Knight's Shortest Path on Chessboard

Question

I\'ve been practicing for an upcoming programming competition and I have stumbled across a question that I am just completely bewildered at. However, I feel as though it\'s

Answer 1

Here is a C version based on Mustafa Serdar Şanlı code that works for a finit board:

#include 
#include 

#define test(x1, y1, x2, y2) (sx == x1 && sy == y1 &&tx == x2 &&ty == y2) || (sx == x2 && sy == y2 && tx == x1 && ty==y1)

int distance(int sx, int sy, int tx, int ty) {
    int x, y, t;
    double delta;

    // special corner cases 
    if (test(1, 1, 2, 2) || 
        test(7, 7, 8, 8) || 
        test(7, 2, 8, 1) || 
        test(1, 8, 2, 7))
        return 4;

    // axes symmetry 
    x = abs(sx - tx);
    y = abs(sy - ty);

    // diagonal symmetry 
    if (x < y) {
        t = x;
        x = y;
        y = t;
    }

    // 2 corner cases
    if (x == 1 && y == 0)
        return 3;
    if (x == 2 && y == 2)
        return 4;

    // main
    delta = x - y;
    if (y > delta) {
        return (int)(delta - 2 * floor((delta - y) / 3));
    }
    else {
        return (int)(delta - 2 * floor((delta - y) / 4));
    }
}

Test it here with proof against a recursive solution