Backtracking Algorithms: A Comprehensive Introduction

Core Concept Backtracking is a systematic search technique that explores all possible solutions by building candidates incrementally and abandoning ("backtracking") a candidate as soon as it determines that the candidate cannot possibly lead to a valid solution. Problems Addressed Backtracking effectively solves the following categori ...

Posted on Sat, 30 May 2026 20:01:14 +0000 by kuri7548

Backtracking Algorithms for Combination Sum and Palindrome Partitioning

Combination Sum (Problem 39) Given a distinct integer array candidates and a target value target, find all unique combinations in candidates where the numbers sum to target. Each number may be used repeatedly. The solution uses backtracking with these key components: Parameters: The recursive function tracks the current sum, path, and starting ...

Posted on Tue, 26 May 2026 18:10:30 +0000 by mfindlay

Implementing Grid-Based Word Search Using Depth-First Search

The task requires determining if a target sequence of characters exists within a two-dimensional matrix. The characters must be formed by traversing adjacent cells horizontally or vertically, ensuring no cell is reused during the path construction for a single attempt. Problem Constraints: Input: A 2D character array board and a string word. O ...

Posted on Sun, 24 May 2026 18:06:08 +0000 by TheSaint97

Algorithmic Solutions for Programming Competition Problems

Everyone Loves to Sleep Convert all times to minutes and store in a sorted set. Use binary search to find the nearest alarm time. If no alarm exists after bedtime, calculate duration untill first alarm next day. #include <iostream> #include <set> #include <climits> using namespace std; void calculateSleepDuration() { int ...

Posted on Fri, 22 May 2026 16:54:24 +0000 by Salkcin

Determining Feasibility of Safe Aircraft Landing Sequence with Single Runway

Problem Description N aircraft are preparing to land at an airport with only one runway. The i-th aircraft arrives above the airport at time Ti and has enough remaining fuel to continue circling for Di units of time. This means it can begin landing at the earleist at time Ti, and at the latest at time Ti + Di. The landing process itself require ...

Posted on Sun, 17 May 2026 06:05:57 +0000 by inkfish

Backtracking the N-Queens Puzzle with Early Output

Given an n × n chessboard, place n queens so that no two attack each other. A valid placement guarantees exactly one queen per row and per column, and at most one queen on every diagonal (both positive and negative slopes). The task is to enumerate every valid configuration, print the first three in lexicographical order, and finally output the ...

Posted on Sat, 16 May 2026 16:22:06 +0000 by mtucker6784

Practical Implementations of Iterative Deepening A* Search

Segment Rotation Optimization When solving permutation puzzles that require rearranging contiguous segments within a fixed array, the branching factor can grow exponentially. For an array of length $n$, selecting a segment of length $i$ yields $n-i+1$ starting positions and $n-i$ insertion points. Accounting for symmetry (forward vs. backward m ...

Posted on Tue, 12 May 2026 15:42:03 +0000 by foochuck

Backtracking for Combination Sum, Combination Sum II, and Palindrome Partitioning

39. Combination Sum Problem: https://leetcode.cn/problems/combination-sum/description/ Find all unique combinations of candidates where the chosen numbers sum to target. The same number may be used a unlimited number of times. class Solution { public: vector<vector<int>> combinationSum(vector<int>& candidates, int targ ...

Posted on Sun, 10 May 2026 15:26:59 +0000 by Jedi Legend

Combination Sum II - Handling Duplicate Elements in Backtracking

Given an array of integers candidates and a target value target, find all unique combinations in candidates where the numbers sum to target. Key constraints: Each number can only be used once in each combination. All numbers (including the target) are positive integers. The result set must not contain duplicate combinations. Examples Example ...

Posted on Sun, 10 May 2026 11:27:21 +0000 by smilley654

Backtracking with Element Tracking for Deduplication

Problem 491: Non-decreasing Subsequences Given an integer array nums, return all the different non-decreasing subsequences that have atleast two elements. The answer can be in any order. When two integers are equal, this counts as a valid increasing sequecne. Example 1: Input: nums = [4,6,7,7] Output: [[4,6],[4,6,7],[4,6,7,7],[4,7],[4,7,7],[6,7 ...

Posted on Fri, 08 May 2026 23:26:45 +0000 by mcccy005