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Queries to check whether a given digit is present in the given Range in C++
In this problem, we have given an array arr[] and some queries each consisting of three values, L and R, and val. Our task is to create a program to solve Queries to check whether a given digit is present in the given Range in C++.
Problem Description−
To solve each query, we need to check if the given element val is present in the given Range between L and R or not.
Let’s take an example to understand the problem,
Input:arr[] = {4, 8, 1, 7, 2, 9, 3, 5, 1}
Q = 3
query = {{1, 4, 3}, {0, 2, 1}, {4, 7, 2 }}
Output: Not Present
Present
Present
Explanation
Query 1: range is [1, 4], subarray = {8, 1, 7, 2}. 3 is not present in this subarray.
Query 2: range is [0, 2], subarray = {4, 8, 1}. 1 is present in this subarray.
Query 1: range is [4, 7], subarray = {2, 9, 3, 5, 1}. 2 is present in this subarray.
Solution Approach
A simple way to solve the problem is by traversing the subarray and checking whether the given element is present in the range.
Example
#include <iostream>
using namespace std;
bool isElementPresent(int arr[], int L, int R, int val){
for(int i = L; i <= R; i++ ){
if(arr[i] == val){
return true;
}
}
return false;
}
int main(){
int arr[] = {4, 8, 1, 7, 2, 9, 3, 5, 1};
int Q = 3;
int query[Q][3] = {{1, 4, 3}, {0, 2, 1}, {4, 7, 2 }};
for(int i = 0; i < Q; i++){
cout<<"For Query "<<(i+1);
if(isElementPresent(arr, query[i][0], query[i][1], query[i][2]))
cout<<": The given digit "<<query[i][2]<<" is present in the given range\n";
else
cout<<": The given digit "<<query[i][2]<<" is not present in the given range\n";
}
return 0;
}Output
For Query 1: The given digit 3 is not present in the given range For Query 2: The given digit 1 is present in the given range For Query 3: The given digit 2 is present in the given range
This is approach uses a loop, hence has a time complexity of the order O(Q * N). Where Q is the number of queries.
A better solution approach could be using a segment Tree to store all possible digits (0 - 9). To avoid duplicate elements in the node we will be using the set data structure (it has a property to eliminate duplicate elements). This will help us reduce the total number of elements in each node to a maximum of 10.
Then, for the query, we will check if the element is present or not in the given range.
Example
#include <bits/stdc++.h>
using namespace std;
set<int> SegTree[36];
void buildSegmentTree(int* arr, int index, int start, int end) {
if (start == end) {
SegTree[index].insert(arr[start]);
return;
}
int middleEle = (start + end) >> 1;
buildSegmentTree(arr, 2 * index, start, middleEle);
buildSegmentTree(arr, 2 * index + 1, middleEle + 1, end);
for (auto it : SegTree[2 * index])
SegTree[index].insert(it);
for (auto it : SegTree[2 * index + 1])
SegTree[index].insert(it);
}
bool isElementPresent(int index, int start, int end, int L, int R, int val){
if (L <= start && end <= R) {
if (SegTree[index].count(val) != 0) {
return true;
}
else
return false;
}
if (R < start || end < L) {
return false;
}
int middleEle = (start + end) >> 1;
bool isPresentInLeftSubArray = isElementPresent((2 * index), start,middleEle, L, R, val);
bool isPresentInRightSubArray = isElementPresent((2 * index + 1),(middleEle + 1), end, L, R, val);
return isPresentInLeftSubArray or isPresentInRightSubArray;
}
int main(){
int arr[] = {4, 8, 1, 7, 2, 9, 3, 5, 1};
int n = sizeof(arr)/sizeof(arr[0]);
int Q = 3;
int query[Q][3] = {{1, 4, 3}, {0, 2, 1}, {4, 7, 2 }};
buildSegmentTree(arr, 1, 0, (n - 1));
for(int i = 0; i < Q; i++){
cout<<"For Query "<<(i+1);
if(isElementPresent(1, 0, (n - 1), query[i][0], query[i][1], query[i][2]))
cout<<": The given digit "<<query[i][2]<<" is present in the given
range\n";
else
cout<<": The given digit "<<query[i][2]<<" is not present in the given range\n";
}
return 0;
}Output
For Query 1: The given digit 3 is not present in the given range For Query 2: The given digit 1 is present in the given range For Query 3: The given digit 2 is present in the given range
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