Please do both fully and show work involved so I can understand.

1. For each algorithm provided below, determine its runtime and space complexity. Express your findings using Big O notation. Consider the worst-case scenario and analyze how the runtime of the algorithm scales with the size of the input. Also, provide a brief explanation for your choices of runtime and space complexity for each algorithm. Justify your analysis with clear and concise reasoning. Algorithm 1: Finding Maximum Cumulative Sum Subarray Let maxSum 0; for i0 to A.length - 1 do thisSum 0; for j0 to A.length - 1 do thisSum thisSum +A[j]; if thisSum > maxSum then maxSum thisSum; end end end Algorithm 2: Printing Powers of 2 Indices in Array A while i A.length do print A[i]; ii2; end 2. For each function f(n) and time t in the following table, determine the largest size n of a problem that can be solved in time t, assuming that the algorithm to solve the problem takes f(n) microseconds. Note: For each time t and each function f(n), find the largest integer n such that f(n)t