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Javascript Program to Find the Longest Bitonic Subsequence | DP-15

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  • Last Updated : 21 Dec, 2021

Given an array arr[0 … n-1] containing n positive integers, a subsequence of arr[] is called Bitonic if it is first increasing, then decreasing. Write a function that takes an array as argument and returns the length of the longest bitonic subsequence. 
A sequence, sorted in increasing order is considered Bitonic with the decreasing part as empty. Similarly, decreasing order sequence is considered Bitonic with the increasing part as empty. 
Examples:

Input arr[] = {1, 11, 2, 10, 4, 5, 2, 1};
Output: 6 (A Longest Bitonic Subsequence of length 6 is 1, 2, 10, 4, 2, 1)

Input arr[] = {12, 11, 40, 5, 3, 1}
Output: 5 (A Longest Bitonic Subsequence of length 5 is 12, 11, 5, 3, 1)

Input arr[] = {80, 60, 30, 40, 20, 10}
Output: 5 (A Longest Bitonic Subsequence of length 5 is 80, 60, 30, 20, 10)

Source: Microsoft Interview Question
 

Solution 
This problem is a variation of standard Longest Increasing Subsequence (LIS) problem. Let the input array be arr[] of length n. We need to construct two arrays lis[] and lds[] using Dynamic Programming solution of LIS problem. lis[i] stores the length of the Longest Increasing subsequence ending with arr[i]. lds[i] stores the length of the longest Decreasing subsequence starting from arr[i]. Finally, we need to return the max value of lis[i] + lds[i] – 1 where i is from 0 to n-1.
Following is the implementation of the above Dynamic Programming solution. 
 

Javascript




<script>
  
/* Dynamic Programming implementation in JavaScript for longest bitonic 
   subsequence problem */    
      
    /* lbs() returns the length of the Longest Bitonic Subsequence in 
    arr[] of size n. The function mainly creates two temporary arrays 
    lis[] and lds[] and returns the maximum lis[i] + lds[i] - 1. 
    
    lis[i] ==> Longest Increasing subsequence ending with arr[i] 
    lds[i] ==> Longest decreasing subsequence starting with arr[i] 
    */
    function lbs(arr,n)
    {
        let i, j; 
        /* Allocate memory for LIS[] and initialize LIS values as 1 for 
            all indexes */
        let lis = new Array(n)
        for (i = 0; i < n; i++) 
            lis[i] = 1;
          
        /* Compute LIS values from left to right */
        for (i = 1; i < n; i++) 
            for (j = 0; j < i; j++) 
                if (arr[i] > arr[j] && lis[i] < lis[j] + 1) 
                    lis[i] = lis[j] + 1; 
    
        /* Allocate memory for lds and initialize LDS values for 
            all indexes */
        let lds = new Array(n); 
        for (i = 0; i < n; i++) 
            lds[i] = 1; 
    
        /* Compute LDS values from right to left */
        for (i = n-2; i >= 0; i--) 
            for (j = n-1; j > i; j--) 
                if (arr[i] > arr[j] && lds[i] < lds[j] + 1) 
                    lds[i] = lds[j] + 1; 
    
    
        /* Return the maximum value of lis[i] + lds[i] - 1*/
        let max = lis[0] + lds[0] - 1; 
        for (i = 1; i < n; i++) 
            if (lis[i] + lds[i] - 1 > max) 
                max = lis[i] + lds[i] - 1; 
    
        return max; 
    }
    let arr=[0, 8, 4, 12, 2, 10, 6, 14, 1, 9, 5, 13, 3, 11, 7, 15]
    let n = arr.length;
    document.write("Length of LBS is "+ lbs( arr, n )); 
          
    // This code is contributed by avanitrachhadiya2155
      
</script>

Output: 

 Length of LBS is 7

Time Complexity: O(n^2) 
Auxiliary Space: O(n)
 

Please refer complete article on Longest Bitonic Subsequence | DP-15 for more details!


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