why is this an infinite loop in python?

I can't seem to figure out why this is an infinite loop in python??

for i in range(n):
    j=1
    while((i*j)<n):
       j+=1

shouldn't the outer loop go n times. incrementing j until开发者_Python百科 its equal to n div i each time?

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i starts at 0, so the while condition stays always true; see the range docs for details.

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You can create a "trace" showing the state changes of the variables.

1. n= 5; i= 0
2. n= 5; i= 0; j= 1
3. i*j < n -> 0 < 5: n= 5; i= 0; j= 2
4. i*j < n -> 0 < 5: n= 5; i= 0; j= 3
5. i*j < n -> 0 < 5: n= 5; i= 0; j= 4
6. i*j < n -> 0 < 5: n= 5; i= 0; j= 5
7. i*j < n -> 0 < 5: n= 5; i= 0; j= 6

etc.

You can prove that your trace is correct by inserting print statements.

When in doubt, print it out.

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i starts at zero, so the condition for the inner loop is always 0*j < n, which will always be true.

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Because the initial value of i is 0.

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The first value in i will be 0. 0 times anything is 0.

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because i is 0!! and i*j=0

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range(n) starts at 0, not 1. 0 * j will always be less than n.

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On the first time through the outer loop, the inner loop becomes an infinite loop. It doesn't matter what happens after that. There's no "after infinity".

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i is 0 rewrite you loop like

for i in range(1,n):
j=1
while((i*j)<n):
   j+=1

using this version of the range function will create a range that starts at 1 instead of 0