42. Trapping Rain Water

Problem

Given n non-negative integers representing an elevation map where the width of each bar is 1, compute how much water it is able to trap after raining.

The above elevation map is represented by array [0,1,0,2,1,0,1,3,2,1,2,1]. In this case, 6 units of rain water (blue section) are being trapped. Thanks Marcos for contributing this image!

Example:

Input: [0,1,0,2,1,0,1,3,2,1,2,1]
Output: 6

Solution

var trap = function(height) {
  var res = 0;
  var left = 0;
  var right = height.length - 1;
  var leftMax = 0;
  var rightMax = 0;

  while (left < right) {
    if (height[left] < height[right]) {
      if (height[left] >= leftMax) {
        leftMax = height[left];
      } else {
        res += leftMax - height[left];
      }
      left++;
    } else {
      if (height[right] >= rightMax) {
        rightMax = height[right];
      } else {
        res += rightMax - height[right];
      }
      right--;
    }
  }

  return res;
};

Explain:

双指针

Complexity:

• Time complexity : O(n).
• Space complexity : O(1).