Please solve a-d, it is required for #1.

Thank you!!! :)

1. (4X4 pts) Give a complete problem formulation for each of the following, i.e., specify the data structure of a state, the initial state as an instance of this data structure, the successor function or actions that can be performed to transform one state to another, and the cost function. Choose a formulation that is precise enough to be implemented via code (inspect the 8-puzzle problem formulation code included in Project 1 for inspiration). Important: Don't attempt to solve these problems yourself; rather formulate them so that they can by solved by a search algorithm a) Using only three colors, you have to color a planar map in such a way that no two adjacent regions have the same color. b) A 3 -foot-tall monkey is in a room where some bananas are suspended from the 8-foot ceiling. He would like to get the bananas. The room contains two stackable, movable, climbable 3-foot-high crates. c) You have three jugs, measuring X gallons, Y gallons, and Z gallons, and a water faucet. You can fill the jugs up or empty them out from one to another or onto the ground. You need to measure out exactly one gallon. d) 3 missionaries and 3 cannibals are on one bank of a river. There is a boat that can be used for trips between banks, but it can hold up to 2 persons at a time. You need to get all 6 to the other bank of the river, but the cannibals must never outnumber the missionaries on either bank