Assume that I want to get sum of all squares from M to N. I googled a bit and found this formula:
(1^2 + 2^2 + 3^2 + ... + N^2) = (N * (N + 1) * (2N + 1)) / 6
so I write this code:
static void Main(string[] args)
{
const int from = 10;
const int to = 50000;
Console.WriteLine(SumSquares(from, to));
Console.WriteLine(SumSquares2(from, to));
}
static long SumSquares(int m, int n)
{
checked
{
long x = m - 1;
long y = n;
return (((y*(y + 1)*(2*y + 1)) - (x*(x + 1)*(2*x + 1)))/6);
}
}
static long SumSquares2(int m, int n)
{
long sum = 0;
for (int i = m; i <= n; ++i)
{
sum += i * i;
}
return sum;
}
it works fine until 40k, but when N becomes 50k
it fails. Output for 50k:
41667916674715
25948336371355
Press any key to continue . . .
I think it's an overflow or something, so I added checked
keyword and tried to change long
to double
, but I got the same result. How can it be explained? How to get correct result without loops?
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