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Find maximum sum of triplets in an array such than i < j < k and a[i] < a[j] < a[k] in Python
Suppose we have an array of positive numbers, there are n elements in that array, we have to find the maximum sum of triplet (ai + aj + ak ) such that 0 <= i < j < k < n and ai< aj< ak.
So, if the input is like A = [3,6,4,2,5,10], then the output will be 19 as triplets are (3 4 5): sum = 12, (3 6 10): sum = 19, (3 4 10): sum = 17, (4 5 10): sum = 19, (2 5 10): sum = 17. So the max is 19
To solve this, we will follow these steps −
n := size of A
res := 0
for i in range 1 to n - 1, do
first_max := 0, second_max := 0
for j in range 0 to i, do
if A[j] < A[i], then
first_max := maximum of first_max, A[j]
for j in range i + 1 to n, do
if A[j] > A[i], then
second_max := maximum of second_max, A[j]
if first_max and second_max is non-zero, then
res := maximum of res, first_max + A[i] + second_max
return res
Example
Let us see the following implementation to get better understanding −
def get_max_triplet_sum(A) : n = len(A) res = 0 for i in range(1, (n - 1)) : first_max = 0 second_max = 0 for j in range(0, i) : if (A[j] < A[i]) : first_max = max(first_max, A[j]) for j in range((i + 1), n) : if (A[j] > A[i]) : second_max = max(second_max, A[j]) if (first_max and second_max): res = max(res, first_max + A[i] + second_max) return res A = [3,6,4,2,5,10] print(get_max_triplet_sum(A))
Input
[3,6,4,2,5,10]
Output
19
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