  We prove the Dubrovin's conjecture for the Stokes matrices for the quantum
cohomology of orbifold projective lines. The conjecture states that the Stokes
matrix of the first structure connection of the Frobenius manifold constructed
from the Gromov-Witten theory coincides with the Euler matrix of a full
exceptional collection of the bounded derived category of the coherent sheaves.
Our proof is based on the homological mirror symmetry, primitive forms of
affine cusp polynomials and the Picard-Lefschetz theory.
