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gistfile1.js

// http://www.facebook.com/groups/javascript.tw/194457013988978/

var n2ed = [ [ [0, 1], [1, 1] ], [ [0, 0], [1, 0], [2, 2], [3, 2] ], [ [2, 1], [3, 1] ] ];

function comp(val, edge) {
    if (edge == 0) return val + 7;
    if (edge == 1) return val / 2;
    if (edge == 2) return val * 3;
    if (edge == 3) return val - 5;
}

function go(node, val, prevEdge, depth) {
    if (val == 2012 && node == 2)
        return " ";
    if (depth++ == 30)
        return;
    for (var i = 0; i < n2ed[node].length; i++) {
        var edge = n2ed[node][i][0];
        var dest = n2ed[node][i][1];
        if (edge != prevEdge) {
            var rtn = go(dest, comp(val, edge), edge, depth);
            if (rtn)
               return ['+7', '/2', '*3', '-5'][edge] + " " + rtn;
        }
    }
}
console.log(go(0, 2011, null, 0));