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| 1 | +//在一个由 0 和 1 组成的二维矩阵内,找到只包含 1 的最大正方形,并返回其面积。 |
| 2 | +// |
| 3 | +// 示例: |
| 4 | +// |
| 5 | +// 输入: |
| 6 | +// |
| 7 | +//1 0 1 0 0 |
| 8 | +//1 0 1 1 1 |
| 9 | +//1 1 1 1 1 |
| 10 | +//1 0 0 1 0 |
| 11 | +// |
| 12 | +//输出: 4 |
| 13 | +// Related Topics 动态规划 |
| 14 | + |
| 15 | + |
| 16 | +//leetcode submit region begin(Prohibit modification and deletion) |
| 17 | +class LeetCode_221_0206 { |
| 18 | + //暴力求解,感觉都很难 |
| 19 | + //遍历矩阵,找到1,就从1开始往下找矩形,0就跳过 |
| 20 | + //怎么从1开始找矩形?找边长,然后遍历最长边长组成的长方形,看是否都是1 |
| 21 | + |
| 22 | + //直接上动态规划 |
| 23 | + //dp[i,j]表示以a[i,j]为右下角的正方形的最大边长 |
| 24 | + //那就可以得出dp方程:dp[i,j] = min(dp[i-1,j], dp[i,j-1], dp[i-1,j-1]) + 1 |
| 25 | + public int maximalSquare(char[][] matrix) { |
| 26 | + if(matrix == null || matrix.length == 0) { |
| 27 | + return 0; |
| 28 | + } |
| 29 | + int[][] dp = new int[matrix.length][matrix[0].length]; |
| 30 | + int maxSide = 0; |
| 31 | + for (int i = 0; i < matrix[0].length; i++) { |
| 32 | + if (matrix[0][i] == '1') { |
| 33 | + dp[0][i] = 1; |
| 34 | + maxSide = 1; |
| 35 | + } |
| 36 | + } |
| 37 | + for (int i = 1; i < matrix.length; i++) { |
| 38 | + if (matrix[i][0] == '1') { |
| 39 | + dp[i][0] = 1; |
| 40 | + maxSide = 1; |
| 41 | + } |
| 42 | + } |
| 43 | + |
| 44 | + for (int i = 1; i < matrix.length; i++) { |
| 45 | + for (int j = 1; j < matrix[0].length; j++) { |
| 46 | + if (matrix[i][j] == '1') { |
| 47 | + dp[i][j] = Math.min(Math.min(dp[i-1][j],dp[i][j-1]),dp[i-1][j-1]) + 1; |
| 48 | + } |
| 49 | + maxSide = Math.max(maxSide, dp[i][j]); |
| 50 | + } |
| 51 | + } |
| 52 | + |
| 53 | + return maxSide * maxSide; |
| 54 | + } |
| 55 | + |
| 56 | + //优化存储空间,使用一维dp方程 |
| 57 | + public int maximalSquare_1(char[][] matrix) { |
| 58 | + if(matrix == null || matrix.length == 0) { |
| 59 | + return 0; |
| 60 | + } |
| 61 | + int[] dp = new int[matrix[0].length + 1]; |
| 62 | + int maxSide = 0; |
| 63 | + int pre = 0; |
| 64 | + for (int i = 1; i <= matrix.length; i++) { |
| 65 | + for (int j = 1; j <= matrix[0].length; j++) { |
| 66 | + int temp = dp[j]; |
| 67 | + if (matrix[i-1][j-1] == '1') { |
| 68 | + dp[j] = Math.min(dp[j-1],Math.min(dp[j], pre)) + 1; |
| 69 | + maxSide = Math.max(dp[j],maxSide); |
| 70 | + } else { |
| 71 | + dp[j] = 0; |
| 72 | + } |
| 73 | + pre = temp; |
| 74 | + } |
| 75 | + } |
| 76 | + return maxSide * maxSide; |
| 77 | + } |
| 78 | +} |
| 79 | +//leetcode submit region end(Prohibit modification and deletion) |
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