alg_problem: number_of_disc_intersections

圆盘交叠算法

最新推荐文章于 2020-07-31 16:27:43 发布

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最新推荐文章于 2020-07-31 16:27:43 发布

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原文链接：http://www.cnblogs.com/cutepig/archive/2011/02/17/1956811.html

本文介绍了一种计算二维平面上圆盘交叠数量的算法。该算法通过输入一系列整数来确定每个圆盘的半径，并据此计算出任意两个圆盘之间的交叠情况。文章提供了一个具体的C++实现示例，可用于解决类似的实际问题。

Given an array A of N integers we draw N discs in a 2D plane, such that i-th disc has center in (0,i) and a radius A[i]. We say that k-th disc and j-th disc intersect, if $k\not =j$ and k-th and j-th discs have at least one common point.

Write a function

int number_of_disc_intersections(int[] A);

which given an array A describing N discs as explained above, returns the number of pairs of intersecting discs. For example, given N=6 and

$\begin{displaymath}A[0]=1 A[1]=5 A[2]=2 A[3]=1 A[4]=4 A[5]=0\end{displaymath}$

there are 11 pairs of intersecting discs:

    0th and 1st
    0th and 2nd
    0th and 4th
    1st and 2nd
    1st and 3rd
    1st and 4th
    1st and 5th
    2nd and 3rd
    2nd and 4th
    3rd and 4th
    4th and 5th

so the function should return 11.

The function should return -1 if the number of intersecting pairs exceeds 10,000,000. The function may assume that N does not exceed 10,000,000.

#include <stdio.h>
#include <vector>

int number_of_disc_intersections ( const std::vector<int> &A ) {
   // write your code here
   size_t n = A.size();
   if(n==0) return -1;


   long long num=0;
   for(size_t i=0; i<n; i++)
   {
       for(size_t j=i+1; j<n; j++)
       {
           if( j-i<= A[i]+A[j] /*&& j -i + A[i] >= A[j] && j-i + A[j] >= A[i] */)
           {
               //printf("%d %d\n", i, j);
               num++;
               if(num>=10000000)
                   return -1;
           }
       }
   }

   return num;
}

int main()
{
   int a[]={1,5,2,1,4,0};
   std::vector<int> A(a, a+sizeof(a)/sizeof(a[0]));
   int i=number_of_disc_intersections(A);
   printf("%d\n",i);
}

http://stackoverflow.com/questions/4801242/algorithm-to-calculate-number-of-intersecting-discs

http://www.devcomments.com/q490073/Algorithm-to-calculate-number-intersecting-discs

转载于:https://www.cnblogs.com/cutepig/archive/2011/02/17/1956811.html