[LeetCode] 73. Set Matrix Zeroes
Given an m x n
matrix. If an element is 0, set its entire row and column to 0. Do it in-place.
Follow up:
- A straight forward solution using O(mn) space is probably a bad idea.
- A simple improvement uses O(m + n) space, but still not the best solution.
- Could you devise a constant space solution?
Example 1:
Input: matrix = [[1,1,1],[1,0,1],[1,1,1]] Output: [[1,0,1],[0,0,0],[1,0,1]]
Example 2:
Input: matrix = [[0,1,2,0],[3,4,5,2],[1,3,1,5]] Output: [[0,0,0,0],[0,4,5,0],[0,3,1,0]]
Constraints:
m == matrix.length
n == matrix[0].length
1 <= m, n <= 200
-231 <= matrix[i][j] <= 231 - 1
矩阵置零。
给定一个 m x n
的矩阵,如果一个元素为 0 ,则将其所在行和列的所有元素都设为 0 。请使用 原地 算法。
数组类型的题有好几道都明确要求不能使用额外空间,这题也不例外。因为不能用到额外空间,所以只能将是否需要赋零的flag记录在input的数组里面,这里我选择记录在第一行和第一列上。但是我此时仍然需要两个flag来分别记录第一行和第一列上有没有0。因为第一行和第一列上的0有可能是因着记录里面的行和列的结果而被赋值成0的。我参考了grandyang大神的思路,非常简洁,列在这里。
- 先扫描第一行第一列,如果有0,则将各自的flag设置为true
- 然后扫描除去第一行第一列的整个数组,如果有0,则将对应的第一行和第一列的数字赋0
- 再次遍历除去第一行第一列的整个数组,如果对应的第一行和第一列的数字有一个为0,则将当前值赋0
- 最后根据第一行第一列的flag来更新第一行第一列
时间O(mn)
空间O(1)
JavaScript实现
1 /** 2 * @param {number[][]} matrix 3 * @return {void} Do not return anything, modify matrix in-place instead. 4 */ 5 var setZeroes = function (matrix) { 6 // corner case 7 if (matrix.length === 0 || matrix === null) return; 8 9 // normal case 10 let m = matrix.length 11 let n = matrix[0].length; 12 let rowZero = false; 13 let colZero = false; 14 // check if first row has zero 15 for (let i = 0; i < m; i++) { 16 if (matrix[i][0] === 0) colZero = true; 17 } 18 19 // check if first column has zero 20 for (let i = 0; i < n; i++) { 21 if (matrix[0][i] === 0) rowZero = true; 22 } 23 24 // scan all the other rows and columns 25 for (let i = 1; i < m; i++) { 26 for (let j = 1; j < n; j++) { 27 if (matrix[i][j] === 0) { 28 matrix[0][j] = 0; 29 matrix[i][0] = 0; 30 } 31 } 32 } 33 34 // scan again to see if we should mark the whole row or column to be zero 35 for (let i = 1; i < m; i++) { 36 for (let j = 1; j < n; j++) { 37 if (matrix[i][0] === 0 || matrix[0][j] === 0) { 38 matrix[i][j] = 0; 39 } 40 } 41 } 42 43 // check if we should mark the first row and first column to be zero 44 if (rowZero) { 45 for (let i = 0; i < n; i++) matrix[0][i] = 0; 46 } 47 if (colZero) { 48 for (let i = 0; i < m; i++) matrix[i][0] = 0; 49 } 50 };
Java实现
1 class Solution { 2 public void setZeroes(int[][] matrix) { 3 // corner case 4 if (matrix == null || matrix.length == 0) { 5 return; 6 } 7 8 // normal case 9 int m = matrix.length; 10 int n = matrix[0].length; 11 boolean row = false; 12 boolean col = false; 13 // mark if first row and first col has zero 14 for (int i = 0; i < m; i++) { 15 for (int j = 0; j < n; j++) { 16 if (matrix[i][j] == 0) { 17 matrix[i][0] = matrix[0][j] = 0; 18 if (i == 0) row = true; 19 if (j == 0) col = true; 20 } 21 } 22 } 23 24 // change the inner part to zeroes based on the first row and first col 25 for (int i = 1; i < m; i++) { 26 if (matrix[i][0] == 0) { 27 for (int j = 1; j < n; j++) { 28 matrix[i][j] = 0; 29 } 30 } 31 } 32 for (int j = 1; j < n; j++) { 33 if (matrix[0][j] == 0) { 34 for (int i = 1; i < m; i++) { 35 matrix[i][j] = 0; 36 } 37 } 38 } 39 40 // change the first row and first col if needed 41 if (row) { 42 for (int j = 0; j < n; j++) { 43 matrix[0][j] = 0; 44 } 45 } 46 if (col) { 47 for (int i = 0; i < m; i++) { 48 matrix[i][0] = 0; 49 } 50 } 51 } 52 }
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