Please write algorithm in psuedocode, and explain your answer for part b) & c)

Problem 1 Starting with a map represented by a rectangular grid with height h and width w. Cells are numbered (0, 0) in the top left to (h-1, w-1) in the bottom right. Each cell in the grid is either empty or contains an impassable object. All movements on the map are done as a single step to a cell that is adjacent horizontally or vertically. No diagonal movement is permitted. (a) [10] Write an algorithm that uses a breadth first search to find the length of the shortest path from (0,0) to (w-1,h-1). Return-1 if no such path exists (b) [5] What is the worst case complexity for your algorithm? Be sure to specify how the input size is measured and show your work. (c) [10] Modify your algorithm from part (a) to return the shortest path from (0,0) to (w-1,h -1) in addition to its length. How does your change affect the time complexity? How does your change affect the amount of memory required