문제
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.
제약 조건
0 ≤ n ≤ 50,000. For n = 0, both sums are 0. All required values fit signed 64-bit integers.
예시
입력:
n = 4
예상 출력:
expected = 70입력:
long long n = 4;
예상 출력:
long long expected = 70;입력:
long n = 4;
예상 출력:
long expected = 70;설명
(1 + 2 + 3 + 4)² = 100. The sum of squares is 1 + 4 + 9 + 16 = 30. Subtract: 100 − 30 = 70.
입력:
n = 1
예상 출력:
expected = 0입력:
long long n = 1;
예상 출력:
long long expected = 0;입력:
long n = 1;
예상 출력:
long expected = 0;설명
Both quantities equal 1, so their difference is 0.
접근 방법
먼저 스스로 풀어 본 뒤 힌트를 하나씩 열어 보세요.
힌트 1
You are comparing two summaries of the same range: one based on summing first, the other based on squaring first.
힌트 2
Use the closed-form expressions for sums of integers and sums of squares instead of looping through every value.
힌트 3
Handle the zero case carefully, since both quantities should be zero there.
예상 복잡도
O(1) time, O(1) extra space
참고 자료
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