Resistor mesh

Resistor mesh is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Given 10 × 10 grid nodes interconnected by 1Ω resistors as shown, find the resistance between point A and B.

See also [[1]]

C

<lang c>#include <stdio.h>

1. include <stdlib.h>

1. define S 10

typedef struct { double v; int fixed; } node;

1. define each(i, x) for(i = 0; i < x; i++)

node **alloc2(int w, int h) { int i; node **a = calloc(1, sizeof(node*)*h + sizeof(node)*w*h); each(i, h) a[i] = i ? a[i-1] + w : (node*)(a + h); return a; }

void set_boundary(node **m) { m[1][1].fixed = 1; m[1][1].v = 1; m[6][7].fixed = -1; m[6][7].v = -1; }

double calc_diff(node **m, node **d, int w, int h) { int i, j, n; double v, total = 0; each(i, h) each(j, w) { v = 0; n = 0; if (i) v += m[i-1][j].v, n++; if (j) v += m[i][j-1].v, n++; if (i+1 < h) v += m[i+1][j].v, n++; if (j+1 < w) v += m[i][j+1].v, n++;

d[i][j].v = v = m[i][j].v - v / n; if (!m[i][j].fixed) total += v * v; } return total; }

double iter(node **m, int w, int h) { node **d = alloc2(w, h); int i, j; double diff = 1e10; double cur[] = {0, 0, 0};

while (diff > 1e-24) { set_boundary(m); diff = calc_diff(m, d, w, h); each(i,h) each(j, w) m[i][j].v -= d[i][j].v; }

each(i, h) each(j, w) cur[ m[i][j].fixed + 1 ] += d[i][j].v * (!!i + !!j + (i < h-1) + (j < w -1));

free(d); return (cur[2] - cur[0])/2; }

int main() { node **mesh = alloc2(S, S); printf("R = %g\n", 2 / iter(mesh, S, S)); return 0; }</lang>

Perl 6

Translation of: c

<lang perl6>my $S = 10;

my @fixed;

sub allocmesh ($w, $h) {

   gather for ^$h {

take [0 xx $w];

   }

}

sub force-fixed(@f) {

   @f[1][1] =  1;
   @f[6][7] = -1;

}

sub force-v(@v) {

   @v[1][1] =  1;
   @v[6][7] = -1;

}

sub calc_diff(@v, @d, Int $w, Int $h) { my $total = 0; for ^$h X ^$w -> $i, $j { my @neighbors = grep *.defined, @v[$i-1][$j], @v[$i][$j-1], @v[$i+1][$j], @v[$i][$j+1]; my $v = [+] @neighbors;

@d[$i][$j] = $v = @v[$i][$j] - $v / +@neighbors; $total += $v * $v unless @fixed[$i][$j]; } return $total; }

sub iter(@v, Int $w, Int $h) { my @d = allocmesh($w, $h); my $diff = 1e10; my @cur = 0, 0, 0;

while $diff > 1e-24 { force-v(@v); $diff = calc_diff(@v, @d, $w, $h); for ^$h X ^$w -> $i, $j { @v[$i][$j] -= @d[$i][$j]; } }

for ^$h X ^$w -> $i, $j { @cur[ @fixed[$i][$j] + 1 ] += @d[$i][$j] * (?$i + ?$j + ($i < $h - 1) + ($j < $w - 1)); }

return (@cur[2] - @cur[0]) / 2; }

my @mesh = allocmesh($S, $S);

@fixed = allocmesh($S, $S); force-fixed(@fixed);

say 2 / iter(@mesh, $S, $S);</lang> Output:

1.60899124172989