Largest interval in an Array that contains the given element X for Q queries

Given an array arr[] of N elements and Q queries of the form [X]. For each query, the task is to find the largest interval [L, R] of the array such that the greatest element in the interval is arr[X], such that 1 ≤ L ≤ X ≤ R.
Note: The array has 1-based indexing.

Examples:

Input: N = 5, arr[] = {2, 1, 2, 3, 2}, Q = 3, query[] = {1, 2, 4}
Output:
[1, 3]
[2, 2]
[1, 5]
Explanation :
In 1st query, x = 1, so arr[x] = 2 and answer is L = 1 and R = 3. here, we can see that max(arr[1], arr[2], arr[3]) = arr[x], which is the maximum intervals.
In 2nd query, x = 2, so arr[x] = 1 and since it is the smallest element of the array, so the interval contains only one element, thus the range is [2, 2].
In 3rd query, x = 4, so arr[x] = 4, which is maximum element of the arr[], so the answer is whole array, L = 1 and R = N.

Input: N = 4, arr[] = { 1, 2, 2, 4}, Q = 2, query[] = {1, 2}
Output:
[1, 1]
[1, 3]
Explanation:
In 1st query, x = 1, so arr[x] = 1 and since it is the smallest element of the array, so the interval contains only one element, thus the range is [1, 1].
In 2nd query, x = 2, so arr[x] = 2 and answer is L = 1 and R = 3. here, we can see that max(arr[1], arr[2], arr[3]) = arr[x] = arr[2] = 2, which is the maximum intervals.

Approach: The idea is to precompute the largest interval for every value K in arr[] from 1 to N. Below are the steps:



  1. For each element K in arr[], fix the index of the element K, then find how much we can extend the interval to it’s left and right.
  2. Decrement left iterator till arr[left] ≤ K and similarly increment right iterator till arr[right] ≤ K.
  3. The final value of left and right represents the starting and the ending index of the interval, which is stored in arrL[] and arrR[] respectively.
  4. After we have precomputed interval range for each value. Then, for each query, we need to print the interval range for arr[x] i.e., arrL[arr[x]] and arrR[arr[x]].

Below is the implementation of the above approach:

C++

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// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;
  
// Function to precompute the interval
// for each query
void utilLargestInterval(int arr[],
                         int arrL[],
                         int arrR[],
                         int N)
{
  
    // For every values [1, N] find
    // the longest intervals
    for (int maxValue = 1;
         maxValue <= N; maxValue++) {
  
        int lastIndex = 0;
  
        // Iterate the array arr[]
        for (int i = 1; i <= N; i++) {
  
            if (lastIndex >= i
                || arr[i] != maxValue)
                continue;
            int left = i, right = i;
  
            // Shift the left pointers
            while (left > 0
                   && arr[left] <= maxValue)
                left--;
  
            // Shift the right pointers
            while (right <= N
                   && arr[right] <= maxValue)
                right++;
  
            left++, right--;
            lastIndex = right;
  
            // Store the range of interval
            // in arrL[] and arrR[].
            for (int j = left; j <= right; j++) {
  
                if (arr[j] == maxValue) {
                    arrL[j] = left;
                    arrR[j] = right;
                }
            }
        }
    }
}
  
// Function to find the largest interval
// for each query in Q[]
void largestInterval(
    int arr[], int query[], int N, int Q)
{
  
    // To store the L and R of X
    int arrL[N + 1], arrR[N + 1];
  
    // Function Call
    utilLargestInterval(arr, arrL,
                        arrR, N);
  
    // Iterate to find ranges for each query
    for (int i = 0; i < Q; i++) {
  
        cout << "[" << arrL[query[i]]
             << ", " << arrR[query[i]]
             << "]\n";
    }
}
  
// Driver Code
int main()
{
    int N = 5, Q = 3;
  
    // Given array arr[]
    int arr[N + 1] = { 0, 2, 1, 2, 3, 2 };
  
    // Given Queries
    int query[Q] = { 1, 2, 4 };
  
    // Function Call
    largestInterval(arr, query, N, Q);
    return 0;
}

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Java

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// Java program for the above approach
class GFG{
  
// Function to precompute the interval
// for each query
static void utilLargestInterval(int arr[],
                                int arrL[],
                                int arrR[],
                                int N)
{
  
    // For every values [1, N] find
    // the longest intervals
    for(int maxValue = 1;
            maxValue <= N; maxValue++)
    {
       int lastIndex = 0;
         
       // Iterate the array arr[]
       for(int i = 1; i <= N; i++) 
       {
          if (lastIndex >= i || 
                 arr[i] != maxValue)
              continue;
          int left = i, right = i;
            
          // Shift the left pointers
          while (left > 0 && 
                 arr[left] <= maxValue)
              left--;
            
          // Shift the right pointers
          while (right <= N && 
                 arr[right] <= maxValue)
              right++;
            
          left++; 
          right--;
          lastIndex = right;
            
          // Store the range of interval
          // in arrL[] and arrR[].
          for(int j = left; j <= right; j++)
          {
             if (arr[j] == maxValue)
             {
                 arrL[j] = left;
                 arrR[j] = right;
             }
          }
       }
    }
}
  
// Function to find the largest interval
// for each query in Q[]
static void largestInterval(int arr[],
                            int query[], 
                            int N, int Q)
{
      
    // To store the L and R of X
    int []arrL = new int[N + 1];
    int []arrR = new int[N + 1];
  
    // Function Call
    utilLargestInterval(arr, arrL,
                        arrR, N);
  
    // Iterate to find ranges for 
    // each query
    for(int i = 0; i < Q; i++) 
    {
       System.out.print("[" + arrL[query[i]] + 
                       ", " + arrR[query[i]] + "]\n");
    }
}
  
// Driver Code
public static void main(String[] args)
{
    int N = 5, Q = 3;
  
    // Given array arr[]
    int arr[] = { 0, 2, 1, 2, 3, 2 };
  
    // Given queries
    int query[] = { 1, 2, 4 };
  
    // Function call
    largestInterval(arr, query, N, Q);
}
}
  
// This code is contributed by Amit Katiyar

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C#

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// C# program for the above approach
using System;
  
class GFG{
  
// Function to precompute the interval
// for each query
static void utilLargestInterval(int []arr,
                                int []arrL,
                                int []arrR,
                                int N)
{
  
    // For every values [1, N] find
    // the longest intervals
    for(int maxValue = 1;
            maxValue <= N; maxValue++)
    {
       int lastIndex = 0;
         
       // Iterate the array []arr
       for(int i = 1; i <= N; i++)
       {
          if (lastIndex >= i || 
                 arr[i] != maxValue)
              continue;
                
          int left = i, right = i;
            
          // Shift the left pointers
          while (left > 0 && 
                 arr[left] <= maxValue)
              left--;
                
          // Shift the right pointers
          while (right <= N && 
                 arr[right] <= maxValue)
              right++;
            
          left++; 
          right--;
          lastIndex = right;
            
          // Store the range of interval
          // in arrL[] and arrR[].
          for(int j = left; j <= right; j++)
          {
             if (arr[j] == maxValue)
             {
                 arrL[j] = left;
                 arrR[j] = right;
             }
          }
       }
    }
}
  
// Function to find the largest interval
// for each query in Q[]
static void largestInterval(int []arr,
                            int []query, 
                            int N, int Q)
{
      
    // To store the L and R of X
    int []arrL = new int[N + 1];
    int []arrR = new int[N + 1];
  
    // Function Call
    utilLargestInterval(arr, arrL,
                        arrR, N);
  
    // Iterate to find ranges for 
    // each query
    for(int i = 0; i < Q; i++) 
    {
       Console.Write("[" + arrL[query[i]] + 
                    ", " + arrR[query[i]] + "]\n");
    }
}
  
// Driver Code
public static void Main(String[] args)
{
    int N = 5, Q = 3;
  
    // Given array []arr
    int []arr = { 0, 2, 1, 2, 3, 2 };
  
    // Given queries
    int []query = { 1, 2, 4 };
  
    // Function call
    largestInterval(arr, query, N, Q);
}
}
  
// This code is contributed by Princi Singh

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Output:

[1, 3]
[2, 2]
[1, 5]

Time Complexity: O(Q + N2)
Auxillary Space: O(N)

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