triangle field两点经过的区域数

A triangle field is numbered with successive integers in the way shown on the picture below. 




The traveller needs to go from the cell with number M to the cell with number N. The traveller is able to enter the cell through cell edges only, he can not travel from cell to cell through vertices. The number of edges the traveller passes makes the length of the traveller's route. 

Write the program to determine the length of the shortest route connecting cells with numbers N and M. 

Input

Input contains two integer numbers M and N in the range from 1 to 1000000000 separated with space(s).

Output

Output should contain the length of the shortest route.

Sample Input

6 12 

Sample Output

3

代码：

#include <stdio.h>

#include <math.h>

void main() {

    unsigned int m,n,ai,aj,bi,bj,ak,bk;

    while (scanf("%d%d",&m,&n)!=EOF) {

        ai = sqrt(m-1)+1;

        bi = sqrt(n-1)+1;

        aj = (m-(ai-1)*(ai-1)-1)/2+1;

        bj = (n-(bi-1)*(bi-1)-1)/2+1;

        ak = (ai*ai-m)/2+1;

        bk = (bi*bi-n)/2+1;

        printf("%d/n",abs(ai-bi)+abs(aj-bj)+abs(ak-bk));

    }

}

 题目大意：数字按照所给图形进行排列，给出两点，求两点距离。

  解题思路：图画大一点，然后找规律：固定这个数字的三维坐标，行很好找，直接将这个数开根号就可以知道是第几行，如果开根号正好是整数的话就直接是行号，否则需要加1，对于列有两个方向都需要进行求解。具体如下图：

  第一种右斜着的列号：第二种是左斜着的列号：

  

  根据这两种进行找规律。

求三角形内两点的最短路径，题目见这里，很容易证明最短的路径就是两点在三个方向的距离之和。