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+# draw dragon line base on requested times
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+'''
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+altorithm:
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+
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+1st move: [F]oward
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+2nd move: [L]eft turn
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+3rd move: [F]oward
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+
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+the n'nd wrap, will create 2^(n-1)'s turnning point, and they follow the order(LRLRLRLR),
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+in the location(1,3,5,..-3,-1), while turning direction at location x would be the opposite of location -x.
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+
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+total turning point would be:
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+
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+1 + 2^(2-1)+2^(3-1)+...+2^(n-1)
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+
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+it's n'nd wrap:
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+
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+location i's turning should be:
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+
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+l_new[i] = 'L' if i%2 == 0 else 'R'
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+l_n[i] = l_new[i/2] if i%2 == 0 else l_(n-1)[int(i/2)]
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+
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+
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+'''
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+
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+
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+class DragonLine:
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+ def __init__(self):
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+
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+ self.__turnflow = []
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+
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+
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+ def turn_flow(self,wrap):
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+
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+ flow_origin = self.turn_flow(wrap-1) if wrap>2 else ['L']
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+ flow_new = ['L' if i%2 ==0 else 'R' for i in range(2**(wrap-1))]
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+ self.__turnflow = [i for i in range(2**wrap-1)]
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+ _range = 2**wrap-1
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+ self.__turnflow = [flow_new[int(i/2)] if i%2 == 0 else flow_origin[int(i/2)] for i in range(_range)]
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+
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+
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+ return self.__turnflow
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+
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+
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+dragonline = DragonLine()
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+
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+print (dragonline.turn_flow(5))
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