[Leetcode] Largest Rectangle in Histogram (Java)

Given n non-negative integers representing the histogram's bar height where the width of each bar is 1, find the area of largest rectangle in the histogram.



Above is a histogram where width of each bar is 1, given height =

[2,1,5,6,2,3]

.



The largest rectangle is shown in the shaded area, which has area =

10

unit.

For example,

Given height =

[2,1,5,6,2,3]

,

return

10

.

找出最大长方形面积

用栈维护一个高度递增序列，栈中存放高度对应的位置，遍历height数组：

1）若此位置高度值大于栈顶元素，则入栈；

2）不大于栈顶元素，则从栈中弹出元素并计算最大面积max

public class Solution {
public int largestRectangleArea(int[] height) {
int max = 0;
Stack<Integer> stack = new Stack<Integer>();
for(int i=0;i<height.length;i++){
if(stack.isEmpty())
stack.add(i);
else {
if(height[stack.peek()]<height[i])
stack.add(i);
else {
while(!stack.isEmpty()&&height[stack.peek()]>height[i]){
int h = stack.pop();
if(stack.isEmpty()){
max = Math.max(max, i*height[h]);
}else {
max = Math.max(max, (i-stack.peek()-1)*height[h]);
}
}
stack.add(i);
}
}
}
while(!stack.isEmpty()){
int h = stack.pop();
if(stack.isEmpty()){
max = Math.max(max, height.length*height[h]);
}else {
max = Math.max(max, (height.length-stack.peek()-1)*height[h]);
}
}
return max;
}
}