Hangzhou Electric 1466 Calculate the line of intersection

DescriptionThere are n straight lines on the plane, and there are no three-wire common points, asking how many different cross-points these straight lines can have.
For example, if n=2, the number of possible intersections is 0 (parallel) or 1 (not parallel).InputThe input data consists of multiple test instances, one row per test instance, each containing a positive integer n (n<=20), and n representing the number of lines.OutputEach test instance corresponds to a row of output, from small to large listing all intersecting scenarios, where each number is the number of possible intersections, separated by a space between the integers in each line.Sample Input

23

Sample Output

0 10 2 3

1 lines: 0 2 lines: 0 1 3 lines: 0 2 3 4 Lines: 0 3 4 5 6 ... The line can be divided into two groups, the first group is parallel to each other straight lines, the second group is a free line, free straight line is not parallel with parallel lines; Set the line is always n, set the first group has I line, then the second group N-i a straight line. analyzed by 4 lines: 1, when i=4,n-i=0, the number of intersections: 0 2, when I=3,n-i=1, the number of intersections: 3 Parallel lines and 1 free line intersection number + 1 free line can form the number of intersections, that is 3+0=3 3, when i=2,n-i=2, the number of intersections: 2*2+{0,1}={4,5} 4, when i=1,n-i=3, the number of intersections: 1*3+{0,2,3}={3,5,6} each free line has an intersection with each parallel line, and the number of intersections of the J free and I parallel lines is j*i, so the intersection of the n lines equals the intersections of the free and parallel lines plus the intersections formed within the free line

1#include <cstdio>2#include <string.h>3 intMain ()4 {5     intN,i,,k, Free;6     intd[ -][ $];//D[i][j] Indicates that the I line has a J intersection Point7memset (D,0,sizeof(d));8      for(i =1; I < +; i++)9     {Tenc[n][0]=1;//An intersection of 0 always exists One          for( Free=0; Free<= i; Free++)//free represents the number of straight lines A         { -              for(k =0; K < Free*( Free+1)/2; k++) -             { the                 if(d[ Free][k] = =1)         -                 { -d[i][ Free* (I- Free) +k]=1;//free* (i-free) +k indicates the number of intersections of the free straight line of the I line (k is the number of intersections of the free line) -                 } +             } -         } +     } A      while(SCANF ("%d", &n)! =EOF) at     { -          for(i =0; I <= N (n1)/2; i++) -         { -             if(i = =0) -printf"0"); -             Else in             { -                 if(D[n][i]) to                 { +printf"%d", i); -                 } the             } *         } $printf"\ n");Panax Notoginseng     } -     return 0; the}

Hangzhou Electric 1466 Calculate the line of intersection