Maximum Sum Triplet Asked in: Directi

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 Problem Description

Given an array A containing N integers.

You need to find the maximum sum of triplet ( Ai + Aj + Ak ) such that 0 <= i < j < k < N and Ai < Aj < Ak.

If no such triplet exist return 0.



Problem Constraints

3 <= N <= 105.

1 <= A[i] <= 108.



Input Format

First argument is an integer array A.



Output Format

Return a single integer denoting the maximum sum of triplet as described in the question.



Example Input

Input 1:

 A = [2, 5, 3, 1, 4, 9]

Input 2:

 A = [1, 2, 3]



Example Output

Output 1:

 16

Output 2:

 6



Example Explanation

Explanation 1:

 All possible triplets are:-
    2 3 4 => sum = 9
    2 5 9 => sum = 16
    2 3 9 => sum = 14
    3 4 9 => sum = 16
    1 4 9 => sum = 14
  Maximum sum = 16

Explanation 2:

 All possible triplets are:-
    1 2 3 => sum = 6
 Maximum sum = 6



Solution:

Fastest :

from bisect import bisect_left 
  
def BinarySearch(a, x): 
    i = bisect_left(a, x) 
    if i: 
        return (i-1) 
    else: 
        return -1
  
class Solution:
    # @param A : list of integers
    # @return an integer
    def solve(self, A):
        n=len(A)
        dp=[0]*n
        dp[n-1]=A[n-1]
        for i in range(n-2,-1,-1):
            dp[i]=max(dp[i+1],A[i])
        lst=[]
        maxe=0
        lst.append(A[0])
        for i in range(1,n-1):
            res = BinarySearch(lst, A[i])
            if(res!=-1):
                if dp[i+1]<=A[i]:
                    continue
                ans=lst[res] + A[i] + dp[i+1]
                maxe=max(maxe,ans)
            lst.insert(res+1,A[i])
        return maxe
        return 0
                
                
        return ans
        
Solution credits:



To insert the element and maintain the asceding order of the array then we need to use bisect:

Bisect Study link: https://www.geeksforgeeks.org/bisect-algorithm-functions-in-python/



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