Consider an undirected graph with n nodes and m edges. The goal is to find a path between two specified nodes u and v that maximizes the minimum weight of any edge along the path. Assume that all edge weights are positive and distinct. Design an algorithm to solve this problem with a time complexity of O(m log n).

a) write the algorithm  b) Briefly explain why the algorithm solves the problem, and the correctness c ) State and briefly explain the running time of your algorithm

I have spent hours on internet to find an example of iterative lengthening search algorithm but found nothing. I need it ASAP. Can anyone help me? Please. It is its definition: Iterative lengthening search is an iterative analogue of uniform-cost search. The basic idea is to use increasing limits on path cost. If a node is generated whose path cost exceeds the current limit, it is immediately discarded. For each new iteration, the limit is set to the lowest path cost of any node discarded in the previous iteration. I dont understand many things in this definition. 1-What is the first limit before we start? 2-Do we delete the discarded node from the graph or what? 3-What is the generated node? Is it expanded or is it just found as neigbor? 4-What is "lowest path cost of any node discarded"?? Path from where to where?? From start to that node or what? 5-What does path cost mean in this problem? Is it from source to the new node or between current node and next chosen node? I am literally…

A two dimensional array of red and green entries represents a maze. Green entries are passable and red entries are blocked (like a wall). Two special green entries en and ex denote the entrance and exit of the maze. (1) Abstract the problem as a graph; (2) Design an efficient algorithm (pseudo code) to find a shortest path from en to ex if it exists and then print out the path; (3) Analyze the complexity of the algorithm.