leetcode 85. Maximal Rectangle | 85. 最大矩形（单调栈）

男娘i 2022-09-11 11:23 82阅读 0赞

## 题目 ##

[https://leetcode.com/problems/maximal-rectangle/][https_leetcode.com_problems_maximal-rectangle]  
![在这里插入图片描述][watermark_type_ZHJvaWRzYW5zZmFsbGJhY2s_shadow_50_text_Q1NETiBA5a-S5rOJSHE_size_20_color_FFFFFF_t_70_g_se_x_16]

## 题解 ##

本题与 [leetcode 84. Largest Rectangle in Histogram | 84. 柱状图中最大的矩形（单调栈）][leetcode 84. Largest Rectangle in Histogram _ 84.] 思路相同，直接抄了原来的代码。

也可参考之前的博客：[左神算法：求最大子矩阵的大小（Java版）][Java]

另外，想到了另外一道类似但思路不同的题：[221. Maximal Square][]

class Solution { 
        public int maximalRectangle(char[][] matrix) { 
            if (matrix.length == 0) return 0;
            int M = matrix.length;
            int N = matrix[0].length;
            
            int[][] heights = new int[M][N]; // 上方有多少个连续的1
            for (int i = 0; i < N; i++) { 
                heights[0][i] = matrix[0][i] - '0';
                for (int j = 1; j < M; j++) { 
                    if (matrix[j][i] == '1') heights[j][i] = heights[j - 1][i] + 1;
                    else heights[j][i] = 0;
                }
            }
            int result = 0;
            for (int i = 0; i < M; i++) { 
                result = Math.max(largestRectangleArea(heights[i]), result);
            }
            return result;
        }
    
        // leetcode 84. Largest Rectangle in Histogram
        public int largestRectangleArea(int[] heights) { 
            int L = heights.length;
            // 找左边第一个小于h[i]的数
            // 从右向左遍历，维护单调不减栈，小数h[i]不断将大数h[j]弹出，则h[i]左边第一个小于h[i]的数为h[j]
            Stack<Integer> valueStack = new Stack<>();
            Stack<Integer> indexStack = new Stack<>();
            int[] leftIndex = new int[L]; // i左边第一个小于i的数的下标
            Arrays.fill(leftIndex, -1);
            for (int i = L - 1; i >= 0; i--) { 
                while (!valueStack.isEmpty() && valueStack.peek() > heights[i]) { 
                    leftIndex[indexStack.pop()] = i;
                    valueStack.pop();
                }
                valueStack.push(heights[i]);
                indexStack.push(i);
            }
            // 找右边第一个小于h[i]的数
            // 从左向右遍历，维护单调不减栈
            valueStack = new Stack<>();
            indexStack = new Stack<>();
            int[] rightIndex = new int[L]; // i右边第一个小于i的数的下标
            Arrays.fill(rightIndex, L);
            for (int i = 0; i < L; i++) { 
                while (!valueStack.isEmpty() && valueStack.peek() > heights[i]) { 
                    rightIndex[indexStack.pop()] = i;
                    valueStack.pop();
                }
                valueStack.push(heights[i]);
                indexStack.push(i);
            }
    
            // 对于每个h[i]，以其自身的高度，分别向左右扩张
            int maxArea = 0;
            for (int i = 0; i < L; i++) { 
                maxArea = Math.max(maxArea, (rightIndex[i] - leftIndex[i] - 1) * heights[i]);
            }
            return maxArea;
        }
    }

![在这里插入图片描述][watermark_type_ZHJvaWRzYW5zZmFsbGJhY2s_shadow_50_text_Q1NETiBA5a-S5rOJSHE_size_20_color_FFFFFF_t_70_g_se_x_16 1]

[https_leetcode.com_problems_maximal-rectangle]: https://leetcode.com/problems/maximal-rectangle/
[watermark_type_ZHJvaWRzYW5zZmFsbGJhY2s_shadow_50_text_Q1NETiBA5a-S5rOJSHE_size_20_color_FFFFFF_t_70_g_se_x_16]: /images/20220828/09426a494c8048249cf92d90672f0209.png
[leetcode 84. Largest Rectangle in Histogram _ 84.]: https://hanquan.blog.csdn.net/article/details/120302405
[Java]: https://blog.csdn.net/sinat_42483341/article/details/110670125
[221. Maximal Square]: https://leetcode.com/problems/maximal-square/
[watermark_type_ZHJvaWRzYW5zZmFsbGJhY2s_shadow_50_text_Q1NETiBA5a-S5rOJSHE_size_20_color_FFFFFF_t_70_g_se_x_16 1]: /images/20220828/a3722f1a7667417fa1ce6ffaec3ee86b.png