explaination of time complexity

Quicksort time complexity

Quickselect only recurses into one side - the side with the element it is searching for. This average complexity is O(n), with a worst case of O(n^2).

Explain the time complexity of using the divide and conquer approach in counting majority element in array

Each recursive call to function performs two recursive calls on subslices of size n/2 and two linear scans of length n. There fore, the time complexity of the divide and conquer approach should be O(n log(n))

The approach is to take the first element of preorder as the root, then using the value of the root to divide the inorder traversal into left and right subtrees. We recursively construct the left and right subtrees of the root using the same approach, then return the root node.

Explain that Construct Binary Tree from Preorder and Inorder Traversal

for each level of recursion, the function generates two more branches of recursion. And since the function dfs is called n times, where n is the length of prices, the total number of recursive calls is 2^n

explain O 2^n

The time complexity of quickselect is typically O(n) on average, the partition step of quickselect divides the input array into roughly two equal-sized subarrays. This means that on average, quickselect only needs to recursively search one of the two subarrays, which takes O(n/2) time. O(n^2) in the worst case, where n is the number of elements in the array. However, in the worst case, the pivot element chosen in the partition step is either the largest or smallest element in the array. This means that quickselect will have to recursively search through the entire array, which takes O(n) time for each recursive call. This results in a worst-case time complexity of O(n) * O(n) = O(n^2).

quickselect time complexity on average and worst

The heapify function takes an iterable and converts it into a heap data structure in O(n) time This step is done k-1 times, where k is the input value. Each heappop function call takes O(log n) time because it needs to adjust the position of the remaining elements in the heap to maintain the heap property. Therefore, this step takes O((k-1) log n) time. In conclusion, the algorithm has O(n+k log n) time complexity

time complexity of heap-related method to find the kth largest element in an unsorted array

The algorithm iterates through each bit of the exponent, performing a constant amount of work for each bit. Since the number of bits in the exponent is logarithmic with respect to the exponent, the time complexity of the algorithm is O(log n).

time complexity of quick pow

BST is a tree that the depths of the two subtrees of every node never differ by more than 1.

what is bST？

auxiliary auxiliary space

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