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题目:
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.
For example,
Given [0,1,0,2,1,0,1,3,2,1,2,1]
, return 6
.
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. (Hard)
分析:
首先考虑对每个位置向左向右找到最小值,然后与本位置的值比较添加存水结果,可以做出来,时间复杂度O(n^2);
考虑利用空间优化时间,开两个数组,分别存当前位置向左的最小值和向右的最小值。
一次从左往右遍历更新leftHeight数组, 一次从右向左遍历更新rightHeight数组,最后一次遍历算利用上述方法算result,只不过这次可以直接从数组里读左右最小值结果。
代码:
1 class Solution { 2 public: 3 int trap(vector<int>& height) { 4 int leftMax[height.size()]; 5 leftMax[0] = 0; 6 for (int i = 1; i < height.size(); ++i) { 7 leftMax[i] = max(height[i - 1], leftMax[i - 1]); 8 } 9 int rightMax[height.size()]; 10 rightMax[height.size() - 1] = 0; 11 for (int i = height.size() - 2; i >= 0; --i) { 12 rightMax[i] = max(height[i + 1], rightMax[i + 1]); 13 } 14 int result = 0; 15 for (int i = 0; i < height.size(); ++i) { 16 if (min(leftMax[i], rightMax[i]) - height[i] > 0) { 17 result += (min(leftMax[i], rightMax[i]) - height[i]); 18 } 19 } 20 return result; 21 } 22 };
上述方法将时间复杂度优化到了O(n),但利用了额外的空间,空间复杂度也提高到了O(n)。
进一步优化,可以考虑Two pointers的思路。
两根指针分别指向头和尾,并维护两个值,表示从左向右到p1的最大值leftHeight和从右向左到p2的最大值RightHeight。
两个最大值中较小的向中间移动,遇到更大的值更新leftHeight或rightHeight,遇到较小的值更新result。
这样可以做到时间复杂度O(n),空间复杂度O(1)。
代码:
1 class Solution { 2 public: 3 int trap(vector<int>& height) { 4 if (height.size() < 2) { 5 return 0; 6 } 7 int left = 0, right = height.size() - 1; 8 int leftHeight = height[0], rightHeight = height[height.size() - 1]; 9 int result = 0; 10 while (left < right) { 11 if (leftHeight <= rightHeight) { 12 left++; 13 if (height[left] < leftHeight) { 14 result += (leftHeight - height[left]); 15 } 16 else { 17 leftHeight = height[left]; 18 } 19 } 20 else { 21 right--; 22 if (height[right] < rightHeight) { 23 result += (rightHeight - height[right]); 24 } 25 else { 26 rightHeight = height[right]; 27 } 28 } 29 } 30 return result; 31 } 32 };
LeetCode42 Trapping Rain Water
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原文地址:http://www.cnblogs.com/wangxiaobao/p/5831437.html