Please help me with this. I am counting how many triangles I can find in the attached image.
Pl. see the attachment. I do not know how to do it the right way and please fix my code. I tried as best as I can to gather all points that make a line. Please show me a simpler way.
Thanks
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#!/usr/bin/perl

use strict;
# I listed as many points as I could find that make up a line
my @points = ([8,0], [8,22,57,120,211,330,477,642,1], [8,21,56,119,210,329,476,651,28,69,138,235,360,513,694,2], [8,20,55,118,209,328,475,650,27,68,137,234,359,512,693,33,79,153,271,405,567,757,3], [8,19,54,117,208,327,474,649,26,67,136,233,358,511,692,32,78,152,270,404,566,756,40,93,174,283,420,585,778,4], [8,18,53,116,207,326,473,648,25,66,135,232,357,510,691,31,77,151,269,403,565,755,39,92,173,282,419,584,777,42,97,180,291,430,597,792,5], [8,17,52,115,206,325,472,647,24,65,134,231,356,509,690,30,76,150,268,402,564,754,38,91,172,281,418,583,776,41,96,179,290,429,596,791,43,99,183,295,435,603,799,6], [8,16,51,114,205,324,471,646,23,64,133,230,355,508,689,29,75,149,267,401,563,753,37,90,171,280,417,582,775,40,95,178,289,428,595,790,42,98,182,294,434,602,798,9,10,11,12,13,14,15,7],
[9,16,17,18,19,20,21,22,0], [9,23,24,25,26,27,28,1], [9,29,30,31,32,33,2], [9,34,35,36,37,3], [9,38,39,40,4], [9,41,42,5], [9,43,6], [9,7],
[10,44,45,46,47,48,49,50,51,52,53,54,55,56,57,0], [10,58,59,60,61,62,63,64,65,66,67,68,69,1], [10,70,71,72,73,74,75,76,77,78,79,2], [10,80,81,82,83,84,85,86,87,3], [10,88,89,90,91,92,93,4], [10,94,95,96,97,5], [10,98,99,6], [10,7],
[11,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,0], [10,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,1], [11,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,2], [11,154,155,156,157,158,159,160,161,162,163,164,165,3], [11,166,167,168,169,170,171,172,173,174,4], [11,175,176,177,178,179,180,5], [11,181,182,183,6], [11,7],
[12,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,0], [12,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,27,228,229,230,231,232,233,234,235,1], [12,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,354,255,2], [12,256,257,258,259,260,261,262,23,264,265,266,267,268,269,270,271,3], [12,272,273,274,275,276,277,278,279,280,281,282,283,4], [12,284,285,286,287,288,289,290,291,5], [12,292,293,294,295,6], [12,7],
[13,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,32,328,329,330,0], [13,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,58,359,360,1], [13,361,362,363,364,365,366,367,368,369,370,371,37,373,374,375,376,377,378,379,380,381,382,383,384,385,2], [13,386..405,3], [13,406..420,4], [13,421,422,423,424,425,426,427,428,429,430,5], [13,431,432,433,434,435,6], [13,7],
[14,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,0], [14,478..513,1], [14,514..543,2], [14,544..567,3], [14,568,569,580,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,4], [14,586,587,588,589,590,591,592,593,594,595,596,597,5], [14,598,599,600,601,602,603,6], [14,7],
[15,604..652,0], [15,653..694,1], [15,695..729,2], [15,730..757,3], [15,758..778,4], [15,779,780,781,782,783,784,785,786,787,788,789,790,791,792,5], [15,793,794,795,796,797,798,799,6], [15,7]
);
my %triangles;
my @line;
my $lineNo=1;

# labelled thelines
for my $lineref (@points) {
for(my $i=0; $i<=$#{$lineref}; $i++) {
for(my $j=0; $j<=$#{$lineref}; $j++) {
next if $i==$j;
$line[$lineref->[$i]][$lineref->[$j]]=$lineNo;
$line[$lineref->[$j]][$lineref->[$i]]=$lineNo;
}
}
$lineNo++;
}

for(my $i=0; $i<800; $i++) {
for(my $j=0; $j<800; $j++) {
for(my $k=0; $k<800; $k++) {
# 3 points form a triangle if
# 1) not all on 1 straight line
# 2) each pair has common line
next if $i==$j || $i==$k || $j==$k;
next if(!$line[$i][$j] || !$line[$i][$k]
|| !$line[$j][$k]);
next if ($line[$i][$j]==$line[$i][$k]);
my @arr = sort ($i,$j,$k);
$triangles{$arr[0],$arr[1],$arr[2]}=1;
}
}
}
printf "No. of triangles %d\n", scalar keys %triangles;