Longest Increasing subarray with one change allowed

Given an array, find the length of the longest increasing subarray (contiguous elements) such that it is possible to change at most one number (change one number to any integer you want) from the sequence to make the sequence strictly increasing.

Examples:

Input  : 6
         7 2 3 1 5 10 
Output : 5
Explanation : 
Here, we can choose subarray 2, 3, 1, 5, 10 
and by changing its 3rd element (that is 1) 
to 4, it will become increasing sequence.

Input  : 2
         10 10
Output : 2
Explanation : 
Here, we can choose subarray 10, 10 and by
changing its 2nd element (that is 10) to 11,
it will become increasing sequence.



Approach :
Step 1: We first compute longest increasing subarray ending at an index for every index in given array. We store these values in l[].
Step 2: Then calculate longest increasing subarray starting at an index for every index in given array. We store these values in r[].
Step 3: Update the answer ans = max ( ans, l[i-1] + r[i+1] + 1), when a[i-1] + 1 < a[i+1].

Below is the implementation of the above approach:

C++

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// CPP program to find longest increasing subarray
// with one change allowed.
#include <bits/stdc++.h>
using namespace std;
  
// Function to find length of
// subsequence
int seg(int a[], int n)
{
    int l[n], r[n+1], ans = 0;
      
    // calculating the l array.
    l[0] = 1;
    for (int i = 1; i < n; i++) {
        if (a[i] > a[i - 1]) {
            l[i] = l[i - 1] + 1;
            ans = max(ans, l[i]);
        }
        else
            l[i] = 1;
    }
    if (ans != n)
        ++ans;
  
    // calculating the r array.
    r[n] = 0;
    for (int i = n - 1; i >= 0; i--) {
        if (a[i] < a[i + 1])
            r[i] = r[i + 1] + 1;
        else
            r[i] = 1;
    }
  
    // updating the answer.
    for (int i = n - 1; i > 0; i--) {
        if (a[i + 1] - a[i - 1] > 1)
            ans = max(ans, l[i - 1] + 
                    r[i + 1] + 1);
    }
    
    return max(ans, r[0]);
}
  
// driver function.
int main()
{
    int a[] = { 9, 4, 5, 1, 13 };
    int n = sizeof(a)/sizeof(a[0]);
    cout << seg(a, n);
    return 0;
}

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Java

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// Java program to find longest increasing subarray 
// with one change allowed.
class GFG
{
  
    // Function to find length of
    // subsequence
    static int seg(int[] a, int n)
    {
        int[] l = new int[n];
        int[] r = new int[n + 1];
        int ans = 0;
  
        // calculating the l array.
        l[0] = 1;
        for (int i = 1; i < n; i++)
        {
            if (a[i] > a[i - 1])
            {
                l[i] = l[i - 1] + 1;
                ans = Math.max(ans, l[i]);
            
            else
                l[i] = 1;
        }
        if (ans != n)
            ++ans;
  
        // calculating the r array.
        r[n] = 0;
        for (int i = n - 1; i > 0; i--)
        {
            if (a[i - 1] < a[i])
                r[i] = r[i + 1] + 1;
            else
                r[i] = 1;
        }
  
        // updating the answer.
        for (int i = n - 2; i > 0; i--) 
        {
            if (a[i + 1] - a[i - 1] > 1)
                ans = Math.max(ans, l[i - 1] + 
                                    r[i + 1] + 1);
        }
        return Math.max(ans, r[0]);
    }
  
    // Driver Code
    public static void main(String[] args) 
    {
        int[] a = { 9, 4, 5, 1, 13 };
        int n = a.length;
  
        System.out.println(seg(a, n));
    }
}
  
// This code is contributed by
// sanjeev2552

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Output:

4

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Improved By : sanjeev2552



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