/*
* Find the inorder predecessor of current
*
* thought process:
* start from input node n2,
* Go to left child first, and then, go the right continuously,
* until the last one, exclude input node - itself (n1),
* return the node (n1);
* Think in a graph of rightmost node in the binary search tree.
* Also, the code will work if the node is set as right child of
* its inordre predecessor.
*
*/
private static TreeNode findTheInorderPredecessorOfCurrent(TreeNode n2)
{
TreeNode n1 = n2.left; // step 1: moving node (n1), go left first step
while (n1.right != null && n1.right != n2) // step 2: then, go right continuously;
// exclude input node itself
n1 = n1.right;
return n1;
}
/*
* previous -> current node
* thought process:
* if the current node visited has a not-null previous node,
* then the two values of nodes should be in increasing order
*
* Base test case:
* tree only have two nodes, switched;
* case A:
* 2 1
* / -> /
* 1 2
* case B:
* 1 2
* \ -> \
* 2 1
* Manually, walk through the code, make sure that v1 and v2 are correct results.
*
* input arguments:
* n1 - previous --
* n2 - current --
* output arguments:
* v1, -- viloation node 1
* v2, -- violation node 2
* found -- usually violation can be found at most twice; first violation, set found = true from false.
* assumption: n2 node is not null
* violation facts:
* 1. first node, it is the one with bigger value, violated;
* but second node, it is the one with smaller value, violated.
* 2. sometimes, only one violation catch; like base case A, switch two nodes, only two nodes
* in the tree. Tree [2,#,1]
* 3. sometimes, two violationes catch.
* Tree [2, 3, 1], inorder traversal result is 3, 2, 1, and then,
* first one of viloations is 3, 2, 3>2, the violation one is 3, bigger value;
* second one of viloations is 2, 1, 2>1, the violation one is 1, smaller value;
* so, 3 and 1 should be swapped back as 1 (2) 3
*/
private static void violationChecking(TreeNode n1,
TreeNode n2,
ref TreeNode v1,
ref TreeNode v2,
ref bool found)
{
if (n1 != null && n1.val > n2.val) // break "increasing order" principle
{
if (!found)
{
v1 = n1; // bigger value violated - first one always
found = true;
}
v2 = n2; // smaller value violated - second one always
}
}
/*
* Problem: Leetcode 99 - recover binary search tree
* Reference:
* https://github.com/jianminchen/Leetcode_C-/blob/master/99RecoverBinarySearchTree.cs
*
* julia's comment:
* 1. Extract two functions:
* findTheInorderPredecessorOfCurrent
* violationChecking
*
* 2. Add test cases for those two functions,
* make them memorizable, testable, maintainable
*
* 3. online judge passes
* 1916 / 1916 test cases passed.
Status: Accepted
Runtime: 324 ms
*
* 4. Read the code, and write down the script:
* Actually it is in Morris order traversal, not using stack; use the existing right
* child pointer connect the traversal nodes, later revert the change.
*
* First, use two violation nodes, 3 nodes: current node, previous node, parent node to help
* tracking the inorder traversal process.
*
* base case discussion: root node is null, return
* start from root node, get in a loop,
*
* if node in the loop (ith)'s left child is null, then,
* do a violation checking function call using parent node (pa), ith node input arguments,
* after the call, recover phase: ith node is set as pa node, ith.right is ith node (go to its right child).
* using example to explain:
* 1
* \
* 3
* / \
* 2 4
* starting from root node (1), (1)'s left child is empty, and then, before moving to next node:
* (1)'s right child (3), do violation check, and then, set ith's node to (3), and parent node as ith's node (1).
*
* else if ith's left child is not null, then,
* find predecessor node of ith's node, denoted as previous node (pr),
* if pr's right child is null, then, threaded link is not set up,
* so, set up the link before moving to ith's node's next one - its left child;
* else if pr's right child is not null, then,
* break the threaded link;
* do violation check, two node, pa, ith;
* recover phase, set parent node pa = ith, and then, move to ith's right node.
*
* using example to explain the work here:
* 4
* /
* 2
* / \
* 1 3
* starting from root node (4), (4)'s left child is not null, and then, find its inorder
* predecessor node (3),
* case A: node (3)'s right child is not set up to node (4), then,
* set up node (3)'s right = node (4), move ith's node's left node, node (2).
*
* case B: node (3)'s right child is already set up to node (4), then
* revert the change, (3).right = null
* do violation check, parent node pa, ith node,
* recover phase: set parent node pa as ith node, and then, move to ith's right node.
*
* What we miss here, Morris order second visit of node 4. how to do traversal?
* visit (4), then, set up (3)'s right = (4), so, continue to travel, 4->2.
* output of inorder traversal only happens two cases:
* one is to travel fake link, right child; second one is to travel to its right child.
*
*
*
*/
public static void recoverTree(TreeNode root)
{
TreeNode v1 = null, // two vilation nodes, v1 and v2
v2 = null;
TreeNode ith, // ith - current node, node will go through inorder traversal
pr, // pr - previous node
pa = null; // pa - parent node
if (root == null)
return;
bool found = false;
ith = root; // start from root node r
// pa = null, and pr = null
while (ith != null) // need to get into the inorder traversal without a stack - O(n) space
{
if (ith.left == null)
{
violationChecking(pa, ith, ref v1, ref v2, ref found);
pa = ith; // recover phase, go to next node;
// no left, then, go to the right.
ith = ith.right;
}
else
{
/* Find the inorder predecessor of current */
pr = findTheInorderPredecessorOfCurrent(ith);
/* Make current as right child of its inorder predecessor */
if (pr.right == null)
{
pr.right = ith;
ith = ith.left; // go to next iteration, left child.
}
/* Revert the changes made in if part to restore the original
tree i.e., fix the right child of predecssor */
else
{
pr.right = null; // revert the change. Why? Remember?
violationChecking(pa, ith, ref v1, ref v2, ref found);
pa = ith;
ith = ith.right; // go to next iteration, no left child, so right child.
} /* End of if condition pre->right == NULL */
} /* End of if condition current->left == NULL*/
} /* End of while */
if (v1 != null && v2 != null) // swap v1 and v2
{
int tmp = v1.val;
v1.val = v2.val;
v2.val = tmp;
}
}