leetcode Set Matrix Zeroes矩阵设置零-优快云博客

本文介绍了一种高效的算法，用于在矩阵中将包含0元素的行和列置零，且不使用额外空间。提供了两种实现方法：一种使用O(m+n)额外空间；另一种使用常数空间，巧妙地利用矩阵自身的第一行和第一列来记录需要置零的行和列。

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Set Matrix Zeroes

Given amxnmatrix, if an element is 0, set its entire row and column to 0. Do it in place.

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?

利用额外空间O(m+n)的做法是很简洁的：

void setZeroes(vector<vector<int> > &matrix) {
		int row = matrix.size();
		if (row < 1) return;
		int col = matrix[0].size();
		vector<bool> colRecorder(col);
		vector<bool> rowRecorder(row);

		for (int i = 0; i < row; i++)
		{
			for (int j = 0; j < col; j++)
			{
				if (matrix[i][j] == 0)
				{
					rowRecorder[i] = true;
					colRecorder[j] = true;
				}
			}
		}

		for (int i = 0; i < row; i++)
		{
			for (int j = 0; j < col; j++)
			{
				if (rowRecorder[i]) matrix[i][j] = 0;
				else if (colRecorder[j]) matrix[i][j] = 0;
			}
		}
	}

利用常数空间也可以：

就需要巧妙地利用原来矩阵的空间，这里利用第一行和第一列保存额外信息：

1 先判断号第一行和第一列是否需要全部置零

2 有任何一个该行或者该列的元素为零那么这个第一行或者第一列的元素必然是零，就保存这个零，最后用来判断整个矩阵的这一行或者这一列是否需要置零。

3 最后再根据前面判断，决定是否把这个第一行和第一列置零。

void setZeroes2(vector<vector<int> > &matrix) 
	{
		int row = matrix.size();
		if (row < 1) return;
		int col = matrix[0].size();
		bool firstRowhasZero = false;
		bool firstColhasZero = false;

		for (int i = 0; i < row && !firstColhasZero; i++)
			if (matrix[i][0] == 0) firstColhasZero = true;	

		for (int i = 0; i < col && !firstRowhasZero; i++)
			if (matrix[0][i] == 0) firstRowhasZero = true;

		for (int i = 0; i < row; i++)
		{
			for (int j = 0; j < col; j++)
			{
				if (matrix[i][j] == 0)
				{
					matrix[i][0] = 0;
					matrix[0][j] = 0;
				}
			}
		}

		//注意：这里从1开始
		for (int i = 1; i < row; i++)
		{
			for (int j = 1; j < col; j++)
			{
				if (matrix[i][0] == 0) matrix[i][j] = 0;
				else if(matrix[0][j] == 0) matrix[i][j] = 0;
			}
		}

		if (firstColhasZero)
		{
			for (int i = 0; i < row; i++)
			{
				matrix[i][0] = 0;
			}
		}

		if (firstRowhasZero)
		{
			for (int i = 0; i < col; i++)
			{
				matrix[0][i] = 0;
			}
		}
	}

和上面差不多，小小改动一下。

class Solution {
public:
	void setZeroes(vector<vector<int> > &matrix)
	{
		int row = matrix.size();
		if (row < 1) return;
		int col = matrix[0].size();
		bool firstRowhasZero = false;
		bool firstColhasZero = false;

		for (int i = 0; i < row; i++)
			if (matrix[i][0] == 0) 
			{
				firstColhasZero = true;	
				break;
			}

		for (int i = 0; i < col; i++)
			if (matrix[0][i] == 0)
			{
				firstRowhasZero = true;
				break;
			}

		for (int i = 0; i < row; i++)
		{
			for (int j = 0; j < col; j++)
			{
				if (matrix[i][j] == 0)
				{
					matrix[i][0] = 0;
					matrix[0][j] = 0;
				}
			}
		}

		for (int i = 1; i < row; i++)
		{
			if (matrix[i][0] == 0)
				for (int j = 1; j < col; j++)
				{
					matrix[i][j] = 0;
				}
		}
		for (int j = 1; j < col; j++)
		{
			if (matrix[0][j] == 0)
				for (int i = 1; i < row; i++)
				{
					matrix[i][j] = 0;
				}
		}

		if (firstColhasZero)
		{
			for (int i = 0; i < row; i++)
			{
				matrix[i][0] = 0;
			}
		}

		if (firstRowhasZero)
		{
			for (int i = 0; i < col; i++)
			{
				matrix[0][i] = 0;
			}
		}
	}
};

//2014-2-11 update
	void setZeroes(vector<vector<int> > &matrix) 
	{
		if (matrix.empty() || matrix[0].empty()) return;
		bool row_flag = false, col_flag = false;

		for (int i = 0; i < matrix.size() && !col_flag; i++)
			if (matrix[i][0]==0) col_flag = true;
		for (int i = 0; i < matrix[0].size() && !row_flag; i++)
			if (matrix[0][i]==0) row_flag = true;

		for (int i = 1; i < matrix.size(); i++)
			for (int j = 1; j < matrix[0].size(); j++)
				if (matrix[i][j]==0) matrix[i][0] = matrix[0][j] = 0;

		for (int i = 1; i < matrix.size(); i++)
			if (matrix[i][0]==0) 
				for (int j = 1; j < matrix[0].size(); j++)
					matrix[i][j] = 0;
		for (int j = 1; j < matrix[0].size(); j++)
			if (matrix[0][j]==0)
				for (int i = 1; i < matrix.size(); i++)
					matrix[i][j] = 0;

		if (row_flag)
			for (int i = 0; i < matrix[0].size(); i++)
				matrix[0][i] = 0;
		if (col_flag)
			for (int i = 0; i < matrix.size(); i++)
				matrix[i][0] = 0;
	}