Add Rain Terraces problem.

Author: trekhleb

README.md

@@ -128,6 +128,7 @@ a set of rules that precisely define a sequence of operations.
   * `B` [Square Matrix Rotation](src/algorithms/uncategorized/square-matrix-rotation) - in-place algorithm
   * `B` [Jump Game](src/algorithms/uncategorized/jump-game) - backtracking, dynamic programming (top-down + bottom-up) and greedy examples 
   * `B` [Unique Paths](src/algorithms/uncategorized/unique-paths) - backtracking, dynamic programming and Pascal's Triangle based examples 
+  * `B` [Rain Terraces](src/algorithms/uncategorized/rain-terraces) - trapping rain water problem
   * `A` [N-Queens Problem](src/algorithms/uncategorized/n-queens)
   * `A` [Knight's Tour](src/algorithms/uncategorized/knight-tour)
 

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

@@ -2,11 +2,20 @@ import rainTerraces from '../rainTerraces';
 
 describe('rainTerraces', () => {
   it('should find the amount of water collected after raining', () => {
+    expect(rainTerraces([1])).toBe(0);
+    expect(rainTerraces([1, 0])).toBe(0);
+    expect(rainTerraces([0, 1])).toBe(0);
+    expect(rainTerraces([0, 1, 0])).toBe(0);
+    expect(rainTerraces([0, 1, 0, 0])).toBe(0);
+    expect(rainTerraces([0, 1, 0, 0, 1, 0])).toBe(2);
+    expect(rainTerraces([0, 2, 0, 0, 1, 0])).toBe(2);
     expect(rainTerraces([2, 0, 2])).toBe(2);
+    expect(rainTerraces([2, 0, 5])).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);
+    expect(rainTerraces([0, 2, 4, 3, 4, 2, 4, 0, 8, 7, 0])).toBe(7);
   });
 });

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

@@ -2,76 +2,84 @@
  * @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;
+  /*
+   * STEPS
+   *
+   * 1. Find the highest terraces on the left and right side of the elevation map:
+   * e.g. for [0, 2, 4, 3, 4, 2, 4, 0, 8, 7, 0] we would have leftMax = 4 and 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 or rightMax.
+   * e.g. [4, 3, 4, 2, 4, 0, 8]
+   *             ^
+   * water = water + (leftMax - 3) = 1
+   *
+   * or if the terrace array was reversed:
+   * e.g. [8, 0, 4, 2, 4, 3, 4]
+   *                   ^
+   * water = water + (rightMax - 3) = 1
+   *
+   * 3. Again, we've essentially shortened the map: [4, 2, 4, 0, 8].
+   * Now we repeat the above steps on the new array.
+   *
+   * Next Iteration:
+   * [4, 2, 4, 0, 8]
+   *        ^
+   * water = water + (leftMax - 2) = 3
+   *
+   * Next Iteration:
+   * [4, 0, 8]
+   *        ^
+   * water = water + (leftMax - 0) = 7
+   *
+   * 4. Return result: 7
+   */
+  let leftIndex = 0;
+  let rightIndex = terraces.length - 1;
+
+  let leftMaxLevel = 0;
+  let rightMaxLevel = 0;
 
-  while (start < end) {
-    // Loop to find left max
-    while (start < end && terraces[start] <= terraces[start + 1]) {
-      start += 1;
+  let waterAmount = 0;
+
+  while (leftIndex < rightIndex) {
+    // Loop to find the highest terrace from the left side.
+    while (leftIndex < rightIndex && terraces[leftIndex] <= terraces[leftIndex + 1]) {
+      leftIndex += 1;
     }
-    leftMax = terraces[start];
 
-    // Loop to find right max
-    while (end > start && terraces[end] <= terraces[end - 1]) {
-      end -= 1;
+    leftMaxLevel = terraces[leftIndex];
+
+    // Loop to find the highest terrace from the right side.
+    while (rightIndex > leftIndex && terraces[rightIndex] <= terraces[rightIndex - 1]) {
+      rightIndex -= 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;
+    rightMaxLevel = terraces[rightIndex];
+
+    // Determine which direction we need to go.
+    if (leftMaxLevel < rightMaxLevel) {
+      // Move from left to right and collect water.
+      leftIndex += 1;
+
+      while (leftIndex < rightIndex && terraces[leftIndex] <= leftMaxLevel) {
+        waterAmount += leftMaxLevel - terraces[leftIndex];
+        leftIndex += 1;
       }
     } else {
-      // Move from left to right and collect water
-      end -= 1;
-      while (end > start && terraces[end] <= rightMax) {
-        water += rightMax - terraces[end];
-        end -= 1;
+      // Move from right to left and collect water.
+      rightIndex -= 1;
+
+      while (leftIndex < rightIndex && terraces[rightIndex] <= rightMaxLevel) {
+        waterAmount += rightMaxLevel - terraces[rightIndex];
+        rightIndex -= 1;
       }
     }
   }
-  return water;
+
+  return waterAmount;
 }