[pkhuong]

GP is referring to https://en.wikipedia.org/wiki/Lagrange_polynomial

Build a table left[j] of product-of-ratios for i < j, and another right[k] for i > k, each in linear-time, and combine the two to find the product-of-ratio for i != m in linear time as well.

[steppi]

Right, and if we are trying to get all coefficients and are thus performing the polynomial multiplications symbolically, then performing the multiplications naively will take O(n^2) time but using FFT allows it to be done in O(n log n) time.