假定有如下的类继承体系: class A extends O class B extends O class C extends O class D extends O class E extends O class K1 extends A, B, C class K2 extends D, B, E class K3 extends D, A class Z extends K1, K2, K3 那么C3运算过程如下: L(O) := [O] // the linearization of O is trivially the singleton list [O], because O has no parents L(A) := [A] + merge(L(O), [O]) // the linearization of A is A plus the merge of its parents' linearizations with the list of parents... = [A] + merge([O], [O]) = [A, O] // ...which simply prepends A to its single parent's linearization L(B) := [B, O] // linearizations of B, C, D and E are computed similar to that of A L(C) := [C, O] L(D) := [D, O] L(E) := [E, O] L(K1) := [K1] + merge(L(A), L(B), L(C), [A, B, C]) // first, find the linearizations of K1's parents, L(A), L(B), and L(C), and merge them with the parent list [A, B, C] = [K1] + merge([A, O], [B, O], [C, O], [A, B, C]) // class A is a good candidate for the first merge step, because it only appears as the head of the first and last lists = [K1, A] + merge([O], [B, O], [C, O], [B, C]) // class O is not a good candidate for the next merge step, because it also appears in the tails of list 2 and 3, but... = [K1, A, B] + merge([O], [O], [C, O], [C]) // ...class B qualified, and so does class C; class O still appears in the tail of list 3 = [K1, A, B, C] + merge([O], [O], [O]) // finally, class O is a valid candidate, which also exhausts all remaining lists = [K1, A, B, C, O]
L(K2) := [K2] + merge(L(D), L(B), L(E), [D, B, E]) = [K2] + merge([D, O], [B, O], [E, O], [D, B, E]) // select D = [K2, D] + merge([O], [B, O], [E, O], [B, E]) // fail O, select B = [K2, D, B] + merge([O], [O], [E, O], [E]) // fail O, select E = [K2, D, B, E] + merge([O], [O], [O]) // select O = [K2, D, B, E, O]
L(K3) := [K3] + merge(L(D), L(A), [D, A]) = [K3] + merge([D, O], [A, O], [D, A]) // select D = [K3, D] + merge([O], [A, O], [A]) // fail O, select A = [K3, D, A] + merge([O], [O]) // select O = [K3, D, A, O]
L(Z) := [Z] + merge(L(K1), L(K2), L(K3), [K1, K2, K3]) = [Z] + merge([K1, A, B, C, O], [K2, D, B, E, O], [K3, D, A, O], [K1, K2, K3]) // select K1 = [Z, K1] + merge([A, B, C, O], [K2, D, B, E, O], [K3, D, A, O], [K2, K3]) // fail A, select K2 = [Z, K1, K2] + merge([A, B, C, O], [D, B, E, O], [K3, D, A, O], [K3]) // fail A, fail D, select K3 = [Z, K1, K2, K3] + merge([A, B, C, O], [D, B, E, O], [D, A, O]) // fail A, select D = [Z, K1, K2, K3, D] + merge([A, B, C, O], [B, E, O], [A, O]) // select A = [Z, K1, K2, K3, D, A] + merge([B, C, O], [B, E, O], [O]) // select B = [Z, K1, K2, K3, D, A, B] + merge([C, O], [E, O], [O]) // select C = [Z, K1, K2, K3, D, A, B, C] + merge([O], [E, O], [O]) // fail O, select E = [Z, K1, K2, K3, D, A, B, C, E] + merge([O], [O], [O]) // select O = [Z, K1, K2, K3, D, A, B, C, E, O] // done
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