Divide and Conquer Algorithm Tower of Hanoi Problem

Mind map outline: A graphically presented thinking tool used to organize, organize and present thoughts and ideas. Divide-and-conquer algorithm: An efficient problem-solving method that divides the problem into smaller sub-problems and solves them one by one, and finally combines the solutions of the sub-problems to get the final result. Tower of Hanoi problem: A classic mathematical problem that requires moving a pile of discs of different sizes from one pillar to another. It is stipulated that the disc can only be enlarged above the small disc and solved through recursive thinking.

Edited at 2022-08-23 00:49:20

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Divide and Conquer Algorithm Tower of Hanoi Problem

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Outline

Divide and Conquer Algorithm: Tower of Hanoi Problem

Overview: The divide-and-conquer algorithm is a problem-solving idea that decomposes the problem into smaller sub-problems and solves them separately, and then obtains the solution to the original problem by merging the solutions to the sub-problems.

Example: Tower of Hanoi problem

Overview: The Tower of Hanoi problem is a classic example of the divide-and-conquer algorithm, where the goal is to move a tower consisting of disks of different sizes from one pillar to another.

Example:

If there is only one disc, just move it from the starting pillar to the target pillar.

If you have multiple discs, you can break it down into three steps

Move the other discs except the largest disc from the starting pillar to the auxiliary pillar.

Move the largest disc from the starting pillar to the target pillar.

Move the disc on the auxiliary pillar to the target pillar.

Example:

Take three disks as an example

Move the two smallest discs from the starting pillar to the auxiliary pillars.

Move the largest disc from the starting pillar to the target pillar.

Move the minimum two discs on the auxiliary pillar to the target pillar.

Example:

The Tower of Hanoi problem can be solved using recursion, by continuously calling itself to solve sub-problems.

Sample code

The function hanoi(n, start, auxiliary, target) means moving n disks from the starting pillar to the target pillar, and the auxiliary pillar is the auxiliary pillar.

If n is greater than 1, n-1 disks except the largest disk are first moved from the starting pillar to the auxiliary pillar.

Move the largest disc from the starting pillar to the target pillar.

Finally, move the n-1 disks on the auxiliary pillar to the target pillar.

Sample code

If n equals 1, move the disc directly from the starting pillar to the target pillar.

Otherwise, the hanoi functions are called in sequence to solve the subproblems.

Summary: The divide-and-conquer algorithm is an idea that decomposes a problem into smaller sub-problems and solves them separately. It is suitable for solving some complex problems. The Tower of Hanoi problem is a typical application example of the divide-and-conquer algorithm. By decomposing the problem into three steps and recursively solving the sub-problems, the disk can finally be moved from the starting pillar to the target pillar.