Unable to start debugging on the web server - 630 ANSWERS TO EXERCISES 46.2 trie with r
630 ANSWERS TO EXERCISES 46.2 trie with r lieves (cf. Section 6.3). The cost associated with an internal node of this trie, having m lieves as descendants, is O(m2(logp)); and the solution to the recurrence A, = (;)+2l-” c(;)Ak is A, = 2(T), by exercise 5.2.2-36. Hence the sum of costs in the given random trie-representing the expected time to factor g(s) completely- is O(r2(logp)3) under this plausible assumption. The plausible assumption becomes rigorously true if we choose t(z) at random of degree < rd instead of restricting it to degree < 2d. 30. Let T(z) = z+z~+…+z~~- and W(Z) = T(t(z))modq(z). Since tag = t(s) in the field of polynomial remainders modulo q(z), we have ~(5)~ = W(Z) in that field; in other words, W(Z) is one of the p roots of the equation yp - y = 0. Hence V(X) is an integer. It follows that &