Segment_Tree_RMQ.java

class SegmentTreeRMQ
{
    int st[]; //array to store segment tree

    // A utility function to get minimum of two numbers
    int minVal(int x, int y) {
        return (x < y) ? x : y;
    }

    // A utility function to get the middle index from corner
    // indexes.
    int getMid(int s, int e) {
        return s + (e - s) / 2;
    }

    /*  A recursive function to get the minimum 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 */

    int getSumUtil(int ss, int se, int qs, int qe, int si)
    {
        // If segment of this node is a part of given range, then return
        // the sum of the segment
        if (qs <= ss && qe >= se)
            return st[si];

        // If segment of this node is outside the given range
        if (se < qs || ss > qe)
            return 0;

        // If a part of this segment overlaps with the given range
        int mid = getMid(ss, se);
        return getSumUtil(ss, mid, qs, qe, 2 * si + 1) +
                getSumUtil(mid + 1, se, qs, qe, 2 * si + 2);
    }

    /* A recursive function to update the nodes which have the given
       index in their range. The following are parameters
        st, si, ss and se are same as getSumUtil()
        i    --> index of the element to be updated. This index is in
                 input array.
       diff --> Value to be added to all nodes which have i in range */
    void updateValueUtil(int ss, int se, int i, int diff, int si)
    {
        // Base Case: If the input index lies outside the range of
        // this segment
        if (i < ss || i > se)
            return;

        // If the input index is in range of this node, then update the
        // value of the node and its children
        st[si] = st[si] + diff;
        if (se != ss) {
            int mid = getMid(ss, se);
            updateValueUtil(ss, mid, i, diff, 2 * si + 1);
            updateValueUtil(mid + 1, se, i, diff, 2 * si + 2);
        }
    }

    // The function to update a value in input array and segment tree.
   // It uses updateValueUtil() to update the value in segment tree
    void updateValue(int arr[], int n, int i, int new_val)
    {
        // Check for erroneous input index
        if (i < 0 || i > n - 1) {
            System.out.println("Invalid Input");
            return;
        }

        // Get the difference between new value and old value
        int diff = new_val - arr[i];

        // Update the value in array
        arr[i] = new_val;

        // Update the values of nodes in segment tree
        updateValueUtil(0, n - 1, i, diff, 0);
    }

    // Return sum of elements in range from index qs (quey start) to
   // qe (query end).  It mainly uses getSumUtil()
    int getSum(int n, int qs, int qe)
    {
        // Check for erroneous input values
        if (qs < 0 || qe > n - 1 || qs > qe) {
            System.out.println("Invalid Input");
            return -1;
        }
        return getSumUtil(0, n - 1, qs, qe, 0);
    }


    int RMQUtil(int ss, int se, int qs, int qe, int index)
    {
        // If segment of this node is a part of given range, then
        // return the min of the segment
        if (qs <= ss && qe >= se)
            return st[index];

        // If segment of this node is outside the given range
        if (se < qs || ss > qe)
            return Integer.MAX_VALUE;

        // If a part of this segment overlaps with the given range
        int mid = getMid(ss, se);
        return minVal(RMQUtil(ss, mid, qs, qe, 2 * index + 1),
                RMQUtil(mid + 1, se, qs, qe, 2 * index + 2));
    }

    // Return minimum of elements in range from index qs (quey
    // start) to qe (query end).  It mainly uses RMQUtil()
    int RMQ(int n, int qs, int qe)
    {
        // Check for erroneous input values
        if (qs < 0 || qe > n - 1 || qs > qe) {
            System.out.println("Invalid Input");
            return -1;
        }

        return RMQUtil(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
    int constructSTUtil(int arr[], int ss, int se, int si)
    {
        // If there is one element in array, store it in current
        //  node of segment tree and return
        if (ss == se) {
            st[si] = arr[ss];
            return arr[ss];
        }

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

    /* Function to construct segment tree from given array. This function
       allocates memory for segment tree and calls constructSTUtil() to
       fill the allocated memory */
    void 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;
        st = new int[max_size]; // allocate memory

        // Fill the allocated memory st
        constructSTUtil(arr, 0, n - 1, 0);
    }

    // Driver program to test above functions
    public static void main(String args[])
    {
        int arr[] = {1, 3, 2, 7, 9, 11};
        int n = arr.length;
        SegmentTreeRMQ tree = new SegmentTreeRMQ();

        // Build segment tree from given array
        tree.constructST(arr, n);

        int qs = 1;  // Starting index of query range
        int qe = 5;  // Ending index of query range

        // Print minimum value in arr[qs..qe]
        System.out.println("Minimum of values in range [" + qs + ", "
                           + qe + "] is = " + tree.RMQ(n, qs, qe));
    }
}


/* OUTPUT
Minimum of values in range [1, 5] is = 2
*/