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Update josephus_improved.py

The equation to the Josepus problem, W(n) = 2L + 1, has a constraint in which L < 2^a (The biggest power of 2 inside the number of soldiers, in this case the variable p). This means if n is a power of 2, the winning position will always be 1, so the formula would be wrong.

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`‎josephus_improved.py‎`

Lines changed: 5 additions & 1 deletion

Original file line number	Diff line number	Diff line change
`@@ -12,7 +12,11 @@ def josephus_v2(people, step=2):`
`12`	`12`	`# the loop runs for O(floor(logN)) time`
`13`	`13`	`while p*2 < N:`
`14`	`14`	`p = p*2`
`15`		`- print((2*(N-p))+1)`
	`15`	`+ # If N is a power of 2, should return 1. So let's check if L (N-p) is < p`
	`16`	`+ if N-p >= p:`
	`17`	`+ print(1)`
	`18`	`+ else:`
	`19`	`+ print((2*(N-p))+1)`
`16`	`20`
`17`	`21`	`num = int(input("Enter the number of soldiers: "))`
`18`	`22`	`soldiers = [i for i in range(1, num+1)] # generates a list of 1..num`

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`‎josephus_improved.py‎`

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