# Queries to check whether a given digit is present in the given Range

Pre-requisites: Segment Tree

Given an array of digits arr[]. Given a number of range [L, R] and a digit X with each range. The task is to check for each given range [L, R] whether the digit X is present within that range in the array arr[].

Examples:

```Input : arr = [1, 3, 3, 9, 8, 7]
l1=0, r1=3, x=2   // Range 1
l1=2, r1=5, x=3   // Range 2
Output : NO
YES
For Range 1: The digit 2 is not present within
range [0, 3] in the array.
For Range 2: The digit 3 is present within the range
[2, 5] at index 2 in the given array.
```

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

Naive Approach: A naive approach is to traverse through each of the given range of the digits in the array and check whether the digit is present or not.

Time Complexity: O(N) for each query.

Better Approach: A better approach is to use Segment Tree. Since there are only 10 digits possible from (0-9), so each node of the segment tree will contain all the digits within the range of that node. We will use Set Data Structure at every node to store the digits. Set is a special data structure which removes redundant elements and store them in ascending order. We have used set data structure since it will be easier to merge 2 child nodes to get the parent node in the segment tree. We will insert all the digits present in the children nodes in the parent set and it will automatically remove the redundant digits. Hence at every set(node) there will be at max 10 elements (0-9 all the digits).

Also there are inbuilt count function which returns the count of the element present in the set which will be helpful in the query function to check whether a digit is present at the node or not. If the count will be greater than 0 that means the element is present in the set we will return true else return false.

Below is the implementation of the above approach:

 `// CPP program to answer Queries to check whether ` `// a given digit is present in the given range ` ` `  `#include ` `#include ` `using` `namespace` `std; ` ` `  `#define N 6 ` ` `  `// Segment Tree with set at each node ` `set<``int``> Tree[6 * N]; ` ` `  `// Funtiom to build the segment tree ` `void` `buildTree(``int``* arr, ``int` `idx, ``int` `s, ``int` `e) ` `{ ` `    ``if` `(s == e) { ` `        ``Tree[idx].insert(arr[s]); ` `        ``return``; ` `    ``} ` ` `  `    ``int` `mid = (s + e) >> 1; ` ` `  `    ``// Left child node ` `    ``buildTree(arr, 2 * idx, s, mid); ` ` `  `    ``// Right child node ` `    ``buildTree(arr, 2 * idx + 1, mid + 1, e); ` ` `  `    ``// Merging child nodes to get parent node. ` `    ``// Since set is used, it will remove ` `    ``// redundant digits. ` `    ``for` `(``auto` `it : Tree[2 * idx]) { ` `        ``Tree[idx].insert(it); ` `    ``} ` `    ``for` `(``auto` `it : Tree[2 * idx + 1]) { ` `        ``Tree[idx].insert(it); ` `    ``} ` `} ` ` `  `// Function to query a range ` `bool` `query(``int` `idx, ``int` `s, ``int` `e, ``int` `qs, ``int` `qe, ``int` `x) ` `{ ` `    ``// Complete Overlapp condition ` `    ``// return true if digit is present. ` `    ``// else false. ` `    ``if` `(qs <= s && e <= qe) { ` `        ``if` `(Tree[idx].count(x) != 0) { ` `            ``return` `true``; ` `        ``} ` `        ``else` `            ``return` `false``; ` `    ``} ` ` `  `    ``// No Overlapp condition ` `    ``// Return false ` `    ``if` `(qe < s || e < qs) { ` `        ``return` `false``; ` `    ``} ` ` `  `    ``int` `mid = (s + e) >> 1; ` ` `  `    ``// If digit is found in any child ` `    ``// return true, else False ` `    ``bool` `LeftAns = query(2 * idx, s, mid, qs, qe, x); ` `    ``bool` `RightAns = query(2 * idx + 1, mid + 1, e, qs, qe, x); ` ` `  `    ``return` `LeftAns or RightAns; ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` `    ``int` `arr[] = { 1, 3, 3, 9, 8, 7 }; ` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]); ` ` `  `    ``// Build the tree ` `    ``buildTree(arr, 1, 0, n - 1); ` ` `  `    ``int` `l, r, x; ` ` `  `    ``// Query 1 ` `    ``l = 0, r = 3, x = 2; ` `    ``if` `(query(1, 0, n - 1, l, r, x)) ` `        ``cout << ``"YES"` `<< ``'\n'``; ` `    ``else` `        ``cout << ``"NO"` `<< ``'\n'``; ` ` `  `    ``// Query 2 ` `    ``l = 2, r = 5, x = 3; ` `    ``if` `(query(1, 0, n - 1, l, r, x)) ` `        ``cout << ``"YES"` `<< ``'\n'``; ` `    ``else` `        ``cout << ``"NO"` `<< ``'\n'``; ` ` `  `    ``return` `0; ` `} `

Output:

```NO
YES
```

Time Complexity: O(N) once for building the segment tree, then O(logN) for each query.

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