Question: 
Write a function to find the maximum sum of increasing subsequence from prefix till ith index and also including a given kth element which is after i, i.e., k > i .


Model's Code:
def max_sum_increasing_subseq(arr, n, i, k):
    max_sum = [0] * n
    max_sum[0] = arr[0]
    
    for j in range(1, i + 1):
        max_sum[j] = arr[j]
        for l in range(0, j):
            if arr[j] > arr[l]:
                max_sum[j] = max(max_sum[j], max_sum[l] + arr[j])
    
    sum_until_i = max(max_sum[:i + 1])
    max_k = 0
    
    for j in range(i + 1, k + 1):
        if arr[j] > arr[i]:
            max_k = max(max_k, arr[j])
    
    return sum_until_i + max_k if max_k > 0 else sum_until_i



Sample Correct Code:
def max_sum_increasing_subseq(a, n, index, k):
	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]


Asserts:
assert max_sum_increasing_subseq([1, 101, 2, 3, 100, 4, 5 ], 7, 4, 6) == 11
assert max_sum_increasing_subseq([1, 101, 2, 3, 100, 4, 5 ], 7, 2, 5) == 7
assert max_sum_increasing_subseq([11, 15, 19, 21, 26, 28, 31], 7, 2, 4) == 71


Tests:
Test 1 of 3: FAIL: AssertionError()

Test 306 of 974: 221/306 (72.22222222222221%): failed