  Nakada's colored hook formula is a vast generalization of many important
formulae in combinatorics, such as the classical hook length formula and the
Peterson's formula for the number of reduced expressions of minuscule Weyl
group elements. In this paper, we utilize cohomological properties of
Segre-MacPherson classes of Schubert cells and varieties to prove a
generalization of a cohomological version of Nakada's formula, in terms of
smoothness properties of Schubert varieties. A key ingredient in the proof is
the study of a decorated version of the Bruhat graph. Summing over weighted
paths of this graph give the terms in the generalized Nakada's formula, and
also provide algorithms to calculate structure constants of multiplications of
Segre-MacPherson classes of Schubert cells. For simply laced Weyl groups, we
also show the equality of `skew' and `straight' Nakada's formulae. This
utilizes a criterion for smoothness in terms of excited diagrams of heaps of
minuscule elements, which might be of independent interest.
