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Given an array nums containing distinct integers, return all possible permutations. You may return the answer in any order. Example 1: <strong>Input:</strong> nums = [1,2,3] <strong>Output:</strong> [[1,2,3],[1,3,2],[2,1,3],[2,3,1],[3,1,2],[3,2,1]] Example 2: <strong>Input:</strong> nums = [0,1] <strong&g ...

The task is to generate all possible combinations of r distinct numbers from the set {1, 2, ..., n}. A combination is an unordered selection, meaning {1, 2, 3} is the same as {3, 2, 1}. We need to print each combination on a new line, with numbers sorted in ascending order and each number occupying exactly three characters of space. The combina ...

This article delves into advanced backtracking techniques for solving common algorithmic problems, specifically focusing on generating increasing subsequences and permutations, including handling duplicates. Generating Increasing Subsequences (Problem 491) Given an integer array, the task is to find all increasing subsequences with a length of ...

Backtracking Algorithm Understanding Backtracking Backtracking solves problems by exploring all possible solutions in a systematic way, often represented as a tree structure. The algorithm recursively searches through subsets, where the size of the original set determines the tree's width, and the recursion depth determines its height. Since re ...

LeetCode 257: Binary Tree All Paths Termination Condition Considerations The statement if (root == nullptr) return; serves multiple critical purposes in recursive tree algorithms: Primary Function Guard When placed in the main function provided by LeetCode, this check handles the empty tree case. If an empty tree is passed to the main function, ...

Understanding Search Paradigms When approaching algorithmic challenges involving traversal, two primary methods dominate: Depth-First Search (DFS) and Breadth-First Search (BFS). While both traverse nodes in a graph or tree, their utility differs based on the problem constraints. BFS is fundamentally tied to the concept of shortest paths in unw ...

Finding the Bottom-Left Node Value Given the root of a binary tree, return the value of the leftmost node at the deepest level. Breadth-First Search (Iterative) A level-order traversal naturally visits nodes layer by layer. The first node encountered in the final level is the answer. #include <queue> int findBottomLeftValue(TreeNode* roo ...

Equalizing Card Piles (Greedy Approach) To distribute cards equally among $N$ piles, calculate the average number of cards per pile and subtract this value from each pile's count. This transforms the problem into finding the minimum number of moves to zero out the differences. Iterating from left to right, if a pile has a non-zero discrpeancy, ...

Valid IP Address Generation Given a string containing only digits, geenrate all possbile valid IP address combinations. A valid IP address consists of four integers between 0-255 separated by dots, with no leading zeros. class IPGenerator { vector<string> validIPs; bool isValidSegment(const string& s, int start, int end) ...

Combination Sum The objective is to find all unique combinations from a list of candidate numbers that sum up to a given target. Each number may be used multiple times. The solution uses recursive backtracking with the following approach: Parameters include the candidate array, target value, current combination, and results collection Terminat ...