Maximum Frequent Subarray Sum MFSS SOLUTION

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Maximum Frequent Subarray Sum MFSS

Akash has just learned the maximum subarray sum problem. And while thinking about the solution, he came up with a new problem, the maximum frequent subarray sum problem.

In this problem, you will be given an array A of N integers. You have to choose a non-empty subarray with the maximum possible score. The score of a subarray is calculated as
score(l,r)=(Al+⋯+Ar)⋅(occurrences)
Here, occurrences is the number of occurrences of that subarray in A.

Now Akash can’t solve this problem, so please help him solve it.

Input
The first line contains an integer T, the number of test cases. Then the test cases follow.
The first line of each test case contains an integer n, the size of the array.
The second line contains n integers A1,…,AN.
Output
For each test case, output the maximum possible score in a new line.

Constraints
1≤T≤2⋅105
1≤n≤105
−107≤Ai≤107
The sum of n over all test cases ≤3⋅105
Subtasks
Subtask 1 (10 points): 1≤n≤100, the sum of n over all test cases ≤300
Subtask 2 (15 points): 1≤n≤1000, the sum of n over all test cases ≤3000
Subtask 3 (75 points): original constraints
Sample Input
2
6
10 8 -20 5 5 5
10
-5 1 7 -1 2 -4 10 0 -11 3
Sample Output
20
15
Explanation
In the first test case, the maximum score is attained by subarray [5,5], its score is (5+5)⋅2=20 since it occurs twice in A.

In the second test case, the maximum score is attained by both subarrays [1,7,−1,2,−4,10] and [1,7,−1,2,−4,10,0]. Both have sum 15 and occur once, so their scores are 15⋅1=15.

Program:


def solve():
    n = int(input())
    arr = list(map(int,input().split()))
    freq, ans = {},-1000000009
    
    for i in range(n):
        for j in range(i,n):
            item = tuple(arr[i:j+1])
            if item in freq.keys():
                freq[item]+=1
            else:
                freq[item]=1 
    
    for key, val in freq.items():
        pts = sum(key)*val
        # print()
        if pts>=ans:
            ans = pts 
            
    print(ans)
    
def main():
    t = int(input())
    for i in range(t):
        solve()
        
main()

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