Problema
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.
Vincoli
0 ≤ n ≤ 50,000. For n = 0, both sums are 0. All required values fit signed 64-bit integers.
Esempi
Input:
n = 4
Output atteso:
expected = 70Input:
long long n = 4;
Output atteso:
long long expected = 70;Input:
long n = 4;
Output atteso:
long expected = 70;Spiegazione
(1 + 2 + 3 + 4)² = 100. The sum of squares is 1 + 4 + 9 + 16 = 30. Subtract: 100 − 30 = 70.
Input:
n = 1
Output atteso:
expected = 0Input:
long long n = 1;
Output atteso:
long long expected = 0;Input:
long n = 1;
Output atteso:
long expected = 0;Spiegazione
Both quantities equal 1, so their difference is 0.
Come affrontarlo
Prova prima da solo, poi apri un suggerimento alla volta.
Suggerimento 1
You are comparing two summaries of the same range: one based on summing first, the other based on squaring first.
Suggerimento 2
Use the closed-form expressions for sums of integers and sums of squares instead of looping through every value.
Suggerimento 3
Handle the zero case carefully, since both quantities should be zero there.
Complessità attesa
O(1) time, O(1) extra space
Riferimenti
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