and store data efficiently. Core Data Structure Types Arrays: Contiguous memory allocation enabling random access with O(1) time complexity for element retrieval Linked...
Given two strings text and pattern, find all starting indices in text where pattern occurs as a contiguous substring. Additionally, for every prefix of pattern, compute the length of its longest proper border—a proper border is a non-empty substring that is both a prefix and a suffix of the given pr...
Algorithmic Solutions for Competitive Programming Problems Extracting Initial Characters from Input Strings When solving problems that require extracting the first letters of words from input strings, a direct character-by-character approach can be effective: #include <iostream> #include <s...
The chunk function is a utility designed to split a single array into multiple sub-arrays of a specific length. If the total number of elements isn't perfectly divisible by the chunk size, the final sub-array contains the remaining elements. This pattern is particularly useful in frontend developmen...
Deleting Nodes by Value in a Linked List A direct approach is to construct a new list containing only the nodes whoce values differ from the target. Traverse the original list, and when a node with a non-matching value is found, append it to the result. Care must be taken to terminate the new list p...