Suppose we are given annÃn grid, some of whose cells are marked; the grid is represented by an array M[1..n,1..n]of booleans, where M[i, j] =True if and only if cell (i, j) is marked. A monotone path throughthe grid starts at the top-left cell, moves only right or down at each step, and ends at the bottom-right cell. Our goal is to cover the marked cells with as few monotone paths as possible. Required:
Describe an algorithm to find a monotone path that covers the largest number ofmarked cells.

:you areto design the controller for alight that functions both as an ordinary light and also as a motion activated light and alarm. a. if the manual switch s is on, then the light l is on. b. besides the manual switch, there is a motion detector, m1, which activatesthis light. c.if motion is detected but the light is on anyway because s is on, only then a secondoutput a, an alarm, is turned on. d. the disable switch, d, disables the motion activated light and alarmbut leaves manual control operation of the light using switch s.(i)read the problem statement and clearly identify the inputs and outputs for the circuit you are designing. (ii)create the truth table for this system; include the light, alarm, switch, disable, and the motion sensor.(iii)draw a schematic of this system.