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Commit f142ca0

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ObiWanKeonitrekhleb
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Add rain-terraces (trapping rain water) algorithm (trekhleb#112)
* Add rain-terraces (trapping rain water) algorithm * Fixed linting errors * Fixed linting errors
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# Rain Terraces (Trapping Rain Water) Problem
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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.
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![Rain Terraces](https://www.geeksforgeeks.org/wp-content/uploads/watertrap.png)
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## Examples
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**Example #1**
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```
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Input: arr[] = [2, 0, 2]
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Output: 2
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Structure is like below
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| |
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|_|
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We can trap 2 units of water in the middle gap.
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```
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**Example #2**
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```
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Input: arr[] = [3, 0, 0, 2, 0, 4]
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Output: 10
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Structure is like below
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|
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| |
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| | |
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|__|_|
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We can trap "3*2 units" of water between 3 an 2,
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"1 unit" on top of bar 2 and "3 units" between 2
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and 4. See below diagram also.
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```
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**Example #3**
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```
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Input: arr[] = [0, 1, 0, 2, 1, 0, 1, 3, 2, 1, 2, 1]
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Output: 6
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|
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| || |
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_|_||_||||||
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Trap "1 unit" between first 1 and 2, "4 units" between
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first 2 and 3 and "1 unit" between second last 1 and last 2
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```
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## Algorithms
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## References
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- [GeeksForGeeks](https://www.geeksforgeeks.org/trapping-rain-water/)
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/**
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* @param {number[]} terraces
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* @return {number}
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*/
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/*
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* STEPS
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* 1. Find the highest terraces on the left and right side of the elevation map:
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* e.g. [0, 2, 4, 3, 1, 2, 4, 0, 8, 7, 0] => (leftMax = 4, rightMax = 8)
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* This is because water will "trail off" the sides of the terraces.
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*
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* 2. At this point, we are essentially dealing with a new map: [4, 3, 4, 2, 4, 0, 8].
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* From here, we loop through the map from the left to the right (if leftMax > rightMax,
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* otherwise we move from right to left), adding water as we go unless we reach a value
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* that is greater than or equal to leftMax || rightMax.
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* e.g. [4, 3, 4, 2, 4, 0, 8]
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* ^
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* water += leftMax - 3 => water = 1
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* or if the terrace array was reversed:
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* e.g. [8, 0, 4, 2, 4, 3, 4]
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* ^
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* water += rightMax - 3 => water = 1
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*
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* 3. Again, we've essentially shortened the map: [4, 2, 4, 0, 8].
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* Now we repeat the above steps on the new array.
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* e.g.
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* Next Iteration:
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* [4, 2, 4, 0, 8]
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* ^
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* water += leftMax - 2 => water = 3
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*
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* Next Iteration:
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* [4, 0, 8]
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* ^
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* water += leftMax - 0 => water = 7
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*
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* return water(7)
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*/
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export default function rainTerraces(terraces) {
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let start = 0;
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let end = terraces.length - 1;
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let water = 0;
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let leftMax = 0;
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let rightMax = 0;
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while (start < end) {
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// Loop to find left max
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while (start < end && terraces[start] <= terraces[start + 1]) {
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start += 1;
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}
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leftMax = terraces[start];
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// Loop to find right max
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while (end > start && terraces[end] <= terraces[end - 1]) {
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end -= 1;
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}
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rightMax = terraces[end];
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// Determine which direction we need to move in
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if (leftMax < rightMax) {
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// Move from left to right and collect water
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start += 1;
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while (start < end && terraces[start] <= leftMax) {
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water += leftMax - terraces[start];
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start += 1;
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}
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} else {
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// Move from left to right and collect water
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end -= 1;
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while (end > start && terraces[end] <= rightMax) {
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water += rightMax - terraces[end];
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end -= 1;
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}
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}
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}
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return water;
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}
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import rainTerraces from '../rainTerraces';
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describe('rainTerraces', () => {
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it('should find the amount of water collected after raining', () => {
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expect(rainTerraces([2, 0, 2])).toBe(2);
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expect(rainTerraces([3, 0, 0, 2, 0, 4])).toBe(10);
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expect(rainTerraces([0, 1, 0, 2, 1, 0, 1, 3, 2, 1, 2, 1])).toBe(6);
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expect(rainTerraces([1, 1, 1, 1, 1])).toBe(0);
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expect(rainTerraces([1, 2, 3, 4, 5])).toBe(0);
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expect(rainTerraces([4, 1, 3, 1, 2, 1, 2, 1])).toBe(4);
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});
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});

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