leetcode85 - Maximal Rectangle - hard

標籤：pop   lse   empty   new   合格   int   contain   code   private   

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：一層一層遍曆，到i層時，第i層是1的位置可以向上延伸所有連續的1作為一個直方條條，按這樣的規律可以把matrix[0:i][:]看做一個長條圖，然後去統計當前情況下的最大rectangle，得到答案後去打擂台。所有層遍曆完了，答案就出來了。 長條圖的儲存：用int[] heights[colLength]來儲存，更新的方法是，掃matrix裡新的一行時，如果看到’0’就清空heights[j]，如果看到’1’就讓heights[j]++。解釋計算長條圖裡的清空操作：直方條的定義是底部非空向上生長。因為histogram問題裡能用stack解決的原因就是，所有長條圖最底部開始都是非空的，那麼算面積是可以只在意頂上高到哪裡，不用擔心底部有沒有懸空，從而記錄高度即可。如果你把matrix的局部轉化成長條圖的時候看到上面有1但底部是0，那這一列都不合格直方條的定義了。上面的1不用擔心，你之前遍曆到前面那行的時候算過了。 相關題目：Largest Rectangle in Histogram。  https://www.cnblogs.com/jasminemzy/p/9764297.html 實現：

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;    }}

 

leetcode85 - Maximal Rectangle - hard