一个布尔矩阵问题
给定一个大小为 MXN 的布尔矩阵 mat[M][N]，修改它使得如果矩阵单元 mat[i][j] 为 1（或真），则使第 i 行第 j 列的所有单元为 1。
Example 1
The matrix
1 0
0 0
should be changed to following
1 1
1 0
Example 2
The matrix
0 0 0
0 0 1
should be changed to following
0 0 1
1 1 1
Example 3
The matrix
1 0 0 1
0 0 1 0
0 0 0 0
should be changed to following
1 1 1 1
1 1 1 1
1 0 1 1方法一（使用两个临时数组）
1) 创建两个临时数组 row[M] 和 col[N]。将 row[] 和 col[] 的所有值初始化为 0。
2）遍历输入矩阵mat[M][N]。如果您看到一个条目 mat[i][j] 为真，则将 row[i] 和 col[j] 标记为真。
3）再次遍历输入矩阵mat[M][N]。对于每个条目 mat[i][j]，检查 row[i] 和 col[j] 的值。如果两个值（row[i] 或 col[j]）中的任何一个为真，则将 mat[i][j] 标记为真。
感谢 Dixit Sethi 提出这种方法。
C++
// C++ Code For A Boolean Matrix Question
#include
using namespace std;
#define R 3
#define C 4
void modifyMatrix(bool mat[R][C])
{
bool row[R];
bool col[C];
int i, j;
/* Initialize all values of row[] as 0 */
for (i = 0; i < R; i++)
{
row[i] = 0;
}
/* Initialize all values of col[] as 0 */
for (i = 0; i < C; i++)
{
col[i] = 0;
}
// Store the rows and columns to be marked as
// 1 in row[] and col[] arrays respectively
for (i = 0; i < R; i++)
{
for (j = 0; j < C; j++)
{
if (mat[i][j] == 1)
{
row[i] = 1;
col[j] = 1;
}
}
}
// Modify the input matrix mat[] using the
// above constructed row[] and col[] arrays
for (i = 0; i < R; i++)
{
for (j = 0; j < C; j++)
{
if ( row[i] == 1 || col[j] == 1 )
{
mat[i][j] = 1;
}
}
}
}
/* A utility function to print a 2D matrix */
void printMatrix(bool mat[R][C])
{
int i, j;
for (i = 0; i < R; i++)
{
for (j = 0; j < C; j++)
{
cout << mat[i][j];
}
cout << endl;
}
}
// Driver Code
int main()
{
bool mat[R][C] = { {1, 0, 0, 1},
{0, 0, 1, 0},
{0, 0, 0, 0}};
cout << "Input Matrix \n";
printMatrix(mat);
modifyMatrix(mat);
printf("Matrix after modification \n");
printMatrix(mat);
return 0;
}
// This code is contributed
// by Akanksha Rai(Abby_akku) Java
// Java Code For A Boolean Matrix Question
class GFG
{
public static void modifyMatrix(int mat[ ][ ], int R, int C)
{
int row[ ]= new int [R];
int col[ ]= new int [C];
int i, j;
/* Initialize all values of row[] as 0 */
for (i = 0; i < R; i++)
{
row[i] = 0;
}
/* Initialize all values of col[] as 0 */
for (i = 0; i < C; i++)
{
col[i] = 0;
}
/* Store the rows and columns to be marked as
1 in row[] and col[] arrays respectively */
for (i = 0; i < R; i++)
{
for (j = 0; j < C; j++)
{
if (mat[i][j] == 1)
{
row[i] = 1;
col[j] = 1;
}
}
}
/* Modify the input matrix mat[] using the
above constructed row[] and col[] arrays */
for (i = 0; i < R; i++)
{
for (j = 0; j < C; j++)
{
if ( row[i] == 1 || col[j] == 1 )
{
mat[i][j] = 1;
}
}
}
}
/* A utility function to print a 2D matrix */
public static void printMatrix(int mat[ ][ ], int R, int C)
{
int i, j;
for (i = 0; i < R; i++)
{
for (j = 0; j < C; j++)
{
System.out.print(mat[i][j]+ " ");
}
System.out.println();
}
}
/* Driver program to test above functions */
public static void main(String[] args)
{
int mat[ ][ ] = { {1, 0, 0, 1},
{0, 0, 1, 0},
{0, 0, 0, 0},};
System.out.println("Matrix Initially");
printMatrix(mat, 3, 4);
modifyMatrix(mat, 3, 4);
System.out.println("Matrix after modification n");
printMatrix(mat, 3, 4);
}
}
// This code is contributed by Kamal RawalPython3
# Python3 Code For A Boolean Matrix Question
R = 3
C = 4
def modifyMatrix(mat):
row = [0] * R
col = [0] * C
# Initialize all values of row[] as 0
for i in range(0, R):
row[i] = 0
# Initialize all values of col[] as 0
for i in range(0, C) :
col[i] = 0
# Store the rows and columns to be marked
# as 1 in row[] and col[] arrays respectively
for i in range(0, R) :
for j in range(0, C) :
if (mat[i][j] == 1) :
row[i] = 1
col[j] = 1
# Modify the input matrix mat[] using the
# above constructed row[] and col[] arrays
for i in range(0, R) :
for j in range(0, C):
if ( row[i] == 1 or col[j] == 1 ) :
mat[i][j] = 1
# A utility function to print a 2D matrix
def printMatrix(mat) :
for i in range(0, R):
for j in range(0, C) :
print(mat[i][j], end = " ")
print()
# Driver Code
mat = [ [1, 0, 0, 1],
[0, 0, 1, 0],
[0, 0, 0, 0] ]
print("Input Matrix n")
printMatrix(mat)
modifyMatrix(mat)
print("Matrix after modification n")
printMatrix(mat)
# This code is contributed by Nikita Tiwari.C#
// C# Code For A Boolean
// Matrix Question
using System;
class GFG
{
public static void modifyMatrix(int [,]mat,
int R, int C)
{
int []row = new int [R];
int []col = new int [C];
int i, j;
/* Initialize all values
of row[] as 0 */
for (i = 0; i < R; i++)
{
row[i] = 0;
}
/* Initialize all values
of col[] as 0 */
for (i = 0; i < C; i++)
{
col[i] = 0;
}
/* Store the rows and columns
to be marked as 1 in row[]
and col[] arrays respectively */
for (i = 0; i < R; i++)
{
for (j = 0; j < C; j++)
{
if (mat[i, j] == 1)
{
row[i] = 1;
col[j] = 1;
}
}
}
/* Modify the input matrix
mat[] using the above
constructed row[] and
col[] arrays */
for (i = 0; i < R; i++)
{
for (j = 0; j < C; j++)
{
if (row[i] == 1 || col[j] == 1)
{
mat[i, j] = 1;
}
}
}
}
/* A utility function to
print a 2D matrix */
public static void printMatrix(int [,]mat,
int R, int C)
{
int i, j;
for (i = 0; i < R; i++)
{
for (j = 0; j < C; j++)
{
Console.Write(mat[i, j] + " ");
}
Console.WriteLine();
}
}
// Driver code
static public void Main ()
{
int [,]mat = {{1, 0, 0, 1},
{0, 0, 1, 0},
{0, 0, 0, 0}};
Console.WriteLine("Matrix Initially");
printMatrix(mat, 3, 4);
modifyMatrix(mat, 3, 4);
Console.WriteLine("Matrix after "+
"modification n");
printMatrix(mat, 3, 4);
}
}
// This code is contributed by ajitPHP
Javascript
C++
#include
using namespace std;
#define R 3
#define C 4
void modifyMatrix(int mat[R][C])
{
// variables to check if there are any 1
// in first row and column
bool row_flag = false;
bool col_flag = false;
// updating the first row and col if 1
// is encountered
for (int i = 0; i < R; i++) {
for (int j = 0; j < C; j++) {
if (i == 0 && mat[i][j] == 1)
row_flag = true;
if (j == 0 && mat[i][j] == 1)
col_flag = true;
if (mat[i][j] == 1) {
mat[0][j] = 1;
mat[i][0] = 1;
}
}
}
// Modify the input matrix mat[] using the
// first row and first column of Matrix mat
for (int i = 1; i < R; i++) {
for (int j = 1; j < C; j++) {
if (mat[0][j] == 1 || mat[i][0] == 1) {
mat[i][j] = 1;
}
}
}
// modify first row if there was any 1
if (row_flag == true) {
for (int i = 0; i < C; i++) {
mat[0][i] = 1;
}
}
// modify first col if there was any 1
if (col_flag == true) {
for (int i = 0; i < R; i++) {
mat[i][0] = 1;
}
}
}
/* A utility function to print a 2D matrix */
void printMatrix(int mat[R][C])
{
for (int i = 0; i < R; i++) {
for (int j = 0; j < C; j++) {
cout << mat[i][j];
}
cout << "\n";
}
}
// Driver function to test the above function
int main()
{
int mat[R][C] = { { 1, 0, 0, 1 },
{ 0, 0, 1, 0 },
{ 0, 0, 0, 0 } };
cout << "Input Matrix :\n";
printMatrix(mat);
modifyMatrix(mat);
cout << "Matrix After Modification :\n";
printMatrix(mat);
return 0;
}
// This code is contributed by Nikita Tiwari Java
class GFG
{
public static void modifyMatrix(int mat[][]){
// variables to check if there are any 1
// in first row and column
boolean row_flag = false;
boolean col_flag = false;
// updating the first row and col if 1
// is encountered
for (int i = 0; i < mat.length; i++ ){
for (int j = 0; j < mat[0].length; j++){
if (i == 0 && mat[i][j] == 1)
row_flag = true;
if (j == 0 && mat[i][j] == 1)
col_flag = true;
if (mat[i][j] == 1){
mat[0][j] = 1;
mat[i][0] = 1;
}
}
}
// Modify the input matrix mat[] using the
// first row and first column of Matrix mat
for (int i = 1; i < mat.length; i ++){
for (int j = 1; j < mat[0].length; j ++){
if (mat[0][j] == 1 || mat[i][0] == 1){
mat[i][j] = 1;
}
}
}
// modify first row if there was any 1
if (row_flag == true){
for (int i = 0; i < mat[0].length; i++){
mat[0][i] = 1;
}
}
// modify first col if there was any 1
if (col_flag == true){
for (int i = 0; i < mat.length; i ++){
mat[i][0] = 1;
}
}
}
/* A utility function to print a 2D matrix */
public static void printMatrix(int mat[][]){
for (int i = 0; i < mat.length; i ++){
for (int j = 0; j < mat[0].length; j ++){
System.out.print( mat[i][j] );
}
System.out.println("");
}
}
// Driver function to test the above function
public static void main(String args[] ){
int mat[][] = {{1, 0, 0, 1},
{0, 0, 1, 0},
{0, 0, 0, 0}};
System.out.println("Input Matrix :");
printMatrix(mat);
modifyMatrix(mat);
System.out.println("Matrix After Modification :");
printMatrix(mat);
}
}
// This code is contributed by Arnav Kr. Mandal.Python3
# Python3 Code For A Boolean Matrix Question
def modifyMatrix(mat) :
# variables to check if there are any 1
# in first row and column
row_flag = False
col_flag = False
# updating the first row and col
# if 1 is encountered
for i in range(0, len(mat)) :
for j in range(0, len(mat)) :
if (i == 0 and mat[i][j] == 1) :
row_flag = True
if (j == 0 and mat[i][j] == 1) :
col_flag = True
if (mat[i][j] == 1) :
mat[0][j] = 1
mat[i][0] = 1
# Modify the input matrix mat[] using the
# first row and first column of Matrix mat
for i in range(1, len(mat)) :
for j in range(1, len(mat) + 1) :
if (mat[0][j] == 1 or mat[i][0] == 1) :
mat[i][j] = 1
# modify first row if there was any 1
if (row_flag == True) :
for i in range(0, len(mat)) :
mat[0][i] = 1
# modify first col if there was any 1
if (col_flag == True) :
for i in range(0, len(mat)) :
mat[i][0] = 1
# A utility function to print a 2D matrix
def printMatrix(mat) :
for i in range(0, len(mat)) :
for j in range(0, len(mat) + 1) :
print( mat[i][j], end = "" )
print()
# Driver Code
mat = [ [1, 0, 0, 1],
[0, 0, 1, 0],
[0, 0, 0, 0] ]
print("Input Matrix :")
printMatrix(mat)
modifyMatrix(mat)
print("Matrix After Modification :")
printMatrix(mat)
# This code is contributed by Nikita tiwari.C#
// C# Code For A Boolean
// Matrix Question
using System;
class GFG
{
public static void modifyMatrix(int[,] mat)
{
// variables to check
// if there are any 1
// in first row and column
bool row_flag = false;
bool col_flag = false;
// updating the first
// row and col if 1
// is encountered
for (int i = 0;
i < mat.GetLength(0); i++ )
{
for (int j = 0;
j < mat.GetLength(1); j++)
{
if (i == 0 && mat[i, j] == 1)
row_flag = true;
if (j == 0 && mat[i, j] == 1)
col_flag = true;
if (mat[i, j] == 1)
{
mat[0, j] = 1;
mat[i,0] = 1;
}
}
}
// Modify the input matrix mat[]
// using the first row and first
// column of Matrix mat
for (int i = 1;
i < mat.GetLength(0); i ++)
{
for (int j = 1;
j < mat.GetLength(1); j ++)
{
if (mat[0, j] == 1 ||
mat[i, 0] == 1)
{
mat[i, j] = 1;
}
}
}
// modify first row
// if there was any 1
if (row_flag == true)
{
for (int i = 0;
i < mat.GetLength(1); i++)
{
mat[0, i] = 1;
}
}
// modify first col if
// there was any 1
if (col_flag == true)
{
for (int i = 0;
i < mat.GetLength(0); i ++)
{
mat[i, 0] = 1;
}
}
}
/* A utility function
to print a 2D matrix */
public static void printMatrix(int[,] mat)
{
for (int i = 0;
i < mat.GetLength(0); i ++)
{
for (int j = 0;
j < mat.GetLength(1); j ++)
{
Console.Write(mat[i, j] + " " );
}
Console.Write("\n");
}
}
// Driver Code
public static void Main()
{
int[,] mat = {{1, 0, 0, 1},
{0, 0, 1, 0},
{0, 0, 0, 0}};
Console.Write("Input Matrix :\n");
printMatrix(mat);
modifyMatrix(mat);
Console.Write("Matrix After " +
"Modification :\n");
printMatrix(mat);
}
}
// This code is contributed
// by ChitraNayalPHP
Javascript
输出：
Input Matrix
1 0 0 1
0 0 1 0
0 0 0 0
Matrix after modification
1 1 1 1
1 1 1 1
1 0 1 1时间复杂度： O(M*N)
辅助空间： O(M + N)
方法 2（方法 1 的空间优化版本）
该方法是上述方法1的空间优化版本。该方法使用输入矩阵的第一行和第一列代替方法1的辅助数组row[]和col[]。所以我们要做的是：首先取关心第一行和第一列，并将关于这两个的信息存储在两个标志变量 rowFlag 和 colFlag 中。一旦我们有了这些信息，我们就可以使用第一行和第一列作为辅助数组，并将方法 1 应用于大小为 (M-1)*(N-1) 的子矩阵（不包括第一行和第一列的矩阵）。
1）扫描第一行并设置一个变量rowFlag来指示我们是否需要在第一行设置全1。
2) 扫描第一列并设置一个变量 colFlag 来指示我们是否需要在第一列中设置全 1。
3）将第一行和第一列分别作为辅助数组row[]和col[]，将矩阵视为从第二行和第二列开始的子矩阵并应用方法1。
4) 最后，如果需要，使用 rowFlag 和 colFlag 更新第一行和第一列。
时间复杂度：O(M*N)
辅助空间：O(1)
感谢 Sidh 提出这种方法。
C++
#include
using namespace std;
#define R 3
#define C 4
void modifyMatrix(int mat[R][C])
{
// variables to check if there are any 1
// in first row and column
bool row_flag = false;
bool col_flag = false;
// updating the first row and col if 1
// is encountered
for (int i = 0; i < R; i++) {
for (int j = 0; j < C; j++) {
if (i == 0 && mat[i][j] == 1)
row_flag = true;
if (j == 0 && mat[i][j] == 1)
col_flag = true;
if (mat[i][j] == 1) {
mat[0][j] = 1;
mat[i][0] = 1;
}
}
}
// Modify the input matrix mat[] using the
// first row and first column of Matrix mat
for (int i = 1; i < R; i++) {
for (int j = 1; j < C; j++) {
if (mat[0][j] == 1 || mat[i][0] == 1) {
mat[i][j] = 1;
}
}
}
// modify first row if there was any 1
if (row_flag == true) {
for (int i = 0; i < C; i++) {
mat[0][i] = 1;
}
}
// modify first col if there was any 1
if (col_flag == true) {
for (int i = 0; i < R; i++) {
mat[i][0] = 1;
}
}
}
/* A utility function to print a 2D matrix */
void printMatrix(int mat[R][C])
{
for (int i = 0; i < R; i++) {
for (int j = 0; j < C; j++) {
cout << mat[i][j];
}
cout << "\n";
}
}
// Driver function to test the above function
int main()
{
int mat[R][C] = { { 1, 0, 0, 1 },
{ 0, 0, 1, 0 },
{ 0, 0, 0, 0 } };
cout << "Input Matrix :\n";
printMatrix(mat);
modifyMatrix(mat);
cout << "Matrix After Modification :\n";
printMatrix(mat);
return 0;
}
// This code is contributed by Nikita Tiwari
Java
class GFG
{
public static void modifyMatrix(int mat[][]){
// variables to check if there are any 1
// in first row and column
boolean row_flag = false;
boolean col_flag = false;
// updating the first row and col if 1
// is encountered
for (int i = 0; i < mat.length; i++ ){
for (int j = 0; j < mat[0].length; j++){
if (i == 0 && mat[i][j] == 1)
row_flag = true;
if (j == 0 && mat[i][j] == 1)
col_flag = true;
if (mat[i][j] == 1){
mat[0][j] = 1;
mat[i][0] = 1;
}
}
}
// Modify the input matrix mat[] using the
// first row and first column of Matrix mat
for (int i = 1; i < mat.length; i ++){
for (int j = 1; j < mat[0].length; j ++){
if (mat[0][j] == 1 || mat[i][0] == 1){
mat[i][j] = 1;
}
}
}
// modify first row if there was any 1
if (row_flag == true){
for (int i = 0; i < mat[0].length; i++){
mat[0][i] = 1;
}
}
// modify first col if there was any 1
if (col_flag == true){
for (int i = 0; i < mat.length; i ++){
mat[i][0] = 1;
}
}
}
/* A utility function to print a 2D matrix */
public static void printMatrix(int mat[][]){
for (int i = 0; i < mat.length; i ++){
for (int j = 0; j < mat[0].length; j ++){
System.out.print( mat[i][j] );
}
System.out.println("");
}
}
// Driver function to test the above function
public static void main(String args[] ){
int mat[][] = {{1, 0, 0, 1},
{0, 0, 1, 0},
{0, 0, 0, 0}};
System.out.println("Input Matrix :");
printMatrix(mat);
modifyMatrix(mat);
System.out.println("Matrix After Modification :");
printMatrix(mat);
}
}
// This code is contributed by Arnav Kr. Mandal.
Python3
# Python3 Code For A Boolean Matrix Question
def modifyMatrix(mat) :
# variables to check if there are any 1
# in first row and column
row_flag = False
col_flag = False
# updating the first row and col
# if 1 is encountered
for i in range(0, len(mat)) :
for j in range(0, len(mat)) :
if (i == 0 and mat[i][j] == 1) :
row_flag = True
if (j == 0 and mat[i][j] == 1) :
col_flag = True
if (mat[i][j] == 1) :
mat[0][j] = 1
mat[i][0] = 1
# Modify the input matrix mat[] using the
# first row and first column of Matrix mat
for i in range(1, len(mat)) :
for j in range(1, len(mat) + 1) :
if (mat[0][j] == 1 or mat[i][0] == 1) :
mat[i][j] = 1
# modify first row if there was any 1
if (row_flag == True) :
for i in range(0, len(mat)) :
mat[0][i] = 1
# modify first col if there was any 1
if (col_flag == True) :
for i in range(0, len(mat)) :
mat[i][0] = 1
# A utility function to print a 2D matrix
def printMatrix(mat) :
for i in range(0, len(mat)) :
for j in range(0, len(mat) + 1) :
print( mat[i][j], end = "" )
print()
# Driver Code
mat = [ [1, 0, 0, 1],
[0, 0, 1, 0],
[0, 0, 0, 0] ]
print("Input Matrix :")
printMatrix(mat)
modifyMatrix(mat)
print("Matrix After Modification :")
printMatrix(mat)
# This code is contributed by Nikita tiwari.
C＃
// C# Code For A Boolean
// Matrix Question
using System;
class GFG
{
public static void modifyMatrix(int[,] mat)
{
// variables to check
// if there are any 1
// in first row and column
bool row_flag = false;
bool col_flag = false;
// updating the first
// row and col if 1
// is encountered
for (int i = 0;
i < mat.GetLength(0); i++ )
{
for (int j = 0;
j < mat.GetLength(1); j++)
{
if (i == 0 && mat[i, j] == 1)
row_flag = true;
if (j == 0 && mat[i, j] == 1)
col_flag = true;
if (mat[i, j] == 1)
{
mat[0, j] = 1;
mat[i,0] = 1;
}
}
}
// Modify the input matrix mat[]
// using the first row and first
// column of Matrix mat
for (int i = 1;
i < mat.GetLength(0); i ++)
{
for (int j = 1;
j < mat.GetLength(1); j ++)
{
if (mat[0, j] == 1 ||
mat[i, 0] == 1)
{
mat[i, j] = 1;
}
}
}
// modify first row
// if there was any 1
if (row_flag == true)
{
for (int i = 0;
i < mat.GetLength(1); i++)
{
mat[0, i] = 1;
}
}
// modify first col if
// there was any 1
if (col_flag == true)
{
for (int i = 0;
i < mat.GetLength(0); i ++)
{
mat[i, 0] = 1;
}
}
}
/* A utility function
to print a 2D matrix */
public static void printMatrix(int[,] mat)
{
for (int i = 0;
i < mat.GetLength(0); i ++)
{
for (int j = 0;
j < mat.GetLength(1); j ++)
{
Console.Write(mat[i, j] + " " );
}
Console.Write("\n");
}
}
// Driver Code
public static void Main()
{
int[,] mat = {{1, 0, 0, 1},
{0, 0, 1, 0},
{0, 0, 0, 0}};
Console.Write("Input Matrix :\n");
printMatrix(mat);
modifyMatrix(mat);
Console.Write("Matrix After " +
"Modification :\n");
printMatrix(mat);
}
}
// This code is contributed
// by ChitraNayal
PHP
Javascript
输出：
Input Matrix :
1001
0010
0000
Matrix After Modification :
1111
1111
1011