Find the time complexity using big O notation for an algorithm, explain how and why

G positive integer decompose, find an algorithm to find the number ofnon-negative number division, or decomposition. The complexity is O(n^2). Example 1:Input: 4Output: 5Explaination:4=44=3+14=2+24=2+1+14=1+1+1+1 Example :Input: 7Output: 15Explaination:7=77=6+17=5+27=5+1+17=4+37=4+2+17=4+1+1+17=3+3+17=3+2+27=3+2+1+17=3+1+1+1+17=2+2+2+17=2+2+1+1+17=2+1+1+1+1+17=1+1+1+1+1+1+1.   """.

Please help and show work

Subject - Design & Anal algorithms Please complete all the questions together.  Thank you in Advance. Consider the following pseudocode for bubblesort:bubblesort(A, n)for i from 1 to n − 1for j from n to i + 1if A[j] < A[j − 1]swap(A[j], A[j − 1])(a) What is the loop invariant for bubblesort?(b) State briefly a proof of correctness.(c) Derive concisely the worst-case running time of bubblesort as a function of the input array sizen? Show your work!(d) Derive concisely the best-case running time as a function of n. Show your work!