سي 3 الخطية (خوارزمية)
وصف > مثال

ليكن لدينا
class O
 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
يتم حساب الخطية لـ Z كـ
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 class B is a good candidate
        = [K1, A, B] + merge([O], [O], [C, O], [C])          // class C is a good candidate; 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