Here is my attempt to check whether a tree is a BST or not:
public boolean isBST() {
return isBSTRecursively(this.root, new Max());
}
class Max {
int value;
}
private boolean isBSTRecursively(Node node, Max max) {
if (node == null) return true; // to handle null root
// to handle scenario when both child nodes are absent
if(node.getLeft() == null && node.getRight() == null) {
max.value = node.getValue();
return true;
}
// if left child is absent, we only investigate right subtree
if(node.getLeft() == null) {
Max rightMax = new Max();
boolean isRightBST = isBSTRecursively(node.getRight(), rightMax);
max.value = Math.max(node.getValue(), rightMax.value);
if(isRightBST && node.getValue() < rightMax.value) {
return true;
} else {
return false;
}
} else {
Max leftMax = new Max();
boolean isLeftBST = isBSTRecursively(node.getLeft(), leftMax);
// if right child is absent, we only investigate left subtree
if(node.getRight() == null) {
max.value = Math.max(node.getValue(), leftMax.value);
if(isLeftBST && node.getValue() > leftMax.value) {
return true;
} else {
return false;
}
} else {
// we investigate both left and right subtrees
Max rightMax = new Max();
boolean isRightBST = isBSTRecursively(node.getRight(), rightMax);
max.value = Math.max(Math.max(leftMax.value, node.getValue()), rightMax.value);
if(isLeftBST && isRightBST && leftMax.value < node.getValue() && node.getValue() < rightMax.value) {
return true;
} else {
return false;
}
}
}
Code works fine as tested with multiple test cases.
But I am not sure if this is a good, clean approach.
Recursive method is big it seems. I am dealing with scenarios like null left node, null right node, node itself null, both child nodes null etc. separately. I guess they all can be handled in a much smaller, and cleaner way.
Moreover, I am always more inclined towards iterative approach(I generally find it better to visualize). Would that be better here (given it can be done iteratively)?
Any suggestions?
CodePudding user response:
A cleaner recursive approach
You could use a bounded approach, i.e. have two variables for every recursion: min
and max
.
Initially
min = INT_MIN
andmax = INT_MAX
if
node = NULL
then return True because an empty BST is a BSTelse check if
node.val < min or node.val > max
if this condition isTrue
then tree is not a BST,return False
Notice : the strict inequality>
and<
are used as BST doesn't allow duplicate elements.recurse for left :
recur(node.left)
withmin
remaining the same andmax = node.val - 1
because the left subtrees should have values not greater thannode.val - 1
.The
max
cannot benode.val
because BST cannot have duplicate elements. Store the boolean return value in sayleft
recurse for right :
recur(node.right)
withmin = node.val 1
andmax
remaining the same.The right subtrees should have values not less than
node.val 1
. Store the boolean return value in sayright
return
left && right
CodePudding user response:
@Aditya gave the ingredients of the more elegant solution.
It is generally not forbidden for a binary search tree to have duplicate values, so there should no be reduction of the "window" with 1.
Here is suggested code:
public boolean isBST() {
return isBSTRecursively(this.root, Integer.MIN_VALUE, Integer.MAX_VALUE);
}
private boolean isBSTRecursively(Node node, int min, int max) {
return node == null
|| node.getValue() >= min && node.getValue() <= max
&& isBSTRecursively(node.getLeft(), min, node.getValue())
&& isBSTRecursively(node.getRight(), node.getValue(), max);
}