12/29/2023 0 Comments Divide and conquer algorithm exampleAt the merge step, it takes about n time to recursively merge all subarrays, So, the total time complexity reaches about O(n log(n)). This technique is generally called Two pointer technique, to sort the arrays.Īt each step in the dividing stage, the problem is divided into 2 equal halves, therefore the time complexity to obtain will be log(n), where n is the length of the array. We keep adding whichever value is the smallest, to the solution array and hence incrementing the pointers until all the elements in both the subarrays are traversed. We take two sorted subarrays, and with a pointer at the left(P1, P2) end of both the subarrays. Here, we will recursively combine the subarrays in a sorted manner until we are left with just one array. Finally, we arrive at the merge stage of the merge sort algorithm. We need to merge all these solutions from subproblems and combine them to get a solution for our real problem. In this step, each block of elements is sorted individually.Ĭombining/Merging: This is a crucial step in this approach to obtain the solution for the given problem. ![]() These obtained solutions are merged in the next stage. Now let's discuss the second individual stage i.e, the Conquer stage.Ĭonquer: This is the intermediary step within the divide and conquers problem-solving approach, where all the individual atomic sub-problems are solved and their solutions are obtained. ![]() The above image it is clearly indicating that the given complex problem is divided into further sub-problems by calculating the midpoint recursively and reaching the atomic stage at the end. Let's look at the below image to get a better understanding of each stage in the divide and conquer technique. This is a brief explanation of the DIVIDE stage in the algorithm. ![]() So, in m=4 Explaining different stages in this Algorithmĭivide: Each sub-array is divided into two halves while calculating mid till it reaches the position where it cannot be divided into halves, ie till we reach one element. The given examples consist of 8 elements ie n (length of the array )=8 and they are divided exactly into two equal parts by calculating mid position and split according to it. Lets the example of the array names as arr as: We will be discussing the prominent Merge Sort algorithm. Here let's discuss the example of the divide and conquer algorithm to get a better understanding of the topic. This can be better explained by the below image. Following this principle, in the divide and conquer algorithm, we keep dividing the given problem into smaller problems to the point that these smaller subproblems can no longer be further divided, that is we will reach the atomic level. It basically revolves around the words like dividing the given complex problem into smaller easily solved subproblems from which we merge the results of these sub-problems and obtain the solution for the given question. Everyone gets stuck due to poor understanding, but it's not very typical. Now let's talk about the implementation part of this technique. In the above section, we have discussed what divide and conquer is and why it is so important in problem-solving. ![]() How does the divide and conquer technique work? Divide and conquer is an important topic to be understood and used during problem-solving to avoid Time Limit Errors and also to solve the given problem in optimized time complexity for the given question. To become a good problem solver, One must be aware of this topic and also learn to apply it whenever required in obtaining the solution in optimised manner.ĭivide and Conquer, the name itself indicates that the problem needs to be solved by dividing it into various subproblems and the solution of all these subproblems is combined/merged to obtain the solution for the given problem. This technique has been used in various famous algorithms which are discussed further. There are many computer science topics that revolve around this algorithm.
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