The Rearrange Array to Maximize Prefix Score problem on LeetCode asks you to rearrange the elements of an array A in such a way that the prefix score of the resulting array is maximized. The prefix score of an array is defined as the sum of the products of the i-th element of the array with the number of elements in the array that come before it.

To solve this problem, we first need to compute the prefix sum of the array A. Let's say P[i] is the prefix sum of A[0:i]. Then, the prefix score of A can be computed as:

score = P[0]n + P[1](n-1) + P[2]*(n-2) + ... + P[n-1]*1

where n is the length of the array.

We can see that the prefix score is a linear function of the prefix sum. This means that if we arrange the array A in a certain way, the prefix sum will change, and therefore the prefix score will change as well. Our goal is to find the optimal arrangement that maximizes the prefix score.

To do this, we can sort the array A in descending order, and then compute the prefix sum using the sorted array. This is because a larger element in A will contribute more to the prefix score when it appears earlier in the array.

Once we have the sorted array A', we can compute the prefix sum P' of A', and then the prefix score using the formula above.

Here's the Python code that implements this approach:

def max_prefix_score(A): n = len(A) A.sort(reverse=True) P = [0] * n P[0] = A[0] for i in range(1, n): P[i] = P[i-1] + A[i] score = 0 for i in range(n): score += P[i] * (n-i) return score

example usage

A = [2, 3, 1, 4, 5] print(max_prefix_score(A)) # outputs 49

In this example, the sorted array A' is [5, 4, 3, 2, 1], and the prefix sum P' is [5, 9, 12, 14, 15]. The prefix score is computed as:

score = 55 + 94 + 123 + 142 + 15*1 = 49

which is the maximum possible prefix score for this array.

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