Red black tree

Red black tree

Characteristics of red black tree:
(1) Each node is either black or red.
(2) The root node is black.
(3) Each leaf node (NIL) is black.
(4) If a node is red, its child nodes must be black.
(5) All the paths from one node to the descendant node of the node contain the same number of black nodes.

Add

case 1. X’s uncle node (U) is red

case2. X’s uncle node (U) is black, and X is a right child (of P).

case3. X’s uncle node (U) is black, and X is a left child (of P).

case 1 can recursion translate into case 2 or 3.
case 2 can translate into case 3.
case 3 can go to end.

Remove

case1. X’s brother node (B) is red.

case 2. X’s brother node (B) is black, the two child nodes (N) of B are black.

case 3. X’s brother node (B) is black, the left child node of B is red, right child node is black.

case 4. X’s brother node (B) is black, the right child node of B is red.

case 1 can translate into case 2 or 3 or 4.
case 2 can recursion translate into case 3 or 4.
case 3 can translate into case 4.
case 4 can go to end.

Java code in JDK

fixAfterInsertion

private void fixAfterInsertion(Entry<K,V> x) {        x.color = RED;        while (x != null && x != root && x.parent.color == RED) {            if (parentOf(x) == leftOf(parentOf(parentOf(x)))) {                Entry<K,V> y = rightOf(parentOf(parentOf(x)));                if (colorOf(y) == RED) {                    setColor(parentOf(x), BLACK);                    setColor(y, BLACK);                    setColor(parentOf(parentOf(x)), RED);                    x = parentOf(parentOf(x));                } else {                    if (x == rightOf(parentOf(x))) {                        x = parentOf(x);                        rotateLeft(x);                    }                    setColor(parentOf(x), BLACK);                    setColor(parentOf(parentOf(x)), RED);                    rotateRight(parentOf(parentOf(x)));                }            } else {                Entry<K,V> y = leftOf(parentOf(parentOf(x)));                if (colorOf(y) == RED) {                    setColor(parentOf(x), BLACK);                    setColor(y, BLACK);                    setColor(parentOf(parentOf(x)), RED);                    x = parentOf(parentOf(x));                } else {                    if (x == leftOf(parentOf(x))) {                        x = parentOf(x);                        rotateRight(x);                    }                    setColor(parentOf(x), BLACK);                    setColor(parentOf(parentOf(x)), RED);                    rotateLeft(parentOf(parentOf(x)));                }            }        }        root.color = BLACK;    }

fixAfterDeletion

private void fixAfterDeletion(Entry<K,V> x) {        while (x != root && colorOf(x) == BLACK) {            if (x == leftOf(parentOf(x))) {                Entry<K,V> sib = rightOf(parentOf(x));                if (colorOf(sib) == RED) {                    setColor(sib, BLACK);                    setColor(parentOf(x), RED);                    rotateLeft(parentOf(x));                    sib = rightOf(parentOf(x));                }                if (colorOf(leftOf(sib))  == BLACK &&                    colorOf(rightOf(sib)) == BLACK) {                    setColor(sib, RED);                    x = parentOf(x);                } else {                    if (colorOf(rightOf(sib)) == BLACK) {                        setColor(leftOf(sib), BLACK);                        setColor(sib, RED);                        rotateRight(sib);                        sib = rightOf(parentOf(x));                    }                    setColor(sib, colorOf(parentOf(x)));                    setColor(parentOf(x), BLACK);                    setColor(rightOf(sib), BLACK);                    rotateLeft(parentOf(x));                    x = root;                }            } else { // symmetric                Entry<K,V> sib = leftOf(parentOf(x));                if (colorOf(sib) == RED) {                    setColor(sib, BLACK);                    setColor(parentOf(x), RED);                    rotateRight(parentOf(x));                    sib = leftOf(parentOf(x));                }                if (colorOf(rightOf(sib)) == BLACK &&                    colorOf(leftOf(sib)) == BLACK) {                    setColor(sib, RED);                    x = parentOf(x);                } else {                    if (colorOf(leftOf(sib)) == BLACK) {                        setColor(rightOf(sib), BLACK);                        setColor(sib, RED);                        rotateLeft(sib);                        sib = leftOf(parentOf(x));                    }                    setColor(sib, colorOf(parentOf(x)));                    setColor(parentOf(x), BLACK);                    setColor(leftOf(sib), BLACK);                    rotateRight(parentOf(x));                    x = root;                }            }        }        setColor(x, BLACK);    }