javascript-algorithms/src/algorithms/uncategorized/rain-terraces/dpRainTerraces.js

/**
 * DYNAMIC PROGRAMMING approach of solving Trapping Rain Water problem.
 *
 * @param {number[]} terraces
 * @return {number}
 */
export default function dpRainTerraces(terraces) {
  let waterAmount = 0;

  // Init arrays that will keep the list of left and right maximum levels for specific positions.
  const leftMaxLevels = new Array(terraces.length).fill(0);
  const rightMaxLevels = new Array(terraces.length).fill(0);

  // Calculate the highest terrace level from the LEFT relative to the current terrace.
  [leftMaxLevels[0]] = terraces;
  for (let terraceIndex = 1; terraceIndex < terraces.length; terraceIndex += 1) {
    leftMaxLevels[terraceIndex] = Math.max(
      terraces[terraceIndex],
      leftMaxLevels[terraceIndex - 1],
    );
  }

  // Calculate the highest terrace level from the RIGHT relative to the current terrace.
  rightMaxLevels[terraces.length - 1] = terraces[terraces.length - 1];
  for (let terraceIndex = terraces.length - 2; terraceIndex >= 0; terraceIndex -= 1) {
    rightMaxLevels[terraceIndex] = Math.max(
      terraces[terraceIndex],
      rightMaxLevels[terraceIndex + 1],
    );
  }

  // Not let's go through all terraces one by one and calculate how much water
  // each terrace may accumulate based on previously calculated values.
  for (let terraceIndex = 0; terraceIndex < terraces.length; terraceIndex += 1) {
    // Pick the lowest from the left/right highest terraces.
    const currentTerraceBoundary = Math.min(
      leftMaxLevels[terraceIndex],
      rightMaxLevels[terraceIndex],
    );

    if (currentTerraceBoundary > terraces[terraceIndex]) {
      waterAmount += currentTerraceBoundary - terraces[terraceIndex];
    }
  }

  return waterAmount;
}