Some of the top mind blowing algorithmic puzzles are the queens problem, producer-consumer problem, binary search tree checker, etc. Know some of the mind blowing puzzles in the article here.
Puzzle Problem Algorithm: Some of the trickiest and most fascinating algorithmic puzzles that will leave your mind in a trans state. How was it possible? Some of the data structures and algorithms solve real life puzzles and games in the smartest way possible. Let us know about 15 puzzle problem algorithms and learn more about each one of them in this article.
What are puzzle problem algorithms?
Puzzle problem algorithms are specially designed algorithms used to solve game and quiz problems. These quizzes are based on certain logic, which is cracked using this algorithm. Knowledge of programming languages and data structures is important for implementing these algorithms.
Algorithms are step-by-step instructions designed to solve a particular task or problem. To develop algorithms, candidates must have good knowledge of programming, problem-solving, logic, mathematics, computer science, etc. They are well-defined methods of solving a complex problem.
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Top Puzzle Problem Algorithm
Given in this article are some of the puzzle problem algorithms. They also help candidates in developing knowledge related to their programming and use of data structures.
1. 15 Puzzle Problem Algorithm
This problem is also known as the magic 15 problem, which consists of rows and columns numbered from 1 to 15. The puzzle was invented by Noyes Palmer Chapman. There are a large number of state spaces to be explored, approximately 1013 . Many mathematicians tried to solve this classical problem with their own approaches. Popular mathematical logic such as linear conflict, manhattan distance, and walking distance were used to solve this problem.
- First, arrange the 4×4 tiles in numerical order from left to right and top to bottom.
- Keep in mind not all the configurations of the 15 puzzle problems can be solved. You must first check whether the problem given is solvable or not.
- Now, any mathematical approach, such as heuristics and A* algorithms, can be used to solve the problem.
- Continue adjusting the tiles until the problem is solved. It will take practice and patience to solve this problem.
- Also, keep in mind that avoiding loops while solving the problem is very important.
- Learn the “15 puzzle problem” to develop a very good understanding of the complex quizzes and their logic, which can be used as an approach.
2. The Tower of Hanoi
The Tower of Hanoi is a famous problem puzzle that consists of three rods and a set of disks of different sizes. The objective of the problem is to move all the discs from the source stack to the destination stack. The disks must be arranged in decreasing order of their size from the base to the top. Check out the important rules of the Tower of Hanoi.
- You can move only one disk at a time.
- Also, you can only move one disc from the top to be transferred to another stack.
- Also, keep in mind that larger discs cannot be placed over smaller ones.
| Problem Puzzle Algorithm: Tower of Hanoi |
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Recursive Algorithm for solving Tower of Hanoi
Here, s stands for source stack, and d means the destination stack. You need to move all the disks from the source (s) to the destination (d)
| Tower of Hanoi Algorithm |
| 1. START
2. Algorithm Hanoi (disk, s, d, aux) 3. IF disk == 1, THEN 4. Move the disk from s to d 5. ELSE 6. Hanoi (disk – 1, s, aux, d) 7. move disk from s to d 8. Hanoi (disk – 1, aux, d, s) 9. END IF 10. END Procedure 11. STOP |
3. Sudoku Solver
Sudoku Solver is an algorithm used for solving the famous Sudoku puzzles. Here, the 9×9 grid must be filled with digits ranging from 1 to 9.
- The squares must be filled with numbers from 1 to 9, with no repetitions in each horizontal or vertical line. The 3×3 matrix inside the puzzle must not contain any repeating numbers.
There are various methods, such as simple brute force, backtracking, bit masks, etc. Learn more about the famous sudoku solver algorithm and learn to play sudoku with practice and logic.
4. Eight Queens Puzzle
This chess puzzle needs to place all the queens on the 8×8 chessboard, where no two queens must threaten each other. Here, you will have to place n queens where n > 0 on a nxn chessboard. Make sure that no two queens must be on the same row, column, or diagonal.
Important Rule of Eight Queens Puzzle
- Each row or column must have only one queen.
- No two queens must threaten each other.
- You must ensure that there are no diagonal attacks possible.
- Predict the safe column or row where no attacks are possible. Always start from the first row and first column.
The 8×8 queen puzzle can be solved by using data structures and algorithmic concepts. Use brute force approaches, backtracking, genetic algorithms, and minimum conflict algorithms.
5. Producer Consumer Problem
The producer-consumer problem is a case of the operating system multi-process synchronization problem. There are two important processes such as producer and consumer.
The producers are used to generate items and put them into the available buffer. In contrast, consumers take items out of the buffer and consume items from the shared buffer. The major objective of using producer-consumer problems are given below.
- To prevent and watch the overflow buffer conditions.
- Consumers must not take items out of an empty buffer.
- Race conditions must be avoided at any cost. Producers and consumers must be synchronized to avoid race conditions.
You can use semaphores, mutual exclusion, condition variables, etc to solve the producer-consumer problem.
6. Binary Search Tree Validator
The algorithm here aims to find whether the binary tree is a binary search tree or not. Some important points must be remembered while validating a binary search tree.
- The value of the node in the left subtree must be less than the value of the current node.
- The value of the right subtree must be greater than the value of the current node.
- Both the left and right subtrees must be a binary search tree.
If any of the binary search tree rules are violated, then it is not a binary search tree. The algorithm may help differentiate between a binary tree and a binary search tree.
7. The Traveling Salesman Problem
It is a problem where you need to find the shortest route between a source point and a destination. It is a classical optimization problem in the field of computer science which can help to find the shortest path from a starting point to the destination point and, at last, return to the starting point. No city can be visited more than once.
With the help of travelling salesman solution, we can find the shortest possible route for a delivery service or travel on the road.
We can solve the travelling salesman problem using the brute force approach, dynamic programming (Held Karp Algorithm), etc.
- The algorithm uses a graph as an input and another graph as a output.
- First, all the edges in the graph are sorted based on their distance in increasing order.
- First, select the edge with the least distance and choose the adjacent edges other than the origin node. Find the minimum distance cost and add it to the output graph.
- Continue the process until the path reaches back to the origin point. Make sure there are no cycles in the graph.
Also Read: Big Data Vs Data Science: Career Guide for 2024
8. Graph Colouring
It is a problem puzzle where we need to colour the vertices of a graph while ensuring that no two adjacent vertices have the same colour. The graph colouring problem can be solved using the greedy algorithm or backtracking method. This problem involves designing a timetable, map colouring, sudoku solving, etc.
9. Knapsack Problem
In the knapsack problem, we need to fill a container to maximise the profit’s value until the maximum limit is crossed. There are two main types of knapsack problems. The fractional knapsack also allows one to keep a fraction of the item or profit to fill the container. While in a 0-1 knapsack problem, either we can pick up the item or not. There are only two options.
These two problems can be solved using the dynamic programming method.
10. Best Subarray Problem (Kadane’s Algorithm)
The algorithm helps find the maximum sum in a contiguous subarray. Kadane’s algorithm is used to find the maximum sum and even the length of the largest contagious array. Given below is the algorithm of the Kadanes algorithm.
| Puzzle algorithm problems |
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Puzzle Problem Algorithm FAQs
What are graph colouring problems?
Graph colouring is a problem where we need to colour the vertices of a graph while ensuring that no two adjacent vertices have the same colour.
What is the difference between the 0-1 knapsack algorithm and the fractional knapsack?
The 0-1 Knapsack only allows you to either pick the item or not pick it. While in a functional knapsack, we can pick up even a fraction of an item until the maximum capacity is reached.
What is a kadane’s algorithm?
Kadane's algorithm helps to find the maximum sum of a contiguous subarray.
Can we solve the travelling salesman algorithm by using greedy methods?
No, you cannot use greedy methods to solve the travelling salesman problem. However, for optimization techniques, candidates can use dynamic programming to find an efficient solution.
Can we use recursion to solve the tower of Hanoi?
Yes, recursion can help in solving the Tower of Hanoi problem.
