
    Design a risk assessment algorithm for a mobile banking app that analyzes transaction patterns to detect potential fraud. The algorithm should calculate the highest cumulative value of progressively increasing transactions up to a current transaction, while also considering a specific future high-value transaction that requires biometric verification. Given a sequence of transaction amounts and a position of a high-value transaction occurring later in the sequence, determine the maximum sum of increasing transactions that could indicate a pattern leading to that high-value transaction. The solution should help identify whether the spending pattern combined with the future high-value transaction represents normal customer behavior or potential fraud.
    

    
def max_sum_increasing_subseq(a, n, index, k):
    """
    Design a risk assessment algorithm for a mobile banking app that analyzes transaction patterns to detect potential fraud. The algorithm should calculate the highest cumulative value of progressively increasing transactions up to a current transaction, while also considering a specific future high-value transaction that requires biometric verification. Given a sequence of transaction amounts and a position of a high-value transaction occurring later in the sequence, determine the maximum sum of increasing transactions that could indicate a pattern leading to that high-value transaction. The solution should help identify whether the spending pattern combined with the future high-value transaction represents normal customer behavior or potential fraud.
    

    """
def max_sum_increasing_subseq(a, n, index, k):
    """
    Design a risk assessment algorithm for a mobile banking app that analyzes transaction patterns to detect potential fraud. The algorithm should calculate the highest cumulative value of progressively increasing transactions up to a current transaction, while also considering a specific future high-value transaction that requires biometric verification. Given a sequence of transaction amounts and a position of a high-value transaction occurring later in the sequence, determine the maximum sum of increasing transactions that could indicate a pattern leading to that high-value transaction. The solution should help identify whether the spending pattern combined with the future high-value transaction represents normal customer behavior or potential fraud.
    

    """
    dp = [[0 for i in range(n)] for i in range(n)]
    for i in range(n):
        if a[i] > a[0]:
            dp[0][i] = a[i] + a[0]
        else:
            dp[0][i] = a[i]
    for i in range(1, n):
        for j in range(n):
            if a[j] > a[i] and j > i:
                if dp[i - 1][i] + a[j] > dp[i - 1][j]:
                    dp[i][j] = dp[i - 1][i] + a[j]
                else:
                    dp[i][j] = dp[i - 1][j]
            else:
                dp[i][j] = dp[i - 1][j]
    return dp[index][k]