Segment Tree / Binary Indexed Tree

The structure of Segment Tree is a binary tree which each node has two attributesstartandenddenote 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 buildmethod.

• 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.

Implement a buildmethod with a given array, so that we can create a corresponding segment tree with every node value represent the corresponding interval max value in the array, return the root of this segment tree.

Build:

/**
 * 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) {
        // write your code here
        return buildHelper(0, A.length -1, A);
    }

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

        SegmentTreeNode left = buildHelper(start, (start + end) / 2, A);
        SegmentTreeNode right = buildHelper((start + end) / 2 + 1, end, A);

        SegmentTreeNode ret = new SegmentTreeNode(start, end, Math.max(left.max, right.max));
        ret.left = left;
        ret.right = right;
        return ret;

    }
}

Query:

/**
 * 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: The root of segment tree.
     * @param start: start value.
     * @param end: end value.
     * @return: The maximum number in the interval [start, end]
     */
    public int query(SegmentTreeNode root, int start, int end) {
        // write your code here
        if (start <= root.start && root.end <= end ) {
            return root.max;
        }

        int mid = (root.start  + root.end) /2;
        int ans = Integer.MIN_VALUE;
        if (mid >= start){
            ans = Math.max(ans, query(root.left, start, end));
        }
        if (mid + 1 <= end){
            ans = Math.max(ans, query(root.right, start, end));
        }

        return ans;
    }
}

Modify:

/**
 * 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: The root of segment tree.
     * @param index: index.
     * @param value: value
     * @return: nothing
     */
    public void modify(SegmentTreeNode root, int index, int value) {
        // write your code here
        if(root.start == root.end && root.end == index){
            root.max = value;
            return;
        }  // can getting rid of the last one? unless the input is within the segment tree range
        int mid = (root.start + root.end) / 2; 
        if (index <= mid){
            modify(root.left, index, value);
            root.max = Math.max(root.left.max, root.right.max);
        }
        else {
            modify(root.right, index, value);
            root.max = Math.max(root.left.max, root.right.max);
        }

        return; 
    }
}