The tight bound is that term which best captures the overall growth characteristics of your function as you increase the value of n
.
In other words, 10c7n^3 + 10c4nlog(n))
is O(n^3)
because the term with n^3 in it has the greatest effect on the computing time of the function, as n increases. All of the other terms in the function have an insignificant effect over the amount of computing time, compared to the cubed term.
What you call the tilde value appears to be merely the term containing the tilde; i.e. the term containing the highest power of n. (the "terms" are those parts of the function separated by a +
or -
sign)