LeetCode 0085 Maximal Rectangle
作者:互联网
1. 题目描述
2. Solution 1
1、思路分析
以 example 1. 为例
matrix = [
["1","0","1","0","0"],
["1","0","1","1","1"],
["1","1","1","1","1"],
["1","0","0","1","0"]
]
分析: 遍历 行(row)
row = 1: 可以得到 heights = [1, 0, 1, 0, 0] 套用 Q84
row = 2: -> heights = [2, 0, 2, 1, 1]
......
2、代码实现
package Q0099.Q0085MaximalRectangle;
import java.util.ArrayDeque;
import java.util.Deque;
/*
以 example 1. 为例
matrix = [
["1","0","1","0","0"],
["1","0","1","1","1"],
["1","1","1","1","1"],
["1","0","0","1","0"]
]
分析: 遍历 行(row)
row = 1: 可以得到 heights = [1, 0, 1, 0, 0] 套用 Q84
row = 2: -> heights = [2, 0, 2, 1, 1]
......
*/
public class Solution1 {
public int maximalRectangle(char[][] matrix) {
if (matrix == null || matrix.length == 0 || matrix[0].length == 0) return 0;
int col = matrix[0].length;
int[] heights = new int[col];
int max = 0;
for (char[] chars : matrix) {
for (int j = 0; j < col; j++) {
if (chars[j] == '1') {
heights[j]++;
} else {
heights[j] = 0;
}
}
int area = largestRectangleArea(heights);
max = Math.max(max, area);
}
return max;
}
// 来自 Q84
public int largestRectangleArea(int[] heights) {
int len = heights.length;
Deque<Integer> s = new ArrayDeque<>();
int maxArea = 0;
for (int i = 0; i <= len; i++) {
int h = (i == len ? 0 : heights[i]);
if (s.isEmpty() || h >= heights[s.peek()]) {
s.push(i);
} else {
int tp = s.pop();
int width = (s.isEmpty() ? i : i - 1 - s.peek());
maxArea = Math.max(maxArea, heights[tp] * width);
i--;
}
}
return maxArea;
}
}
3、复杂度分析
时间复杂度: O(m * n) 其中 dim(matrix) = (m, n)
空间复杂度: O(n) 栈
2. Solution 2
1、思路分析
思路同Solution 1,用数组模拟栈。
2、代码实现
package Q0099.Q0085MaximalRectangle;
public class Solution2 {
/*
执行耗时:2 ms,击败了100.00% 的Java用户
内存消耗:41.8 MB,击败了36.24% 的Java用户
*/
//方案2
public int maximalRectangle(char[][] matrix) {
if (matrix == null || matrix.length == 0 || matrix[0].length == 0) return 0;
int m = matrix.length;
int n = matrix[0].length;
int[] dp = new int[n + 1];//增加一列,简化边界处理
int res = 0;
for (int row = 0; row < m; row++) {
updateHeight(dp, row, matrix);
res = Math.max(res, maxArea(dp));
}
return res;
}
public void updateHeight(int[] dp, int row, char[][] matrix) {
for (int column = 0; column < matrix[row].length; column++) {
dp[column] = matrix[row][column] == '1' ? dp[column] + 1 : 0;
}
}
public int maxArea(int[] heights) {
int l = 0, r = 0;
int n = heights.length;
int[] pos = new int[n + 1];
pos[l] = -1;
int res = 0;
while (r < n) {
while (l > 0 && heights[r] < heights[pos[l]]) {
int h = heights[pos[l--]];
res = Math.max(res, h * (r - pos[l] - 1));
}
pos[++l] = r++;
}
return res;
}
}
3、复杂度分析
时间复杂度: O(m * n) 其中 dim(matrix) = (m, n)
空间复杂度: O(n) 栈
标签:Maximal,matrix,int,res,heights,length,0085,LeetCode,row 来源: https://www.cnblogs.com/junstat/p/16201379.html