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>