Please find a set of operations and draw a search tree to find all best solutions to the following scenario.

You are given two jugs, neither of which has measuring markers on it. 5-gallon jug that can hold up to 5 gallons of water. 3-gallon jug that can hold up to 3 gallons of water. There is a tap that can be used to fill up a jug with water and a sink that can be used to empty a jug. You may fill up a jug from the other if it has enough water. You may empty a jug into the other if it has space. The game starts where the 5-gallon jug is empty, and the 3-gallon jug is full. The desired result is making the 5-gallon jug full and having exactly 1 gallon of water in the 3-gallon jug. You are given two jugs, neither of which has measuring markers on it. 5-gallon jug that can hold up to 5 gallons of water. 3-gallon jug that can hold up to 3 gallons of water. There is a tap that can be used to fill up a jug with water and a sink that can be used to empty a jug. You may fill up a jug from the other if it has enough water. You may empty a jug into the other if it has space. The game starts where the 5-gallon jug is empty, and the 3-gallon jug is full. The desired result is making the 5-gallon jug full and having exactly 1 gallon of water in the 3-gallon jug