Minimum cost path

You are given an integer matrix A that has $N$ rows and $M$ columns.

The rows are numbered from $1$ to $N$ from top to down and the

columns are numbered from $1$ to $M$ from left to right.

You have to find a path from the first column to the last column of

the matrix. There is a cost attached to a path. This cost is defined as

the absolute difference between the maximum and minimum

elements visited along the path. For example, if the path you have

chosen is $P_1,P_2,P_{3}dots{P}_m.$ then cost of this path will be as follows:

$cost=$max$(P)-$min$(P).$ Here, max$(P)$ is the maximum element

on the path $P$ and min$(P)$ is the minimum element on the path $P.$

You are required to find a path that has the minimum cost from the

first column to the last column of the matrix. While you can start from

any row number, you must start from the first column. You can

also end at any row but you must end at the last column.

Your task is to reach the $M_{th}$ column from $1_{at}$ column. If you are in

the $(i,j)$ cell, then you can move to any cell in the $(j+1{)}_{th}$ column.you are given an integer matrix A of dimension N$*$N$,$ such that each row in A is sorted in increasing order and each column in A is sorted in increasing order. Assume that you have a distributed computing system with N nodes. You have to find the minimum value in A a$)$ specify your solution using map and reduce operations b$)$ calculate the number of basic steps in your solution, You may assume that a function min$($x$,$y$)$ to compute the minimum of x and y in $1$ basic step is available c$)$what is the speedup obtained? d$)$ Suppose your system has only P compute nodes$($instead of N$)$ for some P

Give me the code in C$++$ or Python