Add Rain Terraces problem.

This commit is contained in:
Oleksii Trekhleb 2018-07-27 13:00:24 +03:00
parent 3271ee92b9
commit 6fc429975f
3 changed files with 79 additions and 61 deletions

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@ -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)

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@ -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);
});
});

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@ -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;
while (start < end) {
// Loop to find left max
while (start < end && terraces[start] <= terraces[start + 1]) {
start += 1;
let leftMaxLevel = 0;
let rightMaxLevel = 0;
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;
}