Question

我对Wikipedia上的插入操作代码感到困惑。简而言之，我想不出一个示例，在插入后必须进行重新跟踪。由于插入总是发生在叶节点中，因此将Z插入到节点X中。第一次/最早违反AVL树的不变式（平衡因子必须在[-1，1]之内）只能在parent(X)中发生。重新平衡仅包含Z，X和parent(X)的小子树后，此小子树的高度将与以前相同，并且对所有其他子树没有任何影响节点。

为什么我们需要一个一直循环到根的循环？

for (X = parent(Z); X != null; X = parent(Z)) { // Loop (possibly up to the root)
// BalanceFactor(X) has to be updated:
if (Z == right_child(X)) { // The right subtree increases
    if (BalanceFactor(X) > 0) { // X is right-heavy
        // ===> the temporary BalanceFactor(X) == +2
        // ===> rebalancing is required.
        G = parent(X); // Save parent of X around rotations
        if (BalanceFactor(Z) < 0)      // Right Left Case     (see figure 5)
            N = rotate_RightLeft(X, Z); // Double rotation: Right(Z) then Left(X)
        else                           // Right Right Case    (see figure 4)
            N = rotate_Left(X, Z);     // Single rotation Left(X)
        // After rotation adapt parent link
    } else {
        if (BalanceFactor(X) < 0) {
            BalanceFactor(X) = 0; // Z’s height increase is absorbed at X.
            break; // Leave the loop
        }
        BalanceFactor(X) = +1;
        Z = X; // Height(Z) increases by 1
        continue;
    }
} else { // Z == left_child(X): the left subtree increases
    if (BalanceFactor(X) < 0) { // X is left-heavy
        // ===> the temporary BalanceFactor(X) == –2
        // ===> rebalancing is required.
        G = parent(X); // Save parent of X around rotations
        if (BalanceFactor(Z) > 0)      // Left Right Case
            N = rotate_LeftRight(X, Z); // Double rotation: Left(Z) then Right(X)
        else                           // Left Left Case
            N = rotate_Right(X, Z);    // Single rotation Right(X)
        // After rotation adapt parent link
    } else {
        if (BalanceFactor(X) > 0) {
            BalanceFactor(X) = 0; // Z’s height increase is absorbed at X.
            break; // Leave the loop
        }
        BalanceFactor(X) = –1;
        Z = X; // Height(Z) increases by 1
        continue;
    }
}
// After a rotation adapt parent link:
// N is the new root of the rotated subtree
// Height does not change: Height(N) == old Height(X)
parent(N) = G;
if (G != null) {
    if (X == left_child(G))
        left_child(G) = N;
    else
        right_child(G) = N;
    break;
} else {
    tree->root = N; // N is the new root of the total tree
    break;
}
// There is no fall thru, only break; or continue;
}

// Unless loop is left via break, the height of the total tree increases by 1.

AVL树-为什么插入后回溯

0 个答案: