fix: fixed error in the MaxProductOfThree algorithm (TheAlgorithms#1295)

* fix: fixed error in the MaxProductOfThree algorithm

Fixed the error in the MaxProductOfThree by initializing the max and min
variables to null instead of -1. The checks were then altered to check
for null instead of -1.

Also wrote more tests, which randomly generated small arrays and
compared the output of the maxProductOfThree-algorithm to the output of
a slower, but complete, function which calculates all posible
triple-products of the values of the array.

Fixes: TheAlgorithms#1294

* fix: Added newlines at the end of the files

Author: Xolvez

Diff for: Dynamic-Programming/MaxProductOfThree.js

@@ -10,25 +10,25 @@ export function maxProductOfThree (arrayItems) {
   const n = arrayItems.length
   if (n < 3) throw new Error('Triplet cannot exist with the given array')
   let max1 = arrayItems[0]
-  let max2 = -1
-  let max3 = -1
+  let max2 = null
+  let max3 = null
   let min1 = arrayItems[0]
-  let min2 = -1
+  let min2 = null
   for (let i = 1; i < n; i++) {
     if (arrayItems[i] > max1) {
       max3 = max2
       max2 = max1
       max1 = arrayItems[i]
-    } else if (max2 === -1 || arrayItems[i] > max2) {
+    } else if (max2 === null || arrayItems[i] > max2) {
       max3 = max2
       max2 = arrayItems[i]
-    } else if (max3 === -1 || arrayItems[i] > max3) {
+    } else if (max3 === null || arrayItems[i] > max3) {
       max3 = arrayItems[i]
     }
     if (arrayItems[i] < min1) {
       min2 = min1
       min1 = arrayItems[i]
-    } else if (min2 === -1 || arrayItems[i] < min2) {
+    } else if (min2 === null || arrayItems[i] < min2) {
       min2 = arrayItems[i]
     }
   }

Diff for: Dynamic-Programming/tests/MaxProductOfThree.test.js

@@ -15,3 +15,56 @@ describe('MaxProductOfThree', () => {
     expect(maxProductOfThree([10, -6, 5, 3, 1, -10])).toBe(600)
   })
 })
+
+// Tests using random arrays of size 3 to 5, with values rangin from -4 to 4
+// The output is compared to a slower function that calculates all possible products of 3 numbers in the array and returns the largest one
+describe('MaxProductOfThree, random arrays of size 3 to 5', () => {
+  // Slower function that operates in O(n^3), where n is the length of the input array.
+  // Calculates all possible products of 3 numbers in the array and returns the largest
+  function completeMaxThree (array) {
+    let maximumProduct = null
+    for (let i = 0; i < array.length - 2; i++) {
+      for (let j = i + 1; j < array.length - 1; j++) {
+        for (let k = j + 1; k < array.length; k++) {
+          const currentProduct = array[i] * array[j] * array[k]
+          if (maximumProduct === null || currentProduct > maximumProduct) {
+            maximumProduct = currentProduct
+          }
+        }
+      }
+    }
+    return maximumProduct
+  }
+
+  // Set up consts for the tests
+  const maxValue = 4
+  const minValue = -4
+  const maxLength = 5
+  const minLength = 3
+  const numberOfRandomTests = 5000
+
+  // Run each test
+  for (let i = 0; i < numberOfRandomTests; i++) {
+    const arr = []
+    // Randomize the length of the array in the current test
+    const length = Math.floor(Math.random() * (maxLength - minLength) + minLength)
+
+    // Fill the array with random values in the specified range
+    for (let j = 0; j < length + 1; j++) {
+      arr.push(Math.floor(Math.random() * (maxValue - minValue) + minValue))
+    }
+
+    // Calculate the actual max product, slow but completely
+    const expectedProduct = completeMaxThree(arr)
+
+    // Set up the expectation
+    it('Expect the array ' + arr.toString() + ' to return the maximum three product of ' + expectedProduct, () => {
+      // Calculate the max three product using the function being tested
+      const actualProduct = maxProductOfThree(arr)
+
+      // Was unable to use expect().toBe(), since it sometimes compared 0 to -0, and that would not pass
+      // At the same time, standardjs forbid me from checking for === -0 to convert to 0
+      expect(actualProduct === expectedProduct).toBeTruthy()
+    })
+  }
+})