Which Algorithm uses Divide And Conquer Algorithm

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Which Algorithm uses Divide And Conquer Algorithm

Many of you come here by searching Which Algorithm uses Divide And Conquer Algorithm, and yes this article is on same topic. With the divide and conquer method, the problem is broken up into smaller parts, and each element is then solved on its own. When we keep breaking a problem into smaller pieces, there comes the point when we can’t make it any smaller.

At that point, the smaller pieces are solved, and the answers to all of the smaller parts or sub-parts are put together to find the solution to the original problem. This Algorithm is constructive and has a lot of exciting uses, pros, and cons. In this blog, we’ll take a close look at each of them, which will show you why this Algorithm is so helpful in the real world.

The following are the steps of the Divide and Conquer Algorithm

  • Divide: To do this, break the problem up into smaller parts.
  • Conquer: Finding solutions to the more minor issues one at a time.
  • Combine: Use the recursive process to combine the answers to the sub-problems to solve the main problem.

Which Algorithm uses Divide And Conquer Algorithm

If we have a problem similar to the divide and conquer the situation, this Algorithm will help us solve it. We can use this Algorithm when the problem can be broken down into more minor issues.

We require to make sure that the same more minor problems don’t get solved more than once. If the same sub-problem is translated more than once, you should know that this problem is not solved with the Divide and Conquer Algorithm but with a dynamic approach.

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Examples of Divide and Conquer Algorithms

People often use the “divide and conquer” method to solve problems like mergeSort, QuickSort, finding the closest pair of points, etc. Here are two important examples of this kind that every programmer should know.

Example 1: The Tower of Hanoi

The Tower of Hanoi

In this problem, there are N blocks of decreasing size on Tower A, and you need to move all of them from Tower A to Tower C using Tower B. Remember that you can only shift one block at a time, and you can’t put a giant block on top of a smaller one.

Let’s say we have three blocks, and we want to move them from Tower A to Tower C. First, move the block that is the tiniest big to Tower C. This step shows how the problem is split up by changing the number of blocks from N=3 to N=2. So, we can now say that moving two blocks from Tower A to Tower C is our sub-problem.

Then, as shown in the picture below, move the middle block to Tower B. At the source point, we did something similar to the last step and split the sub-problem from N = 2 to N = 1. In this step, we solve the more minor problems by putting the smallest block in Tower B on top of the middle block.

Later, move Tower A’s biggest block to Tower C and Tower B’s smallest block to Tower A’s empty tower. Last, we combine the solutions to get the final answer. We move the middle block over the biggest block from Tower B to Tower C and the lowest block from Tower A to Tower C.

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Example 2: Find the smallest and biggest elements in an array

Find the smallest and biggest elements in an array

In this problem, we are offered an array of numbers, and we need to find the smallest and largest numbers in the collection. We will use the “divide and conquer” method to solve the problem. In this case, the first step of the divide and conquer algorithm is to divide the elements. The second step is to find the minimum and maximum details in the array. The last step is to combine the results to get the final answer.

Divide and Conquer Algorithm Advantages

  • This Algorithm makes the given problem easier to solve because it breaks it up into more minor issues that are easier to solve on their own. Each of these more minor issues is then solved on its own, and then all of their solutions are put together to solve the original problem.
  • The Algorithm makes other algorithms, like quicksort, merge sort, and so on, work better.
  • Most processors can use this Algorithm, especially those with shared memory systems, which makes it easy for processors to talk to each other without having to be pre-programmed.
  • This Algorithm makes efficient use of memory caches.

Divide and Conquer Algorithm Disadvantages

  • The major problem with this Algorithm is that the recursion is slow, making it take more time.
  • Another issue with this Algorithm is that it can get complicated when trying to solve a problem in this way, while the primary iterative method seems easier.
  • Sometimes, the same sub-problems keep coming up when using this method to solve problems. So the most significant thing to do is to save the answer to the repeated sub-problem.
  • When using this Algorithm, make sure the return stack has enough memory. If it doesn’t, processing may fail because the stack may be full.

Applications for Divide and Conquer Algorithm

Applications for Divide and Conquer Algorithm
Image Source: Data Notes

Search in binary

The Divide and Conquer Algorithm is the idea behind this fast search algorithm. For this Algorithm to work, the data needs to be in sorted order. This Algorithm looks for a specific item by comparing the thing in the middle of the group. If there is a match, the object’s index is given back.

If the middle item is more significant than the item, the thing is looked for in the sub-array to the left of the central element. If not, the item is looked for in the thread to the right of the item in the middle. This process continues on the sub-array until its size goes down to zero.

Merge Sort

The Divide and Conquer Algorithm is also used to sort things. First, this Algorithm splits the array into two equal parts. Then, the two parts are placed back together to make sense.

Quick Sort

The same idea is behind this sorting method as well. This Algorithm chooses a pivot element and then rearranges the array of features so that all parts more minor than the pivot element selected move to the left side of the pivot.

All aspects are more significant than the chosen pivot element moving to the right side. Lastly, the Algorithm sorts the sub-arrays to the left and right of the pivot element by going through a loop.

Strassen’s Multiplication of the Matrix

The same idea is also behind this method. This method is an excellent way to multiply two matrices together.

Conclusion

As we’ve learned, Which Algorithm uses Divide And Conquer Algorithm, the divide and conquer Algorithm is a valuable and essential way to solve problems because it has many benefits. Recursively using the top-down Algorithm helps solve complex problems in just three easy steps. This fundamental thought of the divide and conquer Algorithm has a lot of real-world applications, so it is essential to learn and understand it.

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