# Segment Tree

Applications:

http://poj.org/summerschool/gw_interval_tree.pdf

1. find range minimum/maximum

The structure of Segment Tree is a binary tree which each node has two attributes start and end denote an segment / interval.

start and end are both integers, they should be assigned in following rules:

• The root's start and end is given by build method.
• The left child of node A has start=A.left, end=(A.left + A.right) / 2.
• The right child of node A has start=(A.left + A.right) / 2 + 1, end=A.right.
• if start equals to end, there will be no children for this node.

Segment Tree (a.k.a Interval Tree) is an advanced data structure which can support queries like:

• which of these intervals contain a given point
• which of these points are in a given interval

1. Build segment tree

``````/**
* Definition of SegmentTreeNode:
* public class SegmentTreeNode {
*     public int start, end;
*     public SegmentTreeNode left, right;
*     public SegmentTreeNode(int start, int end) {
*         this.start = start, this.end = end;
*         this.left = this.right = null;
*     }
* }
*/

public class Solution {
/**
*@param start, end: Denote an segment / interval
*@return: The root of Segment Tree
*/
public SegmentTreeNode build(int start, int end) {
if (start > end) {
return null;
}
if (start == end) {
return new SegmentTreeNode(start, end);
}

int mid = start + (end-start)/2;
SegmentTreeNode root = new SegmentTreeNode(start, end);
root.left = build(start, mid);
root.right = build(mid+1, end);

return root;
}
}
``````

2. Build segment tree with max value of the interval

``````/**
* Definition of SegmentTreeNode:
* public class SegmentTreeNode {
*     public int start, end, max;
*     public SegmentTreeNode left, right;
*     public SegmentTreeNode(int start, int end, int max) {
*         this.start = start;
*         this.end = end;
*         this.max = max
*         this.left = this.right = null;
*     }
* }
*/
public class Solution {
/**
*@param A: a list of integer
*@return: The root of Segment Tree
*/
public SegmentTreeNode build(int[] A) {
if (A == null || A.length == 0) {
return null;
}
return build(A, 0, A.length-1);
}

public SegmentTreeNode build(int[]A, int start, int end) {
if (start > end) {
return null;
}
if (start == end) {
return new SegmentTreeNode(start, end, A[start]);
}

int mid = start + (end-start)/2;
SegmentTreeNode root = new SegmentTreeNode(start, end, 0);
root.left = build(A, start, mid);
root.right = build(A, mid+1, end);
root.max = Math.max(root.left.max, root.right.max);
return root;
}
}
``````

3. Query the max value in a given interval

``````Runtime 10s

/**
* Definition of SegmentTreeNode:
* public class SegmentTreeNode {
*     public int start, end, max;
*     public SegmentTreeNode left, right;
*     public SegmentTreeNode(int start, int end, int max) {
*         this.start = start;
*         this.end = end;
*         this.max = max
*         this.left = this.right = null;
*     }
* }
*/
public class Solution {
/**
*@param root, start, end: The root of segment tree and
*                         an segment / interval
*@return: The maximum number in the interval [start, end]
*/
public int query(SegmentTreeNode root, int start, int end) {
if (root == null || start > root.end || end < root.start) {
return 0;
}
if (root.start == root.end) {
return root.max;
}
int mid = ((root.start + root.end) / 2);
return Math.max(query(root.left, start, end), query(root.right, start, end));
}
}

Runtime 5s

public class Solution {
/**
*@param root, start, end: The root of segment tree and
*                         an segment / interval
*@return: The maximum number in the interval [start, end]
*/
public int query(SegmentTreeNode root, int start, int end) {
if (root == null || start > root.end || end < root.start) {
return 0;
}
if (root.start >= start && root.end <= end) {
return root.max;
}
int mid = ((root.start + root.end) / 2);
return Math.max(query(root.left, start, Math.min(mid, end)), query(root.right, Math.max(mid, start), end));
}
}
``````

4. Query the count of numbers in a given interval

``````/**
* Definition of SegmentTreeNode:
* public class SegmentTreeNode {
*     public int start, end, count;
*     public SegmentTreeNode left, right;
*     public SegmentTreeNode(int start, int end, int count) {
*         this.start = start;
*         this.end = end;
*         this.count = count;
*         this.left = this.right = null;
*     }
* }
*/
public class Solution {
/**
*@param root, start, end: The root of segment tree and
*                         an segment / interval
*@return: The count number in the interval [start, end]
*/
public int query(SegmentTreeNode root, int start, int end) {