The time complexity of a bubble sort algorithm is O(n^2), where n is the number of elements to be sorted.

  In the worst case scenario, where the input array is in reverse order, the bubble sort algorithm needs to make multiple passes through the array to sort the elements. In each pass, the algorithm compares adjacent pairs of elements and swaps them if they are in the wrong order. This process is repeated until the array is fully sorted.

  In each pass, the largest element in the unsorted portion of the array "bubbles" up to its correct position. Because the algorithm needs to iterate through the entire unsorted portion of the array in each pass, the number of comparisons and swaps grows quadratically with the size of the array.

  Specifically, for an array of size n, the algorithm needs to perform (n-1) comparisons in the first pass, (n-2) comparisons in the second pass, and so on, until only one comparison is needed in the last pass. The total number of comparisons can be calculated by summing up these values: (n-1) + (n-2) + ... + 1, which results in (n^2 - n)/2.

  Since the dominant term in the expansion of (n^2 - n)/2 is n^2, we can conclude that the time complexity of bubble sort is O(n^2).