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C++ Program for Range Minimum Query using Segment Tree

C++ Program for Range Minimum Query using Segment Tree

A segment tree is a heap-like data structure that can be used for solving Range Minimum/Maximum Query Problems.

#include <stdio.h>
#include <math.h>
#include <limits.h>

// 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 RMQUtil(int *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 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 INT_MAX;

// If a part of this segment overlaps with the given range
 int mid = getMid(ss, se);
 return minVal(RMQUtil(st, ss, mid, qs, qe, 2*index+1),
 RMQUtil(st, 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 *st, int n, int qs, int qe)
 // Check for erroneous input values
 if (qs < 0 || qe > n-1 || qs > qe)
 printf("Invalid Input");
 return -1;

return RMQUtil(st, 0, n-1, qs, qe, 0);

// A recursive function that constructs Segment Tree for array[].
// si is index of current node in segment tree st
int constructSTUtil(int arr[], int ss, int se, int *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] = 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, st, si*2+1),
 constructSTUtil(arr, mid+1, se, st, 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 */
int *constructST(int arr[], int n)
 // Allocate memory for segment tree

//Height of segment tree
 int x = (int)(ceil(log2(n)));

// Maximum size of segment tree
 int max_size = 2*(int)pow(2, x) - 1;

int *st = new int[max_size];

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

// Return the constructed segment tree
 return st;

// Driver program to test above functions
int main()
 int arr[] = {1, 3, 2, 7, 9, 11};
 int n = sizeof(arr)/sizeof(arr[0]);

// Build segment tree from given array
 int *st = 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]
 printf("Minimum of values in range [%d, %d] is = %d\n",
 qs, qe, RMQ(st, n, qs, qe));

return 0;