> For the complete documentation index, see [llms.txt](https://mayanktyagi3111.gitbook.io/interview-prep/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://mayanktyagi3111.gitbook.io/interview-prep/dynamic-programming/maximum-sum-bi-tonic-sub-sequence.md).

# Maximum sum Bi-tonic Sub-sequence

Given an array of integers. A [subsequence ](http://en.wikipedia.org/wiki/Subsequence)of arr\[] is called Bitonic if it is first increasing, then decreasing.

**Examples :**

```
Input : arr[] = {1, 15, 51, 45, 33, 
                   100, 12, 18, 9}
Output : 194
Explanation : Bi-tonic Sub-sequence are :
             {1, 51, 9} or {1, 50, 100, 18, 9} or
             {1, 15, 51, 100, 18, 9}  or 
             {1, 15, 45, 100, 12, 9}  or 
             {1, 15, 45, 100, 18, 9} .. so on            
Maximum sum Bi-tonic sub-sequence is 1 + 15 +
51 + 100 + 18 + 9 = 194   

Input : arr[] = {80, 60, 30, 40, 20, 10} 
Output : 210  
```

```java
class Solution {
    public int MaxSumBS(int arr[], int n) {
        int max_sum = Integer.MIN_VALUE;

        // MSIBS[i] ==> Maximum sum Increasing Bi-tonic
        // subsequence ending with arr[i]
        // MSDBS[i] ==> Maximum sum Decreasing Bi-tonic
        // subsequence starting with arr[i]
        // Initialize MSDBS and MSIBS values as arr[i] for
        // all indexes
        int MSIBS[] = new int[n];
        int MSDBS[] = new int[n];
        for (int i = 0; i < n; i++) {
            MSDBS[i] = arr[i];
            MSIBS[i] = arr[i];
        }

        // Compute MSIBS values from left to right */
        for (int i = 1; i < n; i++)
            for (int j = 0; j < i; j++)
                if (arr[i] > arr[j] && MSIBS[i] < MSIBS[j] + arr[i])
                    MSIBS[i] = MSIBS[j] + arr[i];

        // Compute MSDBS values from right to left
        for (int i = n - 2; i >= 0; i--)
            for (int j = n - 1; j > i; j--)
                if (arr[i] > arr[j] && MSDBS[i] < MSDBS[j] + arr[i])
                    MSDBS[i] = MSDBS[j] + arr[i];

        // Find the maximum value of MSIBS[i] +
        // MSDBS[i] - arr[i]
        for (int i = 0; i < n; i++)
            max_sum = Math.max(max_sum, (MSDBS[i] + MSIBS[i] - arr[i]));

        // return max sum of bi-tonic
        // sub-sequence
        return max_sum;
    }
}
```


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