Merge pull request #17 from sir-gon/feature/problem0004

Feature/problem0004

Author: sir-gon

src/helpers/index.ts

@@ -1,2 +1,6 @@
+type nullable<T> = T | null | undefined;
+
 export { divisors } from './divisors';
 export { isPrime } from './prime';
+export { isPalindrome } from './isPalindrome';
+export { nullable };

src/helpers/isPalindrome.test.ts

@@ -0,0 +1,12 @@
+import { isPalindrome } from './isPalindrome';
+
+describe('number is Palindrome', () => {
+  it('some numbers are palindrome', () => {
+    expect.assertions(4);
+
+    expect(isPalindrome(1)).toBe(true);
+    expect(isPalindrome(131)).toBe(true);
+    expect(isPalindrome(1221)).toBe(true);
+    expect(isPalindrome(123454321)).toBe(true);
+  });
+});

src/helpers/isPalindrome.ts

@@ -0,0 +1,4 @@
+export const isPalindrome = (n: number): boolean =>
+  n.toString().split('').reverse().join('') === n.toString();
+
+export default { isPalindrome };

src/problem0004.test.ts

@@ -0,0 +1,32 @@
+/**
+ * Largest palindrome product
+ *
+ * https://projecteuler.net/problem=4
+ *
+ * A palindromic number reads the same both ways.
+ * The largest palindrome made from the product of two 2-digit
+ * numbers is 9009 = 91 × 99.
+ *
+ * Find the largest palindrome made from the product of two 3-digit numbers.
+ */
+
+import logger from './logger';
+
+import { problem0004 } from './problem0004';
+
+describe('problem 0004', () => {
+  it('problem 0004 solution found', () => {
+    expect.assertions(1);
+
+    const solutionFound = 906609;
+
+    const bottom = 111;
+    const top = 999;
+
+    const calculated = problem0004(bottom, top);
+
+    logger.info(`PROBLEM 0004 solution found: ${calculated}`);
+
+    expect(calculated).toBe(solutionFound);
+  });
+});

src/problem0004.ts

@@ -0,0 +1,69 @@
+/**
+ * Largest palindrome product
+ *
+ * https://projecteuler.net/problem=4
+ *
+ * A palindromic number reads the same both ways.
+ * The largest palindrome made from the product of two 2-digit
+ * numbers is 9009 = 91 × 99.
+ *
+ * Find the largest palindrome made from the product of two 3-digit numbers.
+ */
+
+/// ////////////////////////////////////////////////////////////////////////////
+// NOTES ABOUT THE SOLUTION:
+// This solution cycles to test all pairs of factors between 111 and 999 that meet the condition of generating a palindrome and saves the largest found.
+// I think there must be another optimal solution to avoid testing all cases
+// cutting the loop around the largest factor pair
+// That's why I thought about doing the loop from highest to lowest.
+/// ////////////////////////////////////////////////////////////////////////////
+
+/// ////////////////////////////////////////////////////////////////////////////
+
+import logger from './logger';
+
+import { nullable, isPalindrome } from './helpers/index';
+
+function problem0004(_bottom: number, _top: number): nullable<number> {
+  let i;
+  let j;
+  let foundi;
+  let foundj;
+  let foundPalindrome;
+
+  // Find all cases
+  let cycles = 0;
+
+  i = _top;
+  while (i >= _bottom) {
+    j = i;
+    while (j >= _bottom && (!foundj || j >= foundj)) {
+      cycles += 1;
+
+      if (isPalindrome(j * i)) {
+        logger.debug(`FOUND: ${i} x ${j} = ${j * i} is Palindrome`);
+
+        if (!foundPalindrome || i * j > foundPalindrome) {
+          foundi = i;
+          foundj = j;
+          foundPalindrome = i * j;
+        }
+      } else {
+        // console.log(`FOUND: ${i} x ${j} = ${j * i} is NOT Palindrome`);
+      }
+
+      j -= 1;
+    }
+
+    i -= 1;
+  }
+
+  logger.info(
+    `Problem 0004 Largest Palindrome  => ${foundi} 𝗑 ${foundj} = ${foundPalindrome} in ${cycles} cycles`
+  );
+
+  return foundPalindrome;
+}
+
+export default problem0004;
+export { problem0004 };