学步园

问题1: 周长不大于n，边长为整数的三角形有多少个？

解法：

     Function p(ByVal n As Long)'周长n的三角形的个数<br /> If n Mod 2 Then n = n + 3<br /> p = Round(n ^ 2 / 48)<br /> End Function<br /> Sub Main()<br /> Dim i As Long, c<br /> For i = 1 To 10 ^ 6<br /> c = c + p(i)<br /> Next<br /> Debug.Print c<br /> End Sub

返回：6944486111111111

问题2: 周长不大于n，边长为整数，并且至少有一个角为整数（以角度表示）的三角形有多少个？

解法：

Function gcd(ByVal a As Long, ByVal b As Long) As Long<br /> If b = 0 Then gcd = a: Exit Function<br /> gcd = gcd(b, a Mod b)<br /> End Function<br /> Sub main()<br /> Dim p As Long, c As Long<br /> p = 10 ^ 6<br /> c = p / 3 '等边三角形的个数<br /> Dim m As Long, n As Long, k As Long<br /> For n = 1 To Int((Sqr(4 * p + 1) - 3) / 4) + 1<br /> For k = 1 To Int((Sqr(n * n + 2 * p) - 3 * n) / 2)<br /> m = n + k<br /> If gcd(m, n) = 1 Then<br /> If (m - n) Mod 2 = 1 Then c = c + p / (2 * m * (m + n))<br /> If (m - n) Mod 3 > 0 Then c = c + p / (m * (2 * m + 3 * n) + n * n) + p / (5 * m * n + 2 * (m * m + n * n)) + p / (3 * m * (m + n))<br /> End If<br /> Next<br /> Next<br /> Debug.Print c<br /> End Sub

返回：3055201