Problem
Using the integers from 1 through n, calculate two quantities: first add the integers and square the result; separately square each integer and add those squares. Return the first quantity minus the second.
Implement difference_of_squares(n).
Input
n: The last integer to include.
Output
Return square-of-sum minus sum-of-squares.
Constraints
0 ≤ n ≤ 50,000. For n = 0, both sums are 0. All required values fit signed 64-bit integers.
Examples
Input:
n = 4
Expected output:
expected = 70Input:
long long n = 4;
Expected output:
long long expected = 70;Input:
long n = 4;
Expected output:
long expected = 70;Explanation
(1 + 2 + 3 + 4)² = 100. The sum of squares is 1 + 4 + 9 + 16 = 30. Subtract: 100 − 30 = 70.
Input:
n = 1
Expected output:
expected = 0Input:
long long n = 1;
Expected output:
long long expected = 0;Input:
long n = 1;
Expected output:
long expected = 0;Explanation
Both quantities equal 1, so their difference is 0.
How to approach it
Try on your own first, then open one hint at a time.
Hint 1
You are comparing two summaries of the same range: one based on summing first, the other based on squaring first.
Hint 2
Use the closed-form expressions for sums of integers and sums of squares instead of looping through every value.
Hint 3
Handle the zero case carefully, since both quantities should be zero there.
Expected complexity
O(1) time, O(1) extra space
References
This challenge is adapted for CodeUtility. Follow the statement and constraints above.