Add rain-terraces (trapping rain water) algorithm (trekhleb#112)

* Add rain-terraces (trapping rain water) algorithm

* Fixed linting errors

* Fixed linting errors

Author: ObiWanKeoni

src/algorithms/uncategorized/rain-terraces/README.md

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+# Rain Terraces (Trapping Rain Water) Problem
+
+Given an array of non-negative integers representing terraces in an elevation map where the width of each bar is 1, compute how much water it is able to trap after raining.
+
+![Rain Terraces](https://www.geeksforgeeks.org/wp-content/uploads/watertrap.png)
+
+## Examples
+
+**Example #1**
+
+```
+Input: arr[]   = [2, 0, 2]
+Output: 2
+Structure is like below
+| |
+|_|
+We can trap 2 units of water in the middle gap.
+```
+
+**Example #2**
+
+```
+Input: arr[]   = [3, 0, 0, 2, 0, 4]
+Output: 10
+Structure is like below
+     |
+|    |
+|  | |
+|__|_| 
+We can trap "3*2 units" of water between 3 an 2,
+"1 unit" on top of bar 2 and "3 units" between 2 
+and 4.  See below diagram also.
+```
+
+**Example #3**
+
+```
+Input: arr[] = [0, 1, 0, 2, 1, 0, 1, 3, 2, 1, 2, 1]
+Output: 6
+       | 
+   |   || |
+_|_||_||||||
+Trap "1 unit" between first 1 and 2, "4 units" between
+first 2 and 3 and "1 unit" between second last 1 and last 2 
+```
+
+## Algorithms
+
+
+
+## References
+
+- [GeeksForGeeks](https://www.geeksforgeeks.org/trapping-rain-water/)

src/algorithms/uncategorized/rain-terraces/rainTerraces.js

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+/**
+ * @param {number[]} terraces
+ * @return {number}
+ */
+
+/*
+ * STEPS
+ * 1. Find the highest terraces on the left and right side of the elevation map:
+ * e.g. [0, 2, 4, 3, 1, 2, 4, 0, 8, 7, 0] => (leftMax = 4, rightMax = 8)
+ * This is because water will "trail off" the sides of the terraces.
+ *
+ * 2. At this point, we are essentially dealing with a new map: [4, 3, 4, 2, 4, 0, 8].
+ * From here, we loop through the map from the left to the right (if leftMax > rightMax,
+ * otherwise we move from right to left), adding water as we go unless we reach a value
+ * that is greater than or equal to leftMax || rightMax.
+ * e.g. [4, 3, 4, 2, 4, 0, 8]
+ *             ^
+ * water += leftMax - 3 => water = 1
+ * or if the terrace array was reversed:
+ * e.g. [8, 0, 4, 2, 4, 3, 4]
+ *                   ^
+ * water += rightMax - 3 => water = 1
+ *
+ * 3. Again, we've essentially shortened the map: [4, 2, 4, 0, 8].
+ * Now we repeat the above steps on the new array.
+ * e.g.
+ * Next Iteration:
+ * [4, 2, 4, 0, 8]
+ *        ^
+ * water += leftMax - 2 => water = 3
+ *
+ * Next Iteration:
+ * [4, 0, 8]
+ *        ^
+ * water += leftMax - 0 => water = 7
+ *
+ * return water(7)
+ */
+export default function rainTerraces(terraces) {
+  let start = 0;
+  let end = terraces.length - 1;
+  let water = 0;
+  let leftMax = 0;
+  let rightMax = 0;
+
+  while (start < end) {
+    // Loop to find left max
+    while (start < end && terraces[start] <= terraces[start + 1]) {
+      start += 1;
+    }
+    leftMax = terraces[start];
+
+    // Loop to find right max
+    while (end > start && terraces[end] <= terraces[end - 1]) {
+      end -= 1;
+    }
+    rightMax = terraces[end];
+
+    // Determine which direction we need to move in
+    if (leftMax < rightMax) {
+      // Move from left to right and collect water
+      start += 1;
+      while (start < end && terraces[start] <= leftMax) {
+        water += leftMax - terraces[start];
+        start += 1;
+      }
+    } else {
+      // Move from left to right and collect water
+      end -= 1;
+      while (end > start && terraces[end] <= rightMax) {
+        water += rightMax - terraces[end];
+        end -= 1;
+      }
+    }
+  }
+  return water;
+}

src/algorithms/uncategorized/rain-terraces/spec/rainTerraces.test.js

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+import rainTerraces from '../rainTerraces';
+
+describe('rainTerraces', () => {
+  it('should find the amount of water collected after raining', () => {
+    expect(rainTerraces([2, 0, 2])).toBe(2);
+    expect(rainTerraces([3, 0, 0, 2, 0, 4])).toBe(10);
+    expect(rainTerraces([0, 1, 0, 2, 1, 0, 1, 3, 2, 1, 2, 1])).toBe(6);
+    expect(rainTerraces([1, 1, 1, 1, 1])).toBe(0);
+    expect(rainTerraces([1, 2, 3, 4, 5])).toBe(0);
+    expect(rainTerraces([4, 1, 3, 1, 2, 1, 2, 1])).toBe(4);
+  });
+});