The human proof and algorithm for Four-Color Theorem

This paper presents a simple human proof of the Narrow Four-Color Theorem “Given any separation of a plane into contiguous regions, producing a figure called a map, no more than four colors are required to color the regions of the map so that no two adjacent regions have the same color, and all the outermost countries use no more than three colors. (Please refer to “Concept” for the meaning of “outermost countries”)”. And in this proof also shows the algorithm for Four-Color Maps. This paper is from a new way, from first principle (the basic and simple facts) to the final result.