JOJ 1007解题

 1007: Triangles

Result	TIME Limit	MEMORY Limit	Run Times	AC Times	JUDGE
	3s	8192K	7020	2611	Standard

A triangle can be made up out of dots, like the ones shown below:

The number of dots in each one is called a triangular number. More precisely, a number is said to be triangular if it is of the form ½ n(n+1). The numbers 1, 3, 6, 10, and 15 are all triangular.

Given a number, determine if it is triangular. If it is, draw the corresponding right triangle, if it is not, say so.

Input

A positive integer less than 2000. Each case will be on a separate line. A zero (0) denotes the end of input.

Output

The phrase “<num> is a triangular number.” followed by a right triangle of “*” characters, or the phrase “<num> is not a triangular number.” The triangle should be oriented with the hypotenuse on the right and the right angle in the lower left.

Sample Input

3
4
6
0

Sample Output

3 is a triangular number.
*
**
4 is not a triangular number.
6 is a triangular number.
*
**
***

代码如下：

#include <iostream>
#include <queue>
#include <cmath>
using namespace std;

bool isTriangle(int n)
{
    n = 2*n;
    int srt = (int)sqrt(n);
    if (srt * (srt + 1) == n)
        return  true;
    return false;
}

void printTriangle(int n)
{
    for (int i = 1 ; i <= n; i ++)
    {
        for(int j = 1; j <= i ; j ++)
            cout<<"*";
        cout<<endl;
    }
}
int main()
{
    queue<int> input;
    int a;
    while (cin>>a && a!=0)
    {
        input.push(a);
    }
    while (!input.empty())
    {
        if(isTriangle(input.front()))
        {
            cout << input.front() << " is a triangular number."<<endl;
            printTriangle((int)sqrt(input.front()*2));
        }
        else
        {
            cout << input.front() << " is not a triangular number."<<endl;
        }
        input.pop();
    }
    return 0;
}

主要解题思路：

如果一个数是三角数，那么一定有N= 1/2*n(n+1)，因此就有：2*N = n*(n + 1);

可以推出：n < sqrt(n*(n+1)) < n + 1,所以我们可以得出：n = (int)sqrt( n*(n+1))(注：截取整数部分，这个结果一定不是一个整数)

然后再验证是否有：n*(n + 1) == 2*N，如果是，那么N就是三角数，否则就不是三角数。

知道了这些就不难理解上面的解题思路了！！

有不妥之请留言，共同探讨，共同进步！