Longest Increasing subarray with one change allowed

Last Updated : 22 Jul, 2022

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 the longest increasing subarray ending at an index for every index in the given array. We store these values in l[].
Step 2: Then calculate the longest increasing subarray starting at an index for every index in the 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 idea:

C++

// 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 - 2; 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 code.
int main()
{
    int a[] = { 9, 4, 5, 1, 13 };
    int n = sizeof(a) / sizeof(a[0]);
  
    // Function call
    cout << seg(a, n);
    return 0;
}

Java

// 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;

        // Function call
        System.out.println(seg(a, n));
    }
}

// This code is contributed by
// sanjeev2552

Python3

# Python3 program to find 
# longest increasing subarray
# with one change allowed.

# Function to find length of
# subsequence
def seg(a, n):

    l = [0] * n
    r = [0] * (n + 1)
    ans = 0

    # calculating the l array.
    l[0] = 1
    for i in range(1, n):
        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 += 1

    # calculating the 
    # r array.
    r[n] = 0
    for i in range(n - 1, 
                   -1, -1):
        if (a[i - 1] < a[i]):
            r[i] = r[i + 1] + 1
        else:
            r[i] = 1

    # Updating the answer.
    for i in range(n - 2, 
                   0, -1):
        if (a[i + 1] - 
            a[i - 1] > 1):
            ans = max(ans, l[i - 1] + 
                      r[i + 1] + 1)

    return max(ans, r[0])

# Driver code.
if __name__ == "__main__":

    a = [9, 4, 5, 1, 13]
    n = len(a)

    # Function call
    print(seg(a, n))

# This code is contributed by Chitranayal

// C# program to find longest increasing subarray
// with one change allowed.
using System;

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;

        // Function call
        Console.WriteLine(seg(a, n));
    }
}

// This code is contributed by PrinciRaj1992

JavaScript

<script>

// Javascript program to find 
// longest increasing subarray
// with one change allowed.
    
    // Function to find length of
    // subsequence
    function seg(a,n)
    {
        let l = new Array(n);
        let r = new Array(n + 1);
        let ans = 0;
 
        // calculating the l array.
        l[0] = 1;
        for (let 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 (let 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 (let 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.
    let a=[9, 4, 5, 1, 13 ];
    let n = a.length;
    
    document.write(seg(a, n));
    
    // This code is contributed by rag2127
    
</script>

Output

Analysis of Algorithms

Abhishek Sharma 44

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