Using the definition of a c-incremental algorithm from the previous exercise, show that, if a c-incremental algorithm A has a worst-case running time t(N) in the RAM model, as a function of the number of input items, N, for some constant c > 0, then A has running time O(n²t(n)), in terms of the number, n, of bits in a standard binary encoding of the input.

Data From Previous exercise

Let n denote the size of an input in bits and N denote the size in a number of items. Define an algorithm to be c-incremental if any primitive operation involving one or two objects represented with b bits results in an object represented with at most b + c bits, for c ≥ 0. Show that an algorithm using multiplication as a primitive operation may not be c-incremental for any constant c.