C - Count Triangles

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原创最新推荐文章于 2026-04-15 11:52:45 发布 311 阅读 AI 写同款· GEO 优化 ›

在MATLAB中将C语言代码转化为可执行的mexw64文件这样，您可以将高效的C语言算法集成到MATLAB环境中，以便更好地利用MATLAB的功能和特性。请记住，在使用mex转换C语言代码之前，您需要正确编写和测试C语言代码，并确保它与MATLAB的mex接口兼容。MATLAB是一种功能强大的数值计算软件，它提供了一个机制，可以将C语言代码转化为MATLAB可执行的mexw64文件。在上述命令中，"-output"选项指定生成的mex文件的名称，"myfunction"是您选择的名称，"myfunction.c"是要编译的C语言源文件。步骤1：编写C语言代码。阅读详情

Like any unknown mathematician, Yuri has favourite numbers: A, B, C, and D, where A≤B≤C≤D. Yuri also likes triangles and once he thought: how many non-degenerate triangles with integer sides x, y, and z exist, such that A≤x≤B≤y≤C≤z≤D holds?

Yuri is preparing problems for a new contest now, so he is very busy. That’s why he asked you to calculate the number of triangles with described property.

The triangle is called non-degenerate if and only if its vertices are not collinear.

Input
The first line contains four integers: A, B, C and D (1≤A≤B≤C≤D≤5⋅105) — Yuri’s favourite numbers.

Output
Print the number of non-degenerate triangles with integer sides x, y, and z such that the inequality A≤x≤B≤y≤C≤z≤D holds.

Examples
Input
1 2 3 4
Output
4
Input
1 2 2 5
Output
3
Input
500000 500000 500000 500000
Output
1
Note
In the first example Yuri can make up triangles with sides (1,3,3), (2,2,3), (2,3,3) and (2,3,4).

In the second example Yuri can make up triangles with sides (1,2,2), (2,2,2) and (2,2,3).

In the third example Yuri can make up only one equilateral triangle with sides equal to 5⋅105.

首先固定x+y为i那么z的取值范围便是c~min(d,i-1)；
而对于x和y的范围，当i<=2*b时固定y为b则x=i-b（大于同理），然后减小x的值在固定i的条件下y就要增加，这样x和y的最小活动范围长度就是x和y的方案数
令x和y的方案数与z的方案数相乘便得到了x+y==i的方案数
枚举i的取值区间并加和即可得到所有方案数

#include<iostream>
using namespace std;
int main()
{
	int a,b,c,d,x,y,z;
	long long ans=0;
	cin>>a>>b>>c>>d;
	for(int i=a+b;i<=b+c;i++)
	{
		z=min(d,i-1);
		if(z<c) continue;
		z=z-c+1;
		if(i<=2*b)
		{
			x=i-b;
			ans+=1ll*(min(x-a,c-b)+1)*z;
		}
		else
		{
			y=i-b;
			ans+=1ll*(min(b-a,c-y)+1)*z;
		}
	}
	cout<<ans<<endl;
}