LeetCode-84 Largest Rectangle in Histogram

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.

思路：计算以height[i]为最低点时的最大面积。

1. 创建一个栈stack;

1. 从头开始遍历数组，如果数组为空或者当前遍历元素height[i]>=stack.peek()，就将"i"进栈，注意是将"i"而不是height[i];

3. 如果height[i]<stack.peek();

　　计算以height[stack.pop()]为最短高度，长度为i-stack.peek()-1的面积；

　　如果此时stack为空，则长度为"i";

　　如果计算得到的面积大，则更新当前最大面积max;

4. 当遍历到数组结束时，添加一个元素“0”作为终点判断。

代码如下：

public int largestRectangleArea(int[] height) {
        if(height == null || height.length < 1)
            return 0;

        Stack<Integer> stack = new Stack<Integer>();
        int max = 0;
        int current = 0;
        for(int i=0; i<=height.length;) {
            if(i == height.length) {
                current = 0;
            } else {
                current = height[i];
            }

            if(stack.isEmpty() || current >= height[stack.peek()]) {
                stack.push(i);
                i++;
            } else {
                int h = height[stack.pop()];
                int length = (stack.isEmpty() ? i : i-stack.peek()-1);
                max = Math.max(max, h*length);
            }
        }
        return max;
    }