feat: Pascal's Triangle (TheAlgorithms#121)

* feat(data-struct): binary search tree

* fix: improvements part 1

* fix: improvements part 2

* Fix failing tests

* feat: pascals triangle

---------

Co-authored-by: Lars Müller <[email protected]>

Author: zFlxw

maths/pascals_triangle.ts

@@ -0,0 +1,40 @@
+/**
+ * Pascal's Triangle is an array of binomial coefficients. It can be used for unwrapping terms like
+ * (a + b)^5.
+ * To construct Pascal's Triangle you add the numbers above the child entry together. Here are the first five rows:
+ *     1
+ *    1 1
+ *   1 2 1
+ *  1 3 3 1
+ * 1 4 6 4 1
+ *
+ * Time Complexity: quadratic (O(n^2)).
+ *
+ * @param n The exponent / The index of the searched row.
+ * @returns The nth row of Pascal's Triangle
+ * @see https://en.wikipedia.org/wiki/Pascal's_triangle
+ */
+export const pascalsTriangle = (n: number): number[] => {
+  let arr: number[][] = [];
+  for (let i: number = 0; i < n; i++) {
+    if (i === 0) {
+      arr.push([1]);
+      continue;
+    }
+
+    let lastRow: number[] = arr[i - 1];
+    let temp: number[] = [];
+    for (let j: number = 0; j < lastRow.length + 1; j++) {
+      if (j === 0 || j === lastRow.length) {
+        temp.push(1);
+        continue;
+      }
+
+      temp.push(lastRow[j - 1] + lastRow[j]);
+    }
+
+    arr.push(temp);
+  }
+
+  return arr[arr.length - 1];
+};

maths/test/pascals_triangle.test.ts

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+import { pascalsTriangle } from "../pascals_triangle";
+
+describe('pascalsTriangle', () => {
+  it.each([
+    [2, [1, 1]],
+    [4, [1, 3, 3, 1]],
+    [6, [1, 5, 10, 10, 5, 1]],
+  ])('The %i th row should equal to %i', (n, expectation) => {   
+    expect(pascalsTriangle(n)).toEqual(expectation);
+  });
+});