42. 接雨水
接雨水这道题目是 面试中特别高频的一道题，也是单调栈 应用的题目，大家好好做做。
建议是掌握 双指针 和单调栈，因为在面试中 写出单调栈可能 有点难度，但双指针思路更直接一些。
在时间紧张的情况有，能写出双指针法也是不错的，然后可以和面试官在慢慢讨论如何优化。
java
class Solution {
public int trap(int[] height) {
int total = 0;
for (int index = 0; index < height.length; index++) {
if (index == 0 || index == height.length - 1) continue;
int rightMax = height[index];
int leftMax = height[index];
for (int right = index + 1; right < height.length; right++) {
rightMax = Math.max(rightMax, height[right]);
}
for (int left = index - 1; left >= 0; left--) {
leftMax = Math.max(leftMax, height[left]);
}
int waterHeight = Math.min(leftMax, rightMax) - height[index];
if (waterHeight > 0) total += waterHeight;
}
return total;
}
}- 柱状图中最大的矩形
有了之前单调栈的铺垫，这道题目就不难了。
java
class Solution {
public int largestRectangleArea(int[] heights) {
int[] extendedHeights = new int[heights.length + 2];
System.arraycopy(heights, 0, extendedHeights, 1, heights.length);
extendedHeights[0] = 0;
extendedHeights[heights.length + 1] = 0;
Stack<Integer> stack = new Stack<>();
stack.push(0);
int maxArea = 0;
for (int i = 1; i < extendedHeights.length; i++) {
while (!stack.isEmpty() && extendedHeights[i] < extendedHeights[stack.peek()]) {
int topIndex = stack.pop();
int width = i - stack.isEmpty() ? 0 : i - stack.peek() - 1;
int height = extendedHeights[topIndex];
maxArea = Math.max(maxArea, width * height);
}
stack.push(i);
}
return maxArea;
}
}