Calculate the Sum of Powers of Points on a Number Line

To solve this problem, we can use the concept of prefix sums. First, we initialize an array 'prefix' of size 109 with all elements set to 0.

For each point xi, we increment prefix[xi] by 1. This step counts the number of times each point appears in the given coordinates.

Next, we iterate over each point xi again and calculate the sum of fp for s = xi. We can do this by initializing a variable 'sum' to 0 and iterating from 1 to 109. For each integer p, we add prefix[p] to sum if p is less than or equal to xi, otherwise we subtract prefix[p] from sum. This step calculates the sum of fp for each point.

Finally, we output the sum for each test case.

Here is the implementation in Python:

# Function to calculate the sum of fp for each test case
def calculate_sum_of_fp(t, test_cases):
    for _ in range(t):
        n = test_cases[_][0]
        coordinates = test_cases[_][1]

        # Initialize prefix array
        prefix = [0] * 110

        # Count the number of times each point appears
        for point in coordinates:
            prefix[point] += 1

        # Calculate the sum of fp for each point
        result = []
        for xi in coordinates:
            s = xi
            sum = 0
            for p in range(1, 110):
                if p <= s:
                    sum += prefix[p]
                else:
                    sum -= prefix[p]
            result.append(sum)

        # Output the sum for each test case
        print(*result)

# Read input
t = int(input())
test_cases = []
for _ in range(t):
    n = int(input())
    coordinates = list(map(int, input().split()))
    test_cases.append((n, coordinates))

# Calculate and output the sum of fp for each test case
calculate_sum_of_fp(t, test_cases)