complexity analysis for double loops -


if have following code in . net:

for i=0 n     j=0 n         m=i*j     next j next

so have done following complexity analysis:

enter image description here

is correct? in case double loop give o(n) complexity?

in simplest case, complexity of 2 nested loops equal complexity of 1 loop multiplied complexity of other. demonstration identical posted.

therefore, if want complexity of 2 nested loops o(n), make 1 of loops execute in constant time:

for i=0 10   j=0 n     m = i*j   next j next

or have each of them execute in o(n^1/2):

for i=0 sqrt(n)   j=0 sqrt(n)     m = i*j   next j next

or other variations of sort.

a particularly interesting solution when number of iterations in inner loop depends on counter outer loop, don't have example you.


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