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| − | Assuming our binary search tree keeps track of its size we can write a recursive function which checks whether the index is in the left tree, the right, or is this value. There are 3 cases (I am assuming the index is 0-based):
| + | Eat bulaga! |
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| − | # index is equal to the left tree's size => This value is the ith node in sorted order
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| − | # index is less than the left tree's size => The ith node is in the left tree
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| − | # index is greater than the left tree's size + 1 => The ith node is in the right tree
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| − | The implementation below only defines the methods required to answer this question, but clearly a full implementation of a binary search tree would need to have more.
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| − | <source lang="java">
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| − | import java.util.Optional;
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| − | public class BinarySearchTree {
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| − | private Optional<BinarySearchTree> left;
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| − | private Optional<BinarySearchTree> right;
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| − | private int value;
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| − | private int size;
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| − | public BinarySearchTree(final int value, final Optional<BinarySearchTree> left, final Optional<BinarySearchTree> right) {
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| − | this.value = value;
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| − | this.left = left;
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| − | this.right = right;
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| − | this.size = getLeftSize() + getRightSize() + 1;
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| − | }
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| − | private Integer getRightSize() {
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| − | return this.right.map(r -> r.size).orElse(0);
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| − | }
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| − | private Integer getLeftSize() {
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| − | return this.left.map(l -> l.size).orElse(0);
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| − | }
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| − | public int findIthNodeInSortedOrder(final int index) {
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| − | if (index < 0) {
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| − | throw new ArrayIndexOutOfBoundsException("Index cannot be less than 0");
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| − | }
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| − | if (index >= size) {
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| − | throw new ArrayIndexOutOfBoundsException("Index cannot be greater than or equal to size");
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| − | }
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| − | if (index == getLeftSize()) {
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| − | return value;
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| − | } else if (index < getLeftSize()) {
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| − | return left.get().findIthNodeInSortedOrder(index);
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| − | } else {
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| − | return right.get().findIthNodeInSortedOrder(index - (getLeftSize() + 1));
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| − | }
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| − | }
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| − | }
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| − | </source>
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