【leetcode】【73】Set Matrix Zeroes

一、问题描述

Given a m x n matrix, if an element is 0, set its entire row and column to 0. Do it in place.

click to show follow up.

Follow up:

Did you use extra space?
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?

二、问题分析

最简单的想法就是备份另外一个相同矩阵，一个查看一个改，这也是follow up里的第一个解法，显然是bad idea；我们再考虑一下，我们是不是只需要记录有哪些行跟列里有0就行呢，空间复杂度为O（m+n）；不使用额外的空间，我没有考虑出来，参考了别人的想法。

三、Java AC 代码

O(m+n)，我采用了hashset，当然也可以用数组代替，但我感觉hashset更好一点。

public void setZeroes(int[][] matrix) {
		HashSet<Integer> rowSets = new HashSet<Integer>();
		HashSet<Integer> colSets = new HashSet<Integer>();
		if (matrix==null || matrix.length==0 || matrix[0].length==0) {
			return ;
		}
		for (int i = 0; i < matrix.length; i++) {
			for (int j = 0; j < matrix[0].length; j++) {
				if(matrix[i][j]==0){
					rowSets.add(i);
					colSets.add(j);
				}
			}
		}
		for (Integer row : rowSets) {
			for (int i = 0; i < matrix[0].length; i++) {
				matrix[row][i] = 0;
			}
		}
		rowSets.clear();
		for (Integer col : colSets) {
			for (int i = 0; i < matrix.length; i++) {
				matrix[i][col] = 0;
			}
		}
		colSets.clear();
	}

不使用额外空间的解法

public void setZeroes(int[][] matrix) {
    int rownum = matrix.length;
    if (rownum == 0)  return;
    int colnum = matrix[0].length;
    if (colnum == 0)  return;

    boolean hasZeroFirstRow = false, hasZeroFirstColumn = false;

    // Does first row have zero?
    for (int j = 0; j < colnum; ++j) {
        if (matrix[0][j] == 0) {
            hasZeroFirstRow = true;
            break;
        }
    }

    // Does first column have zero?
    for (int i = 0; i < rownum; ++i) {
        if (matrix[i][0] == 0) {
            hasZeroFirstColumn = true;
            break;
        }
    }

    // find zeroes and store the info in first row and column
    for (int i = 1; i < matrix.length; ++i) {
        for (int j = 1; j < matrix[0].length; ++j) {
            if (matrix[i][j] == 0) {
                matrix[i][0] = 0;
                matrix[0][j] = 0;
            }
        }
    }

    // set zeroes except the first row and column
    for (int i = 1; i < matrix.length; ++i) {
        for (int j = 1; j < matrix[0].length; ++j) {
            if (matrix[i][0] == 0 || matrix[0][j] == 0)  matrix[i][j] = 0;
        }
    }

    // set zeroes for first row and column if needed
    if (hasZeroFirstRow) {
        for (int j = 0; j < colnum; ++j) {
            matrix[0][j] = 0;
        }
    }
    if (hasZeroFirstColumn) {
        for (int i = 0; i < rownum; ++i) {
            matrix[i][0] = 0;
        }
    }
}