feat(pascal): create exercise

19_pascal/README.md

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+# Exercise 19 - pascal
+
+The pascal's triangle is modelled as follows:
+- The first row is `1`.
+- Each row can be considered to have a hidden `0` to either sides of it. So the first row could
+also be said to be `0, 1, 0`
+- To obtain the next row, we take each number and add it with its rightmost neighbor.
+
+First row: `[1]`
+Second row: `[0+1, 1+0]` or simply `[1, 1]`
+Third row: `[0+1, 1+1, 1+0]` or simply `[1, 2, 1]`
+Fourth row: `[0+1, 1+2, 2+1, 1+0]` or simply `[1, 3, 3, 1]`
+... 
+
+The pattern continues forever.
+
+Your task is to create a *recursive* function, `pascal` - that will take an input `n` and output the 
+`n`th pascal's row.

19_pascal/pascal.js

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+const pascal = function() {
+
+};
+
+// Do not edit below this line
+module.exports = pascal;

19_pascal/pascal.spec.js

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+const pascal = require('./pascal');
+
+describe('pascal', () => {
+  test('Gets the first row of pascal', () => {
+    expect(pascal(1)).toEqual([1]);
+  });
+
+  test.skip('Gets the second row of pascal', () => {
+    expect(pascal(2)).toEqual([1, 1]);
+  });
+
+  test.skip('Gets the third row of pascal', () => {
+    expect(pascal(3)).toEqual([1, 2, 1]);
+  });
+
+  test.skip('Gets the fourth row of pascal', () => {
+    expect(pascal(4)).toEqual([1, 3, 3, 1]);
+  });
+
+  test.skip('Gets the fifth row of pascal', () => {
+    expect(pascal(5)).toEqual([1, 4, 6, 4, 1]);
+  });
+
+  test.skip('Gets the sixth row of pascal', () => {
+    expect(pascal(6)).toEqual([1, 5, 10, 10, 5, 1]);
+  });
+
+  test.skip('Gets the seventh row of pascal', () => {
+    expect(pascal(7)).toEqual([1, 6, 15, 20, 15, 6, 1]);
+  });
+});

19_pascal/solution/pascal-solution.js

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+const pascal = function (counter, currentLine = [1]) {
+  if (counter === 1) {
+    return currentLine;
+  }
+
+  const halfOfNextLine = currentLine.reduce(
+    (numbers, currentNumber, index) => {
+      const nextNumber = currentLine[index + 1];
+      if (currentNumber <= nextNumber) {
+        return [...numbers, currentNumber + nextNumber];
+      }
+      return numbers;
+    },
+    [1],
+  );
+
+  // Notice that pascal triangle's lines are always palindromic in nature.
+  // We only need the first half to obtain the information to construct the second half
+  const joined = [...halfOfNextLine, ...halfOfNextLine.reverse()];
+
+  // If a given line of the pascal's triangle has an even amount of elements, two things are true:
+  // - the next line will have an odd amount of elements
+  // - the two elements in the middle will always be the same. So it's safe to remove one
+  if (currentLine.length % 2 === 0) {
+    joined.splice(joined.length / 2, 1);
+  }
+
+  return pascal(counter - 1, joined);
+};
+
+// Do not edit below this line
+module.exports = pascal;

19_pascal/solution/pascal-solution.spec.js

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+const pascal = require('./pascal-solution');
+
+describe('pascal', () => {
+  test('Gets the first row of pascal', () => {
+    expect(pascal(1)).toEqual([1]);
+  });
+
+  test('Gets the second row of pascal', () => {
+    expect(pascal(2)).toEqual([1, 1]);
+  });
+
+  test('Gets the third row of pascal', () => {
+    expect(pascal(3)).toEqual([1, 2, 1]);
+  });
+
+  test('Gets the fourth row of pascal', () => {
+    expect(pascal(4)).toEqual([1, 3, 3, 1]);
+  });
+
+  test('Gets the fifth row of pascal', () => {
+    expect(pascal(5)).toEqual([1, 4, 6, 4, 1]);
+  });
+
+  test('Gets the sixth row of pascal', () => {
+    expect(pascal(6)).toEqual([1, 5, 10, 10, 5, 1]);
+  });
+
+  test('Gets the seventh row of pascal', () => {
+    expect(pascal(7)).toEqual([1, 6, 15, 20, 15, 6, 1]);
+  });
+});