Algorithms

Implement merge sort to sort an array of integers in ascending order. Use the divide-and-conquer approach with O(n log n) time complexity.

Given a graph represented as an adjacency list and a starting node, traverse all reachable nodes using depth-first search. Return the list of visited nodes in order.

Given a graph represented as an adjacency list and a starting node, traverse all reachable nodes using breadth-first search. Return the list of visited nodes in level order.

Given an array of integers and a window size k, find the maximum sum of any contiguous subarray of size k. Use the sliding window technique for O(n) efficiency.

Given a sorted array of integers and a target sum, find two numbers that add up to the target. Return their indices. Use the two-pointer technique for O(n) efficiency.

Given an array of positive integers, find the length of the longest increasing subsequence. Use dynamic programming to solve this in O(n^2) time.

Given an array of distinct integers, return all possible permutations. Use backtracking to explore all arrangements systematically.

Given an array of integers and a target sum, return the indices of two numbers that add up to the target. Use a hash map for O(n) lookup.