Min-Max Range Queries in Array

// Java program to find minimum and maximum using segment
// tree
import java.util.*;

public class GFG {
    public static class Node {
        int minimum;
        int maximum;
        Node(int minimum, int maximum)
        {
            this.minimum = minimum;
            this.maximum = maximum;
        }
    }
    // Driver Code
    public static void main(String[] args)
    {
        int[] arr = { 1, 8, 5, 9, 6, 14, 2, 4, 3, 7 };
        int n = arr.length;
        Node[] st = constructST(arr, n);
        int qs = 0; // Starting index of query range
        int qe = 8; // Ending index of query range
        Node result = MaxMin(st, n, qs, qe);

        System.out.println("Minimum = " + result.minimum
                           + " and Maximum = "
                           + result.maximum);
    }
    // A utility function to get the middle index from
    // corner
    // indexes.
    public static int getMid(int s, int e)
    {
        return s + (e - s) / 2;
    }

    /*  A recursive function to get the minimum and maximum
     value in a given range of array indexes. The following
     are parameters for this function.

      st    --> Pointer to segment tree
      index --> Index of current node in the segment tree.
     Initially 0 is passed as root is always at index 0 ss &
     se  --> Starting and ending indexes of the segment
                    represented  by current node, i.e.,
     st[index] qs & qe  --> Starting and ending indexes of
     query range */
    public static Node MaxMinUntill(Node[] st, int ss,
                                    int se, int qs, int qe,
                                    int index)
    {
        // If segment of this node is a part of given range,
        // then return
        //  the minimum and maximum node of the segment
        Node tmp;
        Node left;
        Node right;
        if (qs <= ss && qe >= se)
            return st[index];
        // If segment of this node is outside the given
        // range
        if (se < qs || ss > qe) {
            tmp = new Node(Integer.MAX_VALUE,
                           Integer.MIN_VALUE);
            return tmp;
        }
        // If a part of this segment overlaps with the given
        // range
        int mid = getMid(ss, se);
        left = MaxMinUntill(st, ss, mid, qs, qe,
                            2 * index + 1);
        right = MaxMinUntill(st, mid + 1, se, qs, qe,
                             2 * index + 2);
        tmp = new Node(
            Math.min(left.minimum, right.minimum),
            Math.max(left.maximum, right.maximum));
        return tmp;
    }

    // Return minimum and maximum of elements in range from
    // index qs (query start) to qe (query end).  It mainly
    // uses MaxMinUtill()
    public static Node MaxMin(Node[] st, int n, int qs,
                              int qe)
    {
        Node tmp;
        // Check for erroneous input values
        if (qs < 0 || qe > n - 1 || qs > qe) {
            System.out.println("Invalid Input");
            tmp = new Node(Integer.MAX_VALUE,
                           Integer.MIN_VALUE);
            return tmp;
        }
        return MaxMinUntill(st, 0, n - 1, qs, qe, 0);
    }

    // A recursive function that constructs Segment Tree for
    // array[ss..se]. si is index of current node in segment
    // tree st
    public static void constructSTUtil(int[] arr, int ss,
                                       int se, Node[] st,
                                       int si)
    {
        // If there is one element in array, store it in
        // current
        // node of segment tree and return
        if (ss == se) {
            st[si] = new Node(arr[ss], arr[ss]);
            return;
        }

        // If there are more than one elements, then recur
        // for left and right subtrees and store the minimum
        // and maximum of two values in this node
        int mid = getMid(ss, se);
        constructSTUtil(arr, ss, mid, st, si * 2 + 1);
        constructSTUtil(arr, mid + 1, se, st, si * 2 + 2);
        int min = Math.min(st[si * 2 + 1].minimum,
                           st[si * 2 + 2].minimum);
        int max = Math.max(st[si * 2 + 1].maximum,
                           st[si * 2 + 2].maximum);
        st[si] = new Node(min, max);
    }

    /* Function to construct segment tree from given array.
     This function allocates memory for segment tree and
     calls constructSTUtil() to fill the allocated memory */
    public static Node[] constructST(int[] arr, int n)
    {
        // Allocate memory for segment tree
        // Height of segment tree
        int x = (int)(Math.ceil(Math.log(n) / Math.log(2)));
        // Maximum size of segment tree
        int max_size = 2 * (int)(Math.pow(2, x)) - 1;
        Node[] st = new Node[max_size];
        // Fill the allocated memory st
        constructSTUtil(arr, 0, n - 1, st, 0);
        return st;
    }
}