Longest increasing subarray

Last Updated : 07 Feb, 2023

Given an array containing n numbers. The problem is to find the length of the longest contiguous subarray such that every element in the subarray is strictly greater than its previous element in the same subarray. Time Complexity should be O(n).

Examples:

Input : arr[] = {5, 6, 3, 5, 7, 8, 9, 1, 2}
Output : 5
The subarray is {3, 5, 7, 8, 9}

Input : arr[] = {12, 13, 1, 5, 4, 7, 8, 10, 10, 11}
Output : 4
The subarray is {4, 7, 8, 10}

Algorithm:

lenOfLongIncSubArr(arr, n)
    Declare max = 1, len = 1
    for i = 1 to n-1
    if arr[i] > arr[i-1]
        len++
    else
        if max < len
            max = len
        len = 1
    if max < len
        max = len
    return max

Implementation:

C++

// C++ implementation to find the length of 
// longest increasing contiguous subarray
#include <bits/stdc++.h>
 
using namespace std;
 
// function to find the length of longest increasing 
// contiguous subarray
int lenOfLongIncSubArr(int arr[], int n)
{
    // 'max' to store the length of longest
    // increasing subarray
    // 'len' to store the lengths of longest
    // increasing subarray at different 
    // instants of time
    int max = 1, len = 1;
     
    // traverse the array from the 2nd element
    for (int i=1; i<n; i++)
    {
        // if current element if greater than previous
        // element, then this element helps in building
        // up the previous increasing subarray encountered
        // so far
        if (arr[i] > arr[i-1])
            len++;
        else
        {
            // check if 'max' length is less than the length
            // of the current increasing subarray. If true, 
            // then update 'max'
            if (max < len)    
                max = len;
                 
            // reset 'len' to 1 as from this element
            // again the length of the new increasing
            // subarray is being calculated    
            len = 1;    
        }    
    }
     
    // comparing the length of the last
    // increasing subarray with 'max'
    if (max < len)
        max = len;
     
    // required maximum length
    return max;
}
 
// Driver program to test above
int main()
{
    int arr[] = {5, 6, 3, 5, 7, 8, 9, 1, 2};
    int n = sizeof(arr) / sizeof(arr[0]);
    cout << "Length = "
         << lenOfLongIncSubArr(arr, n);
    return 0;     
}

Java

// JAVA Code to find length of 
// Longest increasing subarray
import java.util.*;
 
class GFG {
     
    // function to find the length of longest
    // increasing contiguous subarray
    public static int lenOfLongIncSubArr(int arr[],
                                            int n)
    {
        // 'max' to store the length of longest
        // increasing subarray
        // 'len' to store the lengths of longest
        // increasing subarray at different 
        // instants of time
        int max = 1, len = 1;
          
        // traverse the array from the 2nd element
        for (int i=1; i<n; i++)
        {
            // if current element if greater than
            // previous element, then this element 
            // helps in building up the previous 
            // increasing subarray encountered
            // so far
            if (arr[i] > arr[i-1])
                len++;
            else
            {
                // check if 'max' length is less 
                // than the length of the current 
                // increasing subarray. If true,
                // than update 'max'
                if (max < len)    
                    max = len;
                      
                // reset 'len' to 1 as from this 
                // element again the length of the 
                // new increasing subarray is being 
                // calculated    
                len = 1;    
            }    
        }
          
        // comparing the length of the last
        // increasing subarray with 'max'
        if (max < len)
            max = len;
          
        // required maximum length
        return max;
    }
     
    /* Driver program to test above function */
    public static void main(String[] args) 
    {
         int arr[] = {5, 6, 3, 5, 7, 8, 9, 1, 2};
            int n = arr.length;
            System.out.println("Length = " +
                      lenOfLongIncSubArr(arr, n));
         
        }
    }
   
// This code is contributed by Arnav Kr. Mandal.

Python3

# Python 3 implementation to find the length of 
# longest increasing contiguous subarray
 
  
# function to find the length of longest 
# increasing contiguous subarray
def lenOfLongIncSubArr(arr, n) :
 
    # 'max' to store the length of longest
    # increasing subarray
    # 'len' to store the lengths of longest
    # increasing subarray at different 
    # instants of time
    m = 1
    l = 1
      
    # traverse the array from the 2nd element
    for i in range(1, n) :
 
        # if current element if greater than previous
        # element, then this element helps in building
        # up the previous increasing subarray encountered
        # so far
        if (arr[i] > arr[i-1]) :
            l =l + 1
        else :
 
            # check if 'max' length is less than the length
            # of the current increasing subarray. If true, 
            # then update 'max'
            if (m < l)  :
                m = l 
 
            # reset 'len' to 1 as from this element
            # again the length of the new increasing
            # subarray is being calculated    
            l = 1
         
         
    # comparing the length of the last
    # increasing subarray with 'max'
    if (m < l) :
        m = l
      
    # required maximum length
    return m
 
# Driver program to test above
 
arr = [5, 6, 3, 5, 7, 8, 9, 1, 2]
n = len(arr)
print("Length = ", lenOfLongIncSubArr(arr, n))
 
 
# This code is contributed
# by Nikita Tiwari.

C#

// C# Code to find length of
// Longest increasing subarray
using System;
 
class GFG {
 
    // function to find the length of longest
    // increasing contiguous subarray
    public static int lenOfLongIncSubArr(int[] arr,
                                             int n)
    {
        // 'max' to store the length of longest
        // increasing subarray
        // 'len' to store the lengths of longest
        // increasing subarray at different
        // instants of time
        int max = 1, len = 1;
 
        // traverse the array from the 2nd element
        for (int i = 1; i < n; i++) {
             
            // if current element if greater than
            // previous element, then this element
            // helps in building up the previous
            // increasing subarray encountered
            // so far
            if (arr[i] > arr[i - 1])
                len++;
            else {
                 
                // check if 'max' length is less
                // than the length of the current
                // increasing subarray. If true,
                // than update 'max'
                if (max < len)
                    max = len;
 
                // reset 'len' to 1 as from this
                // element again the length of the
                // new increasing subarray is being
                // calculated
                len = 1;
            }
        }
 
        // comparing the length of the last
        // increasing subarray with 'max'
        if (max < len)
            max = len;
 
        // required maximum length
        return max;
    }
 
    /* Driver program to test above function */
    public static void Main()
    {
        int[] arr = { 5, 6, 3, 5, 7, 8, 9, 1, 2 };
        int n = arr.Length;
        Console.WriteLine("Length = " + 
                           lenOfLongIncSubArr(arr, n));
    }
}
 
// This code is contributed by Sam007

PHP

<?php
// PHP implementation to find the length of 
// longest increasing contiguous subarray
 
// function to find the length of 
// longest increasing contiguous
// subarray
function lenOfLongIncSubArr($arr, $n)
{
     
    // 'max' to store the length of longest
    // increasing subarray
    // 'len' to store the lengths of longest
    // increasing subarray at different 
    // instants of time
    $max = 1;
    $len = 1;
     
    // traverse the array from 
    // the 2nd element
    for ($i = 1; $i < $n; $i++)
    {
         
        // if current element if 
        // greater than previous
        // element, then this element 
        // helps in building up the
        // previous increasing subarray 
        // encountered so far
        if ($arr[$i] > $arr[$i-1])
            $len++;
        else
        {
             
            // check if 'max' length is
            // less than the length
            // of the current increasing
            // subarray. If true, 
            // then update 'max'
            if ($max < $len) 
                $max = $len;
                 
            // reset 'len' to 1 as
            // from this element
            // again the length of 
            // the new increasing
            // subarray is being
            // calculated 
            $len = 1; 
        } 
    }
     
    // comparing the length of the last
    // increasing subarray with 'max'
    if ($max < $len)
        $max = $len;
     
    // required maximum length
    return $max;
}
 
    // Driver Code
    $arr = array(5, 6, 3, 5, 7, 8, 9, 1, 2);
    $n = sizeof($arr);
    echo "Length = ", lenOfLongIncSubArr($arr, $n);
     
// This code is contributed by nitin mittal.
?>

Javascript

<script>
  
// Javascript implementation to find the length of
// longest increasing contiguous subarray
  
// function to find the length of longest increasing
// contiguous subarray
function lenOfLongIncSubArr(arr, n)
{
    // 'max' to store the length of longest
    // increasing subarray
    // 'len' to store the lengths of longest
    // increasing subarray at different
    // instants of time
    var max = 1, len = 1;
      
    // traverse the array from the 2nd element
    for (var i=1; i<n; i++)
    {
        // if current element if greater than previous
        // element, then this element helps in building
        // up the previous increasing subarray encountered
        // so far
        if (arr[i] > arr[i-1])
            len++;
        else
        {
            // check if 'max' length is less than the length
            // of the current increasing subarray. If true,
            // then update 'max'
            if (max < len)   
            {
                max = len;
            }
                  
            // reset 'len' to 1 as from this element
            // again the length of the new increasing
            // subarray is being calculated   
            len = 1;   
        }   
    }
      
    // comparing the length of the last
    // increasing subarray with 'max'
    if (max < len)
    {
        max = len;
    }
     
    // required maximum length
    return max;
}
  
// Driver program to test above
var arr = [5, 6, 3, 5, 7, 8, 9, 1, 2];
var n = arr.length;
document.write("Length = " + lenOfLongIncSubArr(arr, n)); 
// This code is contributed by shivani.
</script>

Output

Length = 5

Time Complexity: O(n)
Auxiliary Space: O(1)

How to print the subarray?
We can print the subarray by keeping track of the index with the largest length.

Implementation:

C++

// C++ implementation to find the length of 
// longest increasing contiguous subarray
#include <bits/stdc++.h>
using namespace std;
 
// function to find the length of longest increasing 
// contiguous subarray
void printLongestIncSubArr(int arr[], int n)
{
    // 'max' to store the length of longest
    // increasing subarray
    // 'len' to store the lengths of longest
    // increasing subarray at different 
    // instants of time
    int max = 1, len = 1, maxIndex = 0;
     
    // traverse the array from the 2nd element
    for (int i=1; i<n; i++)
    {
        // if current element if greater than previous
        // element, then this element helps in building
        // up the previous increasing subarray encountered
        // so far
        if (arr[i] > arr[i-1])
            len++;
        else
        {
            // check if 'max' length is less than the length
            // of the current increasing subarray. If true, 
            // then update 'max'
            if (max < len)    
            {
                max = len;
                 
                // index assign the starting index of 
                // longest increasing contiguous subarray.   
                maxIndex = i - max;
            }
                 
            // reset 'len' to 1 as from this element
            // again the length of the new increasing
            // subarray is being calculated    
            len = 1;    
        }    
    }
     
    // comparing the length of the last
    // increasing subarray with 'max'
    if (max < len)
    { 
        max = len;
        maxIndex = n - max;
    }
 
    // Print the elements of longest increasing
    // contiguous subarray. 
    for (int i=maxIndex; i<max+maxIndex; i++)
        cout << arr[i] << " ";
}
 
// Driver program to test above
int main()
{
    int arr[] = {5, 6, 3, 5, 7, 8, 9, 1, 2};
    int n = sizeof(arr) / sizeof(arr[0]);
    printLongestIncSubArr(arr, n);
    return 0;     
}
// This code is contributed by Dharmendra kumar

Java

// JAVA Code For Longest increasing subarray
import java.util.*;
 
class GFG {
     
    // function to find the length of longest 
    // increasing contiguous subarray
    public static void printLongestIncSubArr(int arr[], 
                                              int n)
    {
        // 'max' to store the length of longest
        // increasing subarray
        // 'len' to store the lengths of longest
        // increasing subarray at different 
        // instants of time
        int max = 1, len = 1, maxIndex = 0;
          
        // traverse the array from the 2nd element
        for (int i = 1; i < n; i++)
        {
            // if current element if greater than 
            // previous element, then this element 
            // helps in building up the previous 
            // increasing subarray encountered
            // so far
            if (arr[i] > arr[i-1])
                len++;
            else
            {
                // check if 'max' length is less
                // than the length of the current
                // increasing subarray. If true, 
                // then update 'max'
                if (max < len)    
                {
                    max = len;
                      
                    // index assign the starting 
                    // index of longest increasing
                    // contiguous subarray.   
                    maxIndex = i - max;
                }
                      
                // reset 'len' to 1 as from this
                // element again the length of the
                // new increasing subarray is 
                // being calculated    
                len = 1;    
            }    
        }
          
        // comparing the length of the last
        // increasing subarray with 'max'
        if (max < len)
        { 
            max = len;
            maxIndex = n - max;
        }
      
        // Print the elements of longest 
        // increasing contiguous subarray. 
        for (int i = maxIndex; i < max+maxIndex; i++)
            System.out.print(arr[i] + " ");
    }
     
    /* Driver program to test above function */
    public static void main(String[] args) 
    {
        int arr[] = {5, 6, 3, 5, 7, 8, 9, 1, 2};
        int n = arr.length;
        printLongestIncSubArr(arr, n);
         
    }
}
   
// This code is contributed by Arnav Kr. Mandal.

Python3

# Python 3 implementation to find the length of 
# longest increasing contiguous subarray
 
 
# function to find the length of longest increasing 
# contiguous subarray
def printLongestIncSubArr( arr, n) :
 
    # 'max' to store the length of longest
    # increasing subarray
    # 'len' to store the lengths of longest
    # increasing subarray at different 
    # instants of time
    m = 1
    l = 1
    maxIndex = 0
      
    # traverse the array from the 2nd element
    for i in range(1, n) :
 
        # if current element if greater than previous
        # element, then this element helps in building
        # up the previous increasing subarray 
        # encountered so far
        if (arr[i] > arr[i-1]) :
            l =l + 1
        else :
 
            # check if 'max' length is less than the length
            # of the current increasing subarray. If true, 
            # then update 'max'
            if (m < l)  :
                m = l 
 
                # index assign the starting index of 
                # longest increasing contiguous subarray.   
                maxIndex = i - m
                   
            # reset 'len' to 1 as from this element
            # again the length of the new increasing
            # subarray is being calculated    
            l = 1   
         
         
    # comparing the length of the last
    # increasing subarray with 'max'
    if (m < l) :
        m = l
        maxIndex = n - m
     
    # Print the elements of longest
    # increasing contiguous subarray. 
    for i in range(maxIndex, (m+maxIndex)) :
        print(arr[i] , end=" ")
         
# Driver program to test above
arr = [5, 6, 3, 5, 7, 8, 9, 1, 2]
n = len(arr)
printLongestIncSubArr(arr, n)
     
     
# This code is contributed
# by Nikita Tiwari

C#

// C# Code to print 
// Longest increasing subarray
using System;
 
class GFG {
 
    // function to find the length of longest
    // increasing contiguous subarray
    public static void printLongestIncSubArr(int[] arr,
                                                int n)
    {
        // 'max' to store the length of longest
        // increasing subarray
        // 'len' to store the lengths of longest
        // increasing subarray at different
        // instants of time
        int max = 1, len = 1, maxIndex = 0;
 
        // traverse the array from the 2nd element
        for (int i = 1; i < n; i++) {
             
            // if current element if greater than
            // previous element, then this element
            // helps in building up the previous
            // increasing subarray encountered
            // so far
            if (arr[i] > arr[i - 1])
                len++;
            else
            {
                // check if 'max' length is less
                // than the length of the current
                // increasing subarray. If true,
                // then update 'max'
                if (max < len) {
                    max = len;
 
                    // index assign the starting
                    // index of longest increasing
                    // contiguous subarray.
                    maxIndex = i - max;
                }
 
                // reset 'len' to 1 as from this
                // element again the length of the
                // new increasing subarray is
                // being calculated
                len = 1;
            }
        }
 
        // comparing the length of the last
        // increasing subarray with 'max'
        if (max < len) {
            max = len;
            maxIndex = n - max;
        }
 
        // Print the elements of longest
        // increasing contiguous subarray.
        for (int i = maxIndex; i < max + maxIndex; i++)
            Console.Write(arr[i] + " ");
    }
 
    /* Driver program to test above function */
    public static void Main()
    {
        int[] arr = { 5, 6, 3, 5, 7, 8, 9, 1, 2 };
        int n = arr.Length;
        printLongestIncSubArr(arr, n);
    }
}
 
// This code is contributed by Sam007

PHP

<?php
// PHP implementation to find 
// the length of longest increasing 
// contiguous subarray
 
// function to find the length of 
// longest increasing contiguous subarray
function printLongestIncSubArr(&$arr, $n)
{
    // 'max' to store the length of 
    // longest increasing subarray
    // 'len' to store the lengths of 
    // longest increasing subarray at 
    // different instants of time
    $max = 1; 
    $len = 1; 
    $maxIndex = 0;
     
    // traverse the array from 
    // the 2nd element
    for ($i = 1; $i < $n; $i++)
    {
        // if current element if greater 
        // than previous element, then 
        // this element helps in building
        // up the previous increasing 
        // subarray encountered so far
        if ($arr[$i] > $arr[$i - 1])
            $len++;
        else
        {
            // check if 'max' length is less 
            // than the length of the current 
            // increasing subarray. If true, 
            // then update 'max'
            if ($max < $len) 
            {
                $max = $len;
                 
                // index assign the starting 
                // index of longest increasing
                // contiguous subarray. 
                $maxIndex = $i - $max;
            }
                 
            // reset 'len' to 1 as from this
            // element again the length of 
            // the new increasing subarray
            // is being calculated 
            $len = 1; 
        } 
    }
     
    // comparing the length of
    // the last increasing 
    // subarray with 'max'
    if ($max < $len)
    { 
        $max = $len;
        $maxIndex = $n - $max;
    }
 
    // Print the elements of
    // longest increasing
    // contiguous subarray. 
    for ($i = $maxIndex; 
         $i < ($max + $maxIndex); $i++)
        echo($arr[$i] . " ") ;
         
}
 
// Driver Code
$arr = array(5, 6, 3, 5, 7, 
             8, 9, 1, 2);
$n = sizeof($arr);
printLongestIncSubArr($arr, $n);
     
// This code is contributed
// by Shivi_Aggarwal
?>

Javascript

<script>
 
// Javascript implementation to find the length of 
// longest increasing contiguous subarray
 
// function to find the length of longest increasing 
// contiguous subarray
function printLongestIncSubArr(arr, n)
{
    // 'max' to store the length of longest
    // increasing subarray
    // 'len' to store the lengths of longest
    // increasing subarray at different 
    // instants of time
    var max = 1, len = 1, maxIndex = 0;
     
    // traverse the array from the 2nd element
    for (var i=1; i<n; i++)
    {
        // if current element if greater than previous
        // element, then this element helps in building
        // up the previous increasing subarray encountered
        // so far
        if (arr[i] > arr[i-1])
            len++;
        else
        {
            // check if 'max' length is less than the length
            // of the current increasing subarray. If true, 
            // then update 'max'
            if (max < len)    
            {
                max = len;
                 
                // index assign the starting index of 
                // longest increasing contiguous subarray.   
                maxIndex = i - max;
            }
                 
            // reset 'len' to 1 as from this element
            // again the length of the new increasing
            // subarray is being calculated    
            len = 1;    
        }    
    }
     
    // comparing the length of the last
    // increasing subarray with 'max'
    if (max < len)
    { 
        max = len;
        maxIndex = n - max;
    }
 
    // Print the elements of longest increasing
    // contiguous subarray. 
    for (var i=maxIndex; i<max+maxIndex; i++)
        document.write( arr[i] + " ");
}
 
// Driver program to test above
var arr = [5, 6, 3, 5, 7, 8, 9, 1, 2];
var n = arr.length;
printLongestIncSubArr(arr, n);
 
// This code is contributed by rrrtnx.
</script>

Output

3 5 7 8 9

Time Complexity: O(N) where N is the number of elements in the array.
Auxiliary Space: O(1)

Longest Increasing Subsequence (LIS)

GeeksforGeeks

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