calc.js

const next = (n) => [
    (n * 10) + 1,
    n + 12,
    n * 13,
    Math.floor(n / 10),
    parseInt(n.toString().split('').reverse().join(''), 10)
];

const open = [0];
const goal = 196;
const paths = {};

while (open.length > 0) {
    const curr = open.shift();
    const adj = next(curr);
    adj.forEach((p) => {
        if (paths[p] === undefined) {
            open.push(p);
            paths[p] = curr;
        }
    });
    if (paths[goal]) break;
}

const path = [];
let curr = goal;
do {
    path.push(curr);
    curr = paths[curr];
} while (curr !== 0)

console.log(path.reverse());