import math
increment = 0.1
startingPoint = [1, 1]
point1 = [1,3]
point2 = [2,0]
point3 = [1,2]
point4 = [2,1]
def distance(x1, y1, x2, y2):
    dist = math.pow(x2-x1, 2) + math.pow(y2-y1, 2)
    return dist
def sumOfDistances(x1, y1, px1, py1, px2, py2, px3, py3, px4, py4):
    d1 = distance(x1, y1, px1, py1)
    d2 = distance(x1, y1, px2, py2)
    d3 = distance(x1, y1, px3, py3)
    d4 = distance(x1, y1, px4, py4)
    return d1 + d2 + d3 + d4

def newDistance(x1, y1, point1, point2, point3, point4):
    d1 = [x1, y1]
    d1temp = sumOfDistances(x1, y1, point1[0],point1[1], point2[0],point2[1],
    point3[0],point3[1], point4[0],point4[1] )
    d1.append(d1temp)
    return d1
minDistance = sumOfDistances(startingPoint[0], startingPoint[1], point1[0],point1[1], point2[0],point2[1],
point3[0],point3[1], point4[0],point4[1] )
flag = True
def newPoints(minimum, d1, d2, d3, d4):
    if d1[2] == minimum:
        return [d1[0], d1[1]]
    elif d2[2] == minimum:
        return [d2[0], d2[1]]
    elif d3[2] == minimum:
        return [d3[0], d3[1]]
    elif d4[2] == minimum:
        return [d4[0], d4[1]]
i = 1
while flag:
    d1 = newDistance(startingPoint[0]+increment, startingPoint[1], point1, point2, point3, point4)
    d2 = newDistance(startingPoint[0]-increment, startingPoint[1], point1, point2, point3, point4)
    d3 = newDistance(startingPoint[0], startingPoint[1]+increment, point1, point2, point3, point4)
    d4 = newDistance(startingPoint[0], startingPoint[1]-increment, point1, point2, point3, point4)
    print (i,' ', round(startingPoint[0], 2), round(startingPoint[1], 2))
    minimum = min(d1[2], d2[2], d3[2], d4[2])
    if minimum < minDistance:
        startingPoint = newPoints(minimum, d1, d2, d3, d4)
        minDistance = minimum
        i+=1

    else:
        flag = False
