Problem Statement Place N queens on an N×N chessboard such that no two queens threaten each other — i.e., no two share the same row, column, or diagoanl. 1. Basic Backtracking A straightforward recursive backtracking approach places one queen per row and validates column and diagonal constraints bef...
Problem Description Given two integers n and k, return all possible comibnations of k numbers out of the range [1, n]. You may return the answer in any order. Example 1: Input: n = 4, k = 2 Output: [ [2,4], [3,4], [2,3], [1,2], [1,3], [1,4], ] Example 2: Input: n = 1, k = 1 Output: [[1]] Constraints...
Given a string containing digits from 2 to 9, return all possible letter combinations that the number could represent based on standard telephone keypad mapping. Note that digit 1 does not map to any letters. Problem Analysis Each digit expands to multiple characters, creating a combinatorial explos...
Problem Description Given an integer array nums with distinct elements, return all possible subsets (the power set). The solution set cannot contain duplicate subsets. You may return the subsets in any order. Example: Input: nums = [1, 2, 3] Output: [[], [1], [2], [1, 2], [3], [1, 3], [2, 3], [1, 2,...
P1092 NOIP2004 Senior Division: Alphametic Puzzle This problem involves solving an alphametic puzzle where letters represent digits in a base-N addition. The solution uses depth-first search with pruning to assign digits to letters efficient. #include <iostream> #include <vector> #includ...
Depth-first search (DFS) serves as the foundational mechanism for backtracking algorithms, systematically exploring tree or graph structures by advancing along a path until a terminal condition or dead end is reached. The algorithm naturally employs an implicit call stack via recursion, allowing it...
Core Concepts Backtracking is a systematic search method that explores all potential configurations of a solution space. It can be visualized as traversing a tree structure where the width represents the size of the candidate set and the depth corresponds to the recursion level. Genarel Framework A...
The objective is to assemble the longest possible concatenated string from a provided vocabulary list, beginning with a specified initial character. Each vocabulary entry may be utilized a maximum of two times during chain construction. When connecting two words, the trailing substring of the first...
Depth-first search (DFS) is characterized by advancing as far as possible along a single branch before retreating. This retreat occurs only upon encountering a dead end, which arises either from hitting a boundary or from reaching a previously visited location. Upon backtracking, the algorithm retur...