# Queries for the minimum element in an array excluding the given index range

Given an array arr[] of N integers and Q queries where each query consists of an index range [L, R]. For each query, the task is to find the minimum element in the array excluding the elements from the given index range.

Examples:

Input: arr[] = {3, 2, 1, 4, 5}, Q[][] = {{1, 2}, {2, 3}}
Output:
3
2
Query 1: min(arr, arr[3..4]) = min(3, 4, 5) = 3
Query 2: min(arr[0..1], arr) = min(3, 2, 5) = 2

Input: arr[] = {1, 2, 3, 4, 5}, Q[][] = {{0, 2}}
Output:
4

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: In case of multiple queries a segment tree can be built to find the minimum element in any index range. Now, for every query [L, R] the minimum element excluding this range will be min(min(arr[0…L-1]), min(arr[R+1…N-1]))

Below is the implementation of the above approach:

 `// C++ implementation of the approach ` `#include ` `using` `namespace` `std; ` ` `  `// 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 (query 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) { ` `        ``cout << ``"Invalid Input"``; ` `        ``return` `-1; ` `    ``} ` ` `  `    ``return` `RMQUtil(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 ` `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[] = { 3, 2, 1, 4, 5 }; ` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr); ` ` `  `    ``int` `queries[] = { { 1, 2 }, { 2, 3 } }; ` `    ``int` `q = ``sizeof``(queries) / ``sizeof``(queries); ` ` `  `    ``// Build segment tree from given array ` `    ``int``* st = constructST(arr, n); ` ` `  `    ``// Perform queries ` `    ``for` `(``int` `i = 0; i < q; i++) { ` ` `  `        ``// Current index range to be exluded ` `        ``int` `L = queries[i]; ` `        ``int` `R = queries[i]; ` ` `  `        ``// Minimum in the left part ` `        ``int` `left = ((L - 1) < 0) ` `                       ``? INT_MAX ` `                       ``: RMQ(st, n, 0, L - 1); ` ` `  `        ``// Minimum in the right part ` `        ``int` `right = ((R + 1) >= n) ` `                        ``? INT_MAX ` `                        ``: RMQ(st, n, R + 1, n - 1); ` ` `  `        ``// Minimum in the array excluding the given range ` `        ``int` `minn = min(left, right); ` ` `  `        ``// Complete array has been excluded ` `        ``if` `(minn == INT_MAX) ` `            ``cout << -1 << endl; ` `        ``else` `            ``cout << minn << endl; ` `    ``} ` ` `  `    ``return` `0; ` `} `

Output:

```3
2
```

My Personal Notes arrow_drop_up Second year Department of Information Technology Jadavpur University

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