v12.0.0 - initial commit

packages/server/lib/coin-change.js

@@ -0,0 +1,104 @@
+/*
+ * Greedy solver of the coin change problem, based on the following CHICKEN
+ * implementation: https://git.sr.ht/~siiky/coin-change
+ */
+
+/*
+ * prepare_denominations([[d0, count], [d1, count], ...])
+ * => [{ denom, count, csum }, ...]
+ */
+const prepare_denominations = denominations =>
+  JSON.parse(JSON.stringify(denominations))
+    .filter(([, count]) => count > 0)
+    .sort(([d1], [d2]) => d1 - d2)
+    .reduce(
+      ([csum, denoms], [denom, count]) => {
+        csum += denom * count
+        return [csum, [{ denom, count, csum }].concat(denoms)]
+      },
+      [0, []],
+    )[1] /* ([csum, denoms]) => denoms */
+
+const max_denomination_multiplicity = (denom, count, target) =>
+  Math.min(count, Math.floor(target / denom))
+
+/*
+ * @returns null if there's no solution set;
+ *          false if there's no solution;
+ *          solution if there's a solution
+ */
+const memo_get = (memo, target, denom) => {
+  const denom_solutions = memo[target]
+  if (denom_solutions === undefined) return null
+  const solution = denom_solutions[denom]
+  return solution === undefined ? null : solution
+}
+
+const memo_set = (memo, target, denom, solution) => {
+  let denom_solutions = memo[target]
+  if (denom_solutions === undefined) memo[target] = denom_solutions = {}
+  return (denom_solutions[denom] = solution)
+}
+
+const check = (solution, target) =>
+  !solution ||
+  target ===
+    solution.reduce((sum, [denom, provisioned]) => sum + denom * provisioned, 0)
+
+const model = denominations => ({
+  denominations: prepare_denominations(denominations),
+  memo: {},
+})
+
+/*
+ * target :: Int
+ * denominations :: [[d0, count], [d1, count], ...]
+ *
+ * @returns [[d0, provisioned], [d1, provisioned], ... ];
+ *          false if there's no solution.
+ */
+const solve = (model, target) => {
+  const { denominations, memo } = model
+
+  const coin_change = (didx, target) => {
+    if (target === 0) return []
+
+    for (; didx < denominations.length; didx++) {
+      const { denom, count, csum } = denominations[didx]
+
+      /*
+       * There's no solution if the target is greater than the cumulative sum
+       * of the denominations, or if the target is not divisible by any of the
+       * denominations
+       */
+      if (target > csum) return memo_set(memo, target, denom, false)
+
+      let solution = memo_get(memo, target, denom)
+      if (solution === false) continue /* not here, keep looking */
+      if (solution) return solution /* we've previously computed a solution */
+
+      /* solution === null */
+      for (
+        let nd = max_denomination_multiplicity(denom, count, target);
+        nd >= 0;
+        nd--
+      ) {
+        solution = coin_change(didx + 1, target - denom * nd)
+        if (solution)
+          return memo_set(memo, target, denom, [[denom, nd]].concat(solution))
+      }
+
+      memo_set(memo, target, denom, false)
+    }
+
+    return false
+  }
+
+  return coin_change(0, target)
+}
+
+module.exports = {
+  check,
+  model,
+  solve,
+}