Improve ids function reusing smaller ids to construct large ones

Fixes: #5

Author: DzyubSpirit

Exercises/1-ids.js

@@ -1,20 +1,84 @@
 'use strict';
 
-const ids = function* () {
-  const free = ['0'];
-  const prepared = { has: false, value: '' };
-
-  while (true) {
-    if (prepared.has) {
-      prepared.has = false;
-      yield prepared.value;
+const allCombinations = function* (arrs) {
+  const ixs = new Array(arrs.length).fill(0);
+  const combination = arrs.map(arr => arr[0]);
+
+  const incIx = i => {
+    ixs[i]++;
+    combination[i] = arrs[i][ixs[i]];
+  };
+
+  const resetIx = i => {
+    ixs[i] = 0;
+    combination[i] = arrs[i][ixs[i]];
+  };
+
+  while (ixs[0] < arrs[0].length) {
+    yield combination.join('');
+
+    let i = ixs.length - 1;
+    incIx(i);
+
+    while (i > 0 && ixs[i] === arrs[i].length) {
+      incIx(i - 1);
+      resetIx(i);
+      i--;
+    }
+  }
+};
+
+const greedySizes = (totalSize, sizesInCache) => {
+  const sizes = [];
+  let i = sizesInCache.length - 1;
+  while (totalSize > 0) {
+    while (sizesInCache[i] > totalSize) {
+      i--;
+    }
+
+    while (totalSize >= sizesInCache[i]) {
+      totalSize -= sizesInCache[i];
+      sizes.push(sizesInCache[i]);
+    }
+  }
+  return sizes;
+};
+
+const mapGen = function* (g, f) {
+  for (const el of g) {
+    yield f(el);
+  }
+};
+
+const prependOne = s => '1' + s;
+
+const ids = function* (maxSizeInCache = 20, cache = {}) {
+  if (!(1 in cache)) {
+    cache[1] = ['00', '10'];
+  }
+
+  let sizesInCache = Object.keys(cache).sort();
+  for (let size = 1; ; size++) {
+    if (size in cache) {
+      yield* mapGen(cache[size], prependOne);
+      continue;
+    }
+
+    const combinationGroups = greedySizes(size, sizesInCache)
+      .map(size => cache[size]);
+    const combinations = allCombinations(combinationGroups);
+
+    if (size > maxSizeInCache) {
+      yield* mapGen(combinations, prependOne);
+      continue;
+    }
+
+    cache[size] = [];
+    for (const combination of combinations) {
+      cache[size].push(combination);
+      yield prependOne(combination);
     }
-    const nextFree = free.shift();
-    free.push('01' + nextFree);
-    free.push('00' + nextFree);
-    prepared.value = '11' + nextFree;
-    prepared.has = true;
-    yield '10' + nextFree;
+    sizesInCache = Object.keys(cache).sort();
   }
 };