add all the stuffHEADmain

1 files changed, 151 insertions, 0 deletions

diff --git a/examples/sum_of_even_squares.ts b/examples/sum_of_even_squares.ts
new file mode 100644
index 0000000..b4c1aad
--- /dev/null
+++ b/examples/sum_of_even_squares.ts
@@ -0,0 +1,151 @@
+const isEven = (n: number) => {
+  let even = true; // 0 is even
+
+  for (let i = 1; i <= n; i++) {
+    even = !even;
+  }
+
+  return even;
+};
+
+const sumOfEvenSquares = (upTo: number) => {
+  let sum = 0;
+
+  for (let i = 1; i <= upTo; i++) {
+    if (isEven(i)) {
+      sum += i * i;
+    }
+  }
+
+  return sum;
+};
+
+/**
+ * functional
+ */
+
+const isEvenHelper = (curr: number, max: number, previous = false) => {
+  if (curr === max) {
+    return !previous;
+  }
+
+  return isEvenHelper(curr + 1, max, !previous);
+};
+
+const isEvenFn = (n: number) => {
+  return isEvenHelper(0, n);
+};
+
+const map = (
+  transform: (x: number, ind: number) => number,
+  list: number[],
+  index = 0,
+) => {
+  if (list.length === 0) {
+    return [];
+  }
+  const [head, ...tail] = list;
+  const transformed = transform(head, index);
+
+  return [transformed].concat(map(transform, tail, index + 1));
+};
+
+const filter = (predicate: (x: number) => boolean, list: number[]) => {
+  if (list.length === 0) {
+    return [];
+  }
+
+  const [head, ...tail] = list;
+  if (predicate(head)) {
+    return [head].concat(filter(predicate, tail));
+  }
+  return filter(predicate, tail);
+};
+
+const reduce = (
+  accumulation: (x: number, accumulator: number) => number,
+  accumulator: number,
+  list: number[],
+) => {
+  if (list.length === 0) {
+    return accumulator;
+  }
+
+  const [head, ...tail] = list;
+  const newAccumulator = accumulation(head, accumulator);
+  return reduce(accumulation, newAccumulator, tail);
+};
+
+const curriedReduce = (
+  accumulation: (x: number, accumulator: number) => number,
+) => {
+  return (accumulator: number) => {
+    const reduce = (list: number[]) => {
+      if (list.length === 0) {
+        return accumulator;
+      }
+
+      const [head, ...tail] = list;
+      const newAccumulator = accumulation(head, accumulator);
+
+      return curriedReduce(accumulation)(newAccumulator)(tail);
+    };
+
+    return reduce;
+  };
+};
+
+const sum = curriedReduce((x, acc) => x + acc)(0);
+
+const sumOfEvenSquaresFn = (upTo: number) => {
+  const numbersUpTo = Array(upTo + 1)
+    .fill(0)
+    .map((_, i) => i);
+  const squares = numbersUpTo.filter((x) => isEvenFn(x)).map((x) => x * x);
+
+  return sum(squares);
+};
+
+/**
+ * test
+ */
+
+const assert = (predicate: () => boolean, message: string) => {
+  const start = performance.now();
+
+  console.log(message + "...");
+  const result = predicate();
+
+  const runtimeFmt = ` in ${(performance.now() - start).toFixed(5)}ms`;
+  if (result) {
+    console.log("  ... PASSED" + runtimeFmt);
+    return;
+  }
+
+  console.error("  ... FAILED" + runtimeFmt);
+  throw new Error("predicate failed for test: " + message);
+};
+
+/*
+  Σ(2i)^2 = 4 * Σ(i)^2 = 4 * (n * (n + 1) * (2 * n + 1)) / 6
+ */
+const constantTimeMathMagic = (x: number) => {
+  const n = Math.floor(x / 2); // even numbers
+  return (4 * (n * (n + 1) * (2 * n + 1))) / 6;
+};
+
+const test = (sumEvenSquarer: (x: number) => number) => {
+  assert(() => sumEvenSquarer(5) === 2 ** 2 + 4 ** 2, "up to 5");
+  assert(
+    () => sumEvenSquarer(10) === 2 ** 2 + 4 ** 2 + 6 ** 2 + 8 ** 2 + 10 ** 2,
+    "up to 10",
+  );
+
+  //assert(
+  //  () => sumEvenSquarer(75_000) === constantTimeMathMagic(75_000),
+  //  "up to 75,000",
+  //);
+};
+
+test(sumOfEvenSquares);
+test(sumOfEvenSquaresFn);