Commit 81cd29b

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Amogh Singhal

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Merge pull request devAmoghS#2 from luiz-surian/master

Add josephus_improved_v3.py

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	`1`	`+# The effective time complexity of this improved version is O(1).`
	`2`	+# For the problem statement, refer `josephus.py`
	`3`	`+`
	`4`	`+def josephus_v3(soldiers):`
	`5`	`+ # Convert to binary.`
	`6`	`+ binary = bin(soldiers)`
	`7`	`+ # Get the first digit and put it as last.`
	`8`	`+ shift = '0b' + binary[3::] + binary[2:3:]`
	`9`	`+ # Convert to decimal.`
	`10`	`+ return int(shift, 2)`
	`11`	`+`
	`12`	`+winning = josephus_v3(soldiers=41)`
	`13`	`+print(winning) #Winning Soldier: 19`
	`14`	`+`
	`15`	`+winning = josephus_v3(soldiers=100)`
	`16`	`+print(winning) #Winning Soldier: 73`
	`17`	`+`
	`18`	`+winning = josephus_v3(soldiers=1000)`
	`19`	`+print(winning) #Winning Soldier: 977`
	`20`	`+`
	`21`	`+# Testing:`
	`22`	`+test_josephus = {`
	`23`	`+ 1: 1,`
	`24`	`+ 2: 1,`
	`25`	`+ 3: 3,`
	`26`	`+ 4: 1,`
	`27`	`+ 5: 3,`
	`28`	`+ 6: 5,`
	`29`	`+ 7: 7,`
	`30`	`+ 8: 1,`
	`31`	`+ 9: 3,`
	`32`	`+ 10: 5,`
	`33`	`+ 11: 7,`
	`34`	`+ 12: 9,`
	`35`	`+ 13: 11,`
	`36`	`+ 16: 1,`
	`37`	`+ 41: 19`
	`38`	`+}`
	`39`	`+for soldiers, expected_winner in test_josephus.items():`
	`40`	`+ assert josephus_v3(soldiers=soldiers) == expected_winner`

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