[Algorithm] Delete a node from Binary Search Tree
The solution for the problem can be divided into three cases:
case 1: if the delete node is leaf node, then we can simply remove it
case 2: if the delete node is has single side or substree
case 3: it has two children, then to keep it as a valid binary search tree, we can copy the min value from right subtree to delete node, to convert the problem into case 2
function Node(val) {
return {
val,
left: null,
right: null
};
} function Tree() {
return {
root: null,
addLeft(val, root) {
const node = Node(val);
root.left = node;
return root.left;
},
addRight(val, root) {
const node = Node(val);
root.right = node;
return root.right;
}
};
} const tree = new Tree();
const root = Node();
tree.root = root;
const n1 = tree.addLeft(, root);
const n2 = tree.addRight(, root);
const n3 = tree.addLeft(, n1);
const n4 = tree.addRight(, n1);
tree.addLeft(, n3);
tree.addRight(, n4);
const n5 = tree.addLeft(, n2);
tree.addRight(, n5);
const n6 = tree.addRight(, n2);
const n7 = tree.addRight(, n6);
tree.addLeft(, n7); /**
*
12
/ \
5 15
/ \ / \
3 7 13 17
/ \ \ \
1 9 14 20
/
18 Delete 15
First copy 17 to 15
12
/ \
5 17
/ \ / \
3 7 13 17
/ \ \ \
1 9 14 20
/
18
Then remove original 17
12
/ \
5 17
/ \ / \
3 7 13 20
/ \ \ /
1 9 14 18 */ function deleteNode(root, val) {
// base case, if leaf node, return
if (root === null) {
return root;
} else if (val > root.val) {
// if delete value is larger than root, search on right side of tree
root.right = deleteNode(root.right, val);
} else if (val < root.val) {
// if delete value is smaller than root, search on left side of tree
root.left = deleteNode(root.left, val);
} else {
// if found the delete value and it is leaf node
if (root.left === null && root.right === null) {
// set leaf node to null
root = null;
}
// if found the delete node and its right side has children
// set root to null and link to its right node
else if (root.left === null && root.right !== null) {
let temp = root.right;
root = null;
root = temp;
}
// if found the delete node and its left side and children
// set root to null and link to its left node
else if (root.left !== null && root.right === null) {
let temp = root.left;
root = null;
root = temp;
}
// the found node has children on both sides
// then pick the min value from rgiht side (or max value from left side)
// copy to current node
// reset it right side (or left side)
else {
const temp = root.right; // get the min on the right side or max on the left side
root.val = temp.val;
root.right = deleteNode(root.right, temp.val);
} return root;
}
} deleteNode(tree.root, ); console.log(JSON.stringify(tree.root.left, null, ));
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