the "knights-dialer" problem

1.js

// https://medium.com/@alexgolec/google-interview-questions-deconstructed-the-knights-dialer-f780d516f029

function nearby(number) {
   return (
      number === 0 ? [4,6] :
      number == 1 ?  [6,8] :
      number == 2 ?  [7,9] :
      number == 3 ?  [4,8] :
      number == 4 ?  [3,9,0] :
      number == 6 ?  [1,7,0] :
      number == 7 ?  [2,6] :
      number == 8 ?  [1,3] :
      number == 9 ?  [2,4] :
      []
   );
}

var countPaths = memoize(countPaths);

function memoize(fn) {
   var cache = {};
   return function memoized(start,length){
      if (!cache[`${start}:${length}`]) {
         cache[`${start}:${length}`] = fn(start,length);
      }
      return cache[`${start}:${length}`];      
   };
}

function countPaths(startDigit,hopCount = 0) {
   if (hopCount == 0) return 1;
   var pathCount = 0;
   for (let digit of nearby(startDigit)) {
      pathCount += countPaths(digit,hopCount-1);
   }
   return pathCount;
}

function countPaths2(startDigit,hopCount = 0) {
   if (hopCount == 0) return 1;
   var priorPathCounts = Array(10).fill(1);
   var pathCounts;
   var hops = 1;
   while (hops <= hopCount) {
      pathCounts = Array(10).fill(0);
      hops++;
      for (let digit = 0; digit <= 9; digit++) {
         for (let n of nearby(digit)) {
            pathCounts[digit] += priorPathCounts[n];
         }
      }
      priorPathCounts = pathCounts;
   }
   return pathCounts[startDigit];
}


countPaths(1,50);     // 894498933328314400
countPaths2(1,50);    // 894498933328314400

2.js

function followPath(path) {
   let nextHops = nearby(path[path.length-1]);
   var pathForwardFound = false;
   for (let nextHop of nextHops) {
      if (!path.includes(nextHop)) {
         pathForwardFound = true;
         let nextPath = [...path,nextHop];
         followPath(nextPath);
      }
   }
   if (!pathForwardFound) {
      console.log(path);
      return;
   }
}

function uniqueDigitPaths() {
   for (let i = 0; i <= 9; i++) {
      let nextHops = nearby(i);
      for (let nextHop of nextHops) {
         let path = [i,nextHop];
         followPath(path);
      }
      console.log("");
   }
}

uniqueDigitPaths();
// [0, 4, 3, 8, 1, 6, 7, 2, 9]
// [0, 4, 9, 2, 7, 6, 1, 8, 3]
// [0, 6, 1, 8, 3, 4, 9, 2, 7]
// [0, 6, 7, 2, 9, 4, 3, 8, 1]

// [1, 6, 7, 2, 9, 4, 3, 8]
// [1, 6, 7, 2, 9, 4, 0]
// [1, 6, 0, 4, 3, 8]
// [1, 6, 0, 4, 9, 2, 7]
// [1, 8, 3, 4, 9, 2, 7, 6, 0]
// [1, 8, 3, 4, 0, 6, 7, 2, 9]

// [2, 7, 6, 1, 8, 3, 4, 9]
// [2, 7, 6, 1, 8, 3, 4, 0]
// [2, 7, 6, 0, 4, 3, 8, 1]
// [2, 7, 6, 0, 4, 9]
// [2, 9, 4, 3, 8, 1, 6, 7]
// [2, 9, 4, 3, 8, 1, 6, 0]
// [2, 9, 4, 0, 6, 1, 8, 3]
// [2, 9, 4, 0, 6, 7]

// [3, 4, 9, 2, 7, 6, 1, 8]
// [3, 4, 9, 2, 7, 6, 0]
// [3, 4, 0, 6, 1, 8]
// [3, 4, 0, 6, 7, 2, 9]
// [3, 8, 1, 6, 7, 2, 9, 4, 0]
// [3, 8, 1, 6, 0, 4, 9, 2, 7]

// [4, 3, 8, 1, 6, 7, 2, 9]
// [4, 3, 8, 1, 6, 0]
// [4, 9, 2, 7, 6, 1, 8, 3]
// [4, 9, 2, 7, 6, 0]
// [4, 0, 6, 1, 8, 3]
// [4, 0, 6, 7, 2, 9]

// [6, 1, 8, 3, 4, 9, 2, 7]
// [6, 1, 8, 3, 4, 0]
// [6, 7, 2, 9, 4, 3, 8, 1]
// [6, 7, 2, 9, 4, 0]
// [6, 0, 4, 3, 8, 1]
// [6, 0, 4, 9, 2, 7]

// [7, 2, 9, 4, 3, 8, 1, 6, 0]
// [7, 2, 9, 4, 0, 6, 1, 8, 3]
// [7, 6, 1, 8, 3, 4, 9, 2]
// [7, 6, 1, 8, 3, 4, 0]
// [7, 6, 0, 4, 3, 8, 1]
// [7, 6, 0, 4, 9, 2]

// [8, 1, 6, 7, 2, 9, 4, 3]
// [8, 1, 6, 7, 2, 9, 4, 0]
// [8, 1, 6, 0, 4, 3]
// [8, 1, 6, 0, 4, 9, 2, 7]
// [8, 3, 4, 9, 2, 7, 6, 1]
// [8, 3, 4, 9, 2, 7, 6, 0]
// [8, 3, 4, 0, 6, 1]
// [8, 3, 4, 0, 6, 7, 2, 9]

// [9, 2, 7, 6, 1, 8, 3, 4, 0]
// [9, 2, 7, 6, 0, 4, 3, 8, 1]
// [9, 4, 3, 8, 1, 6, 7, 2]
// [9, 4, 3, 8, 1, 6, 0]
// [9, 4, 0, 6, 1, 8, 3]
// [9, 4, 0, 6, 7, 2]