![]() Conquer: Recursively sort both subproblems.Here partition process will return the index of the pivot element. Divide: Divide the problem into two smaller sub-problems by partitioning the array around the pivot.We divide the array into two sub-arrays using the partition algorithm and sort each sub-array recursively to get the final sorted array. Base case: When l = r, the sub-array has one element left, which is trivially sorted.Combine: Merge both sorted halves to sort the whole array.Conquer: Recursively sort both smaller halves.Divide: Calculate the mid index, i.e., mid = l + (r - l)/2.We divide the array of size n into two equal sub-arrays of size n/2, recursively sort both sub-arrays and merge the sorted halves to sort the complete array. Median of two sorted arrays of the same sizeĭivide and conquer using two sub-problems Merge sort algorithm.Euclidean algorithm of finding GCD of two numbers.Recursive solution of calculating power function.Recursive algorithm of searching an element in a BST.In other words, the case of a single-element is the base case. Note: Assume that l <= k <= r.īase case: If l = r, return X. So there is no need to combine the sub-problems. If (pos - l + 1 So array X will look like this: X k), recursively search kth smallest in the left subarray. ![]() After the partition, partition algorithm will return the index of the pivot. Quick-select algorithm of finding kth smallestĭivide: We divide the array into two subarray using the partition algorithm (partition process similar to quick sort). If (X > key), recursively search the key in the left half.In other words, we solve the searching problem of size n using one sub-problem of size of n/2.ĭivide: Calculate the mid index, i.e., mid = l + (r - l)/2. This process will continue until we find the target value or reach the base case. In most cases, the cost of these operations can be O(1), O(log n), O(n), or O(n^2).ĭivide and conquer using one subproblem (Decrease and conquer) Binary search algorithmīased on a comparison with the middle value, we recursively search for the target value in either the left or right half. To implement the combine step, we must identify the correct operation for combining the solutions of subproblems.So we need to carefully identify the smallest version of the problem. The correct base case is crucial for the correctness of the divide and conquer algorithm.So we need to carefully determine the input parameters for the recursive call of each subproblem. In most situations, we divide the problem into two equal size subproblems. So we need to choose the correct subproblems to find the solution. ![]()
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