leetcode85 - Maximal Rectangle - hard

Posted jasminemzy

tags:

篇首语:本文由小常识网(cha138.com)小编为大家整理,主要介绍了leetcode85 - Maximal Rectangle - hard相关的知识,希望对你有一定的参考价值。

Given a 2D binary matrix filled with 0\'s and 1\'s, find the largest rectangle containing only 1\'s and return its area.
Example:
Input:
[
  ["1","0","1","0","0"],
  ["1","0","1","1","1"],
  ["1","1","1","1","1"],
  ["1","0","0","1","0"]
]
Output: 6
 
 
Iterative的largest rectangle in histogram.
思路:一层一层遍历,到i层时,第i层是1的位置可以向上延伸所有连续的1作为一个直方条条,按这样的规律可以把matrix[0:i][:]看做一个直方图,然后去统计当前情况下的最大rectangle,得到答案后去打擂台。所有层遍历完了,答案就出来了。
 
直方图的储存:用int[] heights[colLength]来储存,更新的方法是,扫matrix里新的一行时,如果看到’0’就清空heights[j],如果看到’1’就让heights[j]++。
解释计算直方图里的清空操作:直方条的定义是底部非空向上生长。因为histogram问题里能用stack解决的原因就是,所有直方图最底部开始都是非空的,那么算面积是可以只在意顶上高到哪里,不用担心底部有没有悬空,从而记录高度即可。如果你把matrix的局部转化成直方图的时候看到上面有1但底部是0,那这一列都不合格直方条的定义了。上面的1不用担心,你之前遍历到前面那行的时候算过了。
 
相关题目:Largest Rectangle in Histogram。  https://www.cnblogs.com/jasminemzy/p/9764297.html
 
实现:
class Solution {
    public int maximalRectangle(char[][] matrix) {
        // invalid input.
        if (matrix == null || matrix.length == 0 || matrix[0].length == 0) {
            return 0;
        }
        
        int ans = 0;
        int[] heights = new int[matrix[0].length];
        for (int i = 0; i < matrix.length; i++) {
            for (int j = 0; j < matrix[0].length; j++) {
                if (matrix[i][j] == \'0\') {
                    heights[j] = 0;
                } else {
                    heights[j]++;
                }
            }
            ans = Math.max(ans, maxRecInHistogram(heights));
        }
        return ans;
    }
    
    private int maxRecInHistogram(int[] heights) {
        int ans = 0;
        Stack<Integer> stack = new Stack<>();
        for (int i = 0; i <= heights.length; i++) {
            while (!stack.isEmpty() && (i == heights.length || heights[i] < heights[stack.peek()])) {
                int height = heights[stack.pop()];
                int width = stack.isEmpty() ? i : i - stack.peek() - 1;
                ans = Math.max(ans, height * width);
            }
            stack.push(i);
        }
        return ans;
    }
}

 

以上是关于leetcode85 - Maximal Rectangle - hard的主要内容,如果未能解决你的问题,请参考以下文章

Leetcode 85. Maximal Rectangle

Leetcode 85. Maximal Rectangle

LeetCode 85: Maximal Recetangle

LeetCode(85) Maximal Rectangle

leetcode 85. Maximal Rectangle

[leetcode]85. Maximal Rectangle 最大矩形