Breadth-first search (BFS) is a graph traversal algorithm that explores all vertices at the same level before moving to the next level. In the worst case, BFS visits each vertex once and each edge once, resulting in a time complexity proportional to the sum of the number of vertices (V) and the number of edges (E). Hence, the time complexity of BFS is O(V + E).

In a depth-first search (DFS) algorithm on a directed acyclic graph (DAG), each vertex is visited once, and each edge is traversed once. The time complexity of DFS on a DAG is proportional to the sum of the number of vertices (V) and the number of edges (E), denoted as O(V + E).

Bubble sort is a simple comparison-based sorting algorithm that repeatedly steps through the array, compares adjacent elements, and swaps them if they are in the wrong order. In the worst case, where the array is sorted in reverse order, each pass of the algorithm will result in the largest unsorted element "bubbling" to the end of the array. This requires n-1 comparisons in the first pass, n-2 in the second pass, and so on, resulting in a quadratic time complexity of O(n^2).

In a breadth-first search (BFS) algorithm on a tree, each node is visited exactly once, and each edge is traversed once. As a tree has N-1 edges for N nodes, the time complexity of BFS on a tree is proportional to the number of nodes, denoted as O(N).

Binary heaps are a type of complete binary tree used to implement priority queues. In the worst case, when inserting an element into a binary heap, it needs to compare the element with the parent node and potentially swap them to maintain the heap property. As the height of a binary heap is logarithmic to the number of elements (n), the worst-case insertion operation has a time complexity of O(log n).

Quicksort is a comparison-based sorting algorithm that divides the array into two subarrays based on a pivot element, recursively sorts the subarrays, and combines them. In the worst case, if the pivot selection consistently results in unbalanced partitions, quicksort degrades to its quadratic time complexity. This occurs when the pivot is always the minimum or maximum element, leading to n recursive calls and resulting in a time complexity of O(n^2).

Bubble sort is a simple comparison-based sorting algorithm that repeatedly swaps adjacent elements if they are in the wrong order. In the worst case, where the array is reverse sorted, each pass of the algorithm requires traversing the entire array and potentially swapping adjacent elements. This results in a quadratic time complexity of O(n^2).

Merge sort is a divide-and-conquer sorting algorithm that recursively divides the array into smaller subarrays, sorts them individually, and then merges them back together. In each recursive call, the array is split in half, resulting in a logarithmic number of divisions. Afterward, the merging process takes linear time to combine the sorted subarrays. Therefore, the time complexity of merge sort in the worst case is O(n log n).

In the worst case, a hash table's insertion operation may require rehashing or resizing the underlying array, which involves copying elements. As a result, the worst-case time complexity of an insertion operation in a hash table is linear to the number of elements (n), denoted as O(n).

In a balanced binary search tree, such as an AVL tree or a red-black tree, the average-case search operation is efficient. The tree's balanced structure ensures that the height remains logarithmic to the number of elements (n), resulting in a time complexity of O(log n) for search operations.