Problem 238 (#35)

* add initial solution

* add optimal solution

* update readme

Author: curtisbarnard

README.md

@@ -45,7 +45,7 @@ As I work through this list I figure I would make a GitHub repo with my solution
 34. [Course Schedule #207](https://github.com/curtisbarnard/leetcode-grind75-javascript/blob/main/medium/course-schedule-207.md)
 35. [Implement Trie (Prefix Tree) #208](https://github.com/curtisbarnard/leetcode-grind75-javascript/blob/main/medium/implement-trie-208.md)
 36. [Coin Change #322](https://github.com/curtisbarnard/leetcode-grind75-javascript/blob/main/medium/coin-change-322.md)
-37. Product of Array Except Self #238
+37. [Product of Array Except Self #238](https://github.com/curtisbarnard/leetcode-grind75-javascript/blob/main/medium/product-of-array-238.md)
 38. Min Stack #155
 39. Validate Binary Search Tree #98
 40. Number of Islands #200
@@ -110,6 +110,7 @@ In order to practice with similar data structures I'll be placing each problem i
 - [Maximum Units on a Truck #1710](https://github.com/curtisbarnard/leetcode-grind75-javascript/blob/main/easy/max-units-truck-1710.md)
 - [Meeting Rooms II](https://github.com/curtisbarnard/leetcode-grind75-javascript/blob/main/medium/meeting-rooms-ii-253.md)
 - [Coin Change #322](https://github.com/curtisbarnard/leetcode-grind75-javascript/blob/main/medium/coin-change-322.md)
+- [Product of Array Except Self #238](https://github.com/curtisbarnard/leetcode-grind75-javascript/blob/main/medium/product-of-array-238.md)
 
 ### Queue
 

medium/product-of-array-238.md

@@ -0,0 +1,98 @@
+# Product of Array Except Self
+
+Page on leetcode: https://leetcode.com/problems/product-of-array-except-self/
+
+## Problem Statement
+
+Given an integer array nums, return an array answer such that answer[i] is equal to the product of all the elements of nums except nums[i].
+
+The product of any prefix or suffix of nums is guaranteed to fit in a 32-bit integer.
+
+You must write an algorithm that runs in O(n) time and without using the division operation.
+
+### Constraints
+
+- 2 <= nums.length <= 105
+- -30 <= nums[i] <= 30
+- The product of any prefix or suffix of nums is guaranteed to fit in a 32-bit integer.
+
+### Example
+
+```
+Input: nums = [1,2,3,4]
+Output: [24,12,8,6]
+```
+
+```
+Input: nums = [-1,1,0,-3,3]
+Output: [0,0,9,0,0]
+```
+
+## Solution
+
+- Calculate the total product and store in variable
+- Iterate thru array a second time and subtrack product of current element
+- Can I store product left and right?
+- Will flipping or doing something in reverse work?
+
+### Initial Solution
+
+This solution has a time and space complexity of O(n).
+
+```javascript
+const productExceptSelf = function (nums) {
+  // Calculate left and right products
+  const left = [];
+  for (let i = 0; i < nums.length; i++) {
+    if (i > 0) {
+      const product = nums[i - 1] * left[left.length - 1];
+      left.push(product);
+    } else {
+      left.push(1);
+    }
+  }
+  const right = [];
+  for (let i = nums.length - 1; i >= 0; i--) {
+    if (i < nums.length - 1) {
+      const product = nums[i + 1] * right[0];
+      right.unshift(product);
+    } else {
+      right.unshift(1);
+    }
+  }
+  console.log(left, right);
+  // Calculate result based on what is left and right of current number
+  const answer = [];
+  for (let i = 0; i < nums.length; i++) {
+    answer.push(left[i] * right[i]);
+  }
+  return answer;
+};
+```
+
+### Optimized Solution
+
+This solution has O(n) time complexity and O(1) space complexity. You can see an explanation of this solution here: https://www.youtube.com/watch?v=bNvIQI2wAjk
+
+```javascript
+const productExceptSelf = function (nums) {
+  // Create initial array and put initial value of 1
+  const output = Array(nums.length).fill(1);
+
+  // Iterate thru nums and add prefixes to output
+  let prefix = 1;
+  for (let i = 0; i < nums.length; i++) {
+    output[i] = prefix;
+    prefix *= nums[i];
+  }
+
+  // Iterate thru nums backwards and calculate total with pre and post fix.
+  let postfix = 1;
+  for (let i = nums.length - 1; i >= 0; i--) {
+    output[i] *= postfix;
+    postfix *= nums[i];
+  }
+
+  return output;
+};
+```