给定一个二进制矩阵，任务是查找行交换或列交换是否给出全为1的最大大小子矩阵。在行交换中，我们可以交换任意两行。在列交换中，我们可以交换任何两个列。输出“行交换”或“列交换”以及最大大小。
例子：
Input : 1 1 1
1 0 1
Output : Column Swap
4
By swapping column 1 and column 2(0-based indexing),
index (0, 0) to (1, 1) makes the largest binary
sub-matrix.
Input : 0 0 0
1 1 0
1 1 0
0 0 0
1 1 0
Output : Row Swap
6
Input : 1 1 0
0 0 0
0 0 0
1 1 0
1 1 0
0 0 0
1 1 0
Output : Row Swap
8
想法是找到行交换和列交换最大大小的二进制子矩阵并进行比较。
要找到允许进行行交换的最大大小的二进制子矩阵，请制作一个二维数组，例如dp [i] [j]。 dp [i] [j]的每个值都包含第i行(i，j)右侧连续的1的数量。现在，将每一列一一存储在一维临时数组中，说b []并排序，并找到最大b [i] *(n – i)，因为b [i]表示子矩阵的宽度和(n – i)是子矩阵的高度。
同样，要查找允许进行列交换的最大大小的二进制子矩阵，请找到dp [i] [j]，其中每个值都包含第j列(i，j)下的连续1的数目。类似地，将每一行一一存储在一维临时数组中，例如b []并进行排序。找到最大的b [i] *(m – i)，因为b [i]表示子矩阵的高度，而(n – i)是子矩阵的宽度。
以下是此方法的实现：
C++
// C++ program to find maximum binary sub-matrix
// with row swaps and column swaps.
#include
#define R 5
#define C 3
using namespace std;
// Precompute the number of consecutive 1 below the
// (i, j) in j-th column and the number of consecutive 1s
// on right side of (i, j) in i-th row.
void precompute(int mat[R][C], int ryt[][C + 2],
int dwn[R + 2][C + 2])
{
// Travesing the 2d matrix from top-right.
for (int j=C-1; j>=0; j--)
{
for (int i=0; i= 0; i--)
{
for (int j = 0; j < C; ++j)
{
// If (i,j) contain 0, do nothing
if (mat[i][j] == 0)
dwn[i][j] = 0;
// Counting consecutive 1 down to (i,j).
else
dwn[i][j] = dwn[i + 1][j] + 1;
}
}
}
// Return maximum size submatrix with row swap allowed.
int solveRowSwap(int ryt[R + 2][C + 2])
{
int b[R] = { 0 }, ans = 0;
for (int j=0; j cswap)? (cout << "Row Swap\n" << rswap << endl):
(cout << "Column Swap\n" << cswap << endl);
}
// Driven Program
int main()
{
int mat[R][C] = {{ 0, 0, 0 },
{ 1, 1, 0 },
{ 1, 1, 0 },
{ 0, 0, 0 },
{ 1, 1, 0 }};
findMax1s(mat);
return 0;
} Java
import java.util.Arrays;
// Java program to find maximum binary sub-matrix
// with row swaps and column swaps.
class GFG {
static int R = 5;
static int C = 3;
// Precompute the number of consecutive 1 below the
// (i, j) in j-th column and the number of consecutive 1s
// on right side of (i, j) in i-th row.
static void precompute(int mat[][], int ryt[][],
int dwn[][]) {
// Travesing the 2d matrix from top-right.
for (int j = C - 1; j >= 0; j--) {
for (int i = 0; i < R; ++i) {
// If (i,j) contain 0, do nothing
if (mat[i][j] == 0) {
ryt[i][j] = 0;
} // Counting consecutive 1 on right side
else {
ryt[i][j] = ryt[i][j + 1] + 1;
}
}
}
// Travesing the 2d matrix from bottom-left.
for (int i = R - 1; i >= 0; i--) {
for (int j = 0; j < C; ++j) {
// If (i,j) contain 0, do nothing
if (mat[i][j] == 0) {
dwn[i][j] = 0;
} // Counting consecutive 1 down to (i,j).
else {
dwn[i][j] = dwn[i + 1][j] + 1;
}
}
}
}
// Return maximum size submatrix with row swap allowed.
static int solveRowSwap(int ryt[][]) {
int b[] = new int[R], ans = 0;
for (int j = 0; j < C; j++) {
// Copying the column
for (int i = 0; i < R; i++) {
b[i] = ryt[i][j];
}
// Sort the copied array
Arrays.sort(b);
// Find maximum submatrix size.
for (int i = 0; i < R; ++i) {
ans = Math.max(ans, b[i] * (R - i));
}
}
return ans;
}
// Return maximum size submatrix with column
// swap allowed.
static int solveColumnSwap(int dwn[][]) {
int b[] = new int[C], ans = 0;
for (int i = 0; i < R; ++i) {
// Copying the row.
for (int j = 0; j < C; ++j) {
b[j] = dwn[i][j];
}
// Sort the copied array
Arrays.sort(b);
// Find maximum submatrix size.
for (int k = 0; k < C; ++k) {
ans = Math.max(ans, b[k] * (C - k));
}
}
return ans;
}
static void findMax1s(int mat[][]) {
int ryt[][] = new int[R + 2][C + 2], dwn[][] = new int[R + 2][C + 2];
precompute(mat, ryt, dwn);
// Solving for row swap and column swap
int rswap = solveRowSwap(ryt);
int cswap = solveColumnSwap(dwn);
// Comparing both.
if (rswap > cswap) {
System.out.println("Row Swap\n" + rswap);
} else {
System.out.println("Column Swap\n" + cswap);
}
}
// Driven Program
public static void main(String[] args) {
int mat[][] = {{0, 0, 0},
{1, 1, 0},
{1, 1, 0},
{0, 0, 0},
{1, 1, 0}};
findMax1s(mat);
}
}
/* This Java code is contributed by PrinciRaj1992*/Python3
# Python3 program to find maximum binary
# sub-matrix with row swaps and column swaps.
R, C = 5, 3
# Precompute the number of consecutive 1
# below the (i, j) in j-th column and the
# number of consecutive 1s on right side
# of (i, j) in i-th row.
def precompute(mat, ryt, dwn):
# Travesing the 2d matrix from top-right.
for j in range(C - 1, -1, -1):
for i in range(0, R):
# If (i,j) contain 0, do nothing
if mat[i][j] == 0:
ryt[i][j] = 0
# Counting consecutive 1 on right side
else:
ryt[i][j] = ryt[i][j + 1] + 1
# Travesing the 2d matrix from bottom-left.
for i in range(R - 1, -1, -1):
for j in range(0, C):
# If (i,j) contain 0, do nothing
if mat[i][j] == 0:
dwn[i][j] = 0
# Counting consecutive 1 down to (i,j).
else:
dwn[i][j] = dwn[i + 1][j] + 1
# Return maximum size submatrix
# with row swap allowed.
def solveRowSwap(ryt):
b = [0] * R
ans = 0
for j in range(0, C):
# Copying the column
for i in range(0, R):
b[i] = ryt[i][j]
# Sort the copied array
b.sort()
# Find maximum submatrix size.
for i in range(0, R):
ans = max(ans, b[i] * (R - i))
return ans
# Return maximum size submatrix
# with column swap allowed.
def solveColumnSwap(dwn):
b = [0] * C
ans = 0
for i in range(0, R):
# Copying the row.
for j in range(0, C):
b[j] = dwn[i][j]
# Sort the copied array
b.sort()
# Find maximum submatrix size.
for i in range(0, C):
ans = max(ans, b[i] * (C - i))
return ans
def findMax1s(mat):
ryt = [[0 for i in range(C + 2)]
for j in range(R + 2)]
dwn = [[0 for i in range(C + 2)]
for j in range(R + 2)]
precompute(mat, ryt, dwn)
# Solving for row swap and column swap
rswap = solveRowSwap(ryt)
cswap = solveColumnSwap(dwn)
# Comparing both.
if rswap > cswap: print("Row Swap\n", rswap)
else: print("Column Swap\n", cswap)
# Driver Code
if __name__ == "__main__":
mat = [[0, 0, 0],
[1, 1, 0],
[1, 1, 0],
[0, 0, 0],
[1, 1, 0]]
findMax1s(mat)
# This code is contributed by Rituraj JainC#
// C# program to find maximum binary sub-matrix
// with row swaps and column swaps.
using System;
public class GFG {
static int R = 5;
static int C = 3;
// Precompute the number of consecutive 1 below the
// (i, j) in j-th column and the number of consecutive 1s
// on right side of (i, j) in i-th row.
static void precompute(int [,]mat, int [,]ryt,
int [,]dwn) {
// Travesing the 2d matrix from top-right.
for (int j = C - 1; j >= 0; j--) {
for (int i = 0; i < R; ++i) {
// If (i,j) contain 0, do nothing
if (mat[i,j] == 0) {
ryt[i,j] = 0;
} // Counting consecutive 1 on right side
else {
ryt[i,j] = ryt[i,j + 1] + 1;
}
}
}
// Travesing the 2d matrix from bottom-left.
for (int i = R - 1; i >= 0; i--) {
for (int j = 0; j < C; ++j) {
// If (i,j) contain 0, do nothing
if (mat[i,j] == 0) {
dwn[i,j] = 0;
} // Counting consecutive 1 down to (i,j).
else {
dwn[i,j] = dwn[i + 1,j] + 1;
}
}
}
}
// Return maximum size submatrix with row swap allowed.
static int solveRowSwap(int [,]ryt) {
int []b = new int[R]; int ans = 0;
for (int j = 0; j < C; j++) {
// Copying the column
for (int i = 0; i < R; i++) {
b[i] = ryt[i,j];
}
// Sort the copied array
Array.Sort(b);
// Find maximum submatrix size.
for (int i = 0; i < R; ++i) {
ans = Math.Max(ans, b[i] * (R - i));
}
}
return ans;
}
// Return maximum size submatrix with column
// swap allowed.
static int solveColumnSwap(int [,]dwn) {
int []b = new int[C];int ans = 0;
for (int i = 0; i < R; ++i) {
// Copying the row.
for (int j = 0; j < C; ++j) {
b[j] = dwn[i,j];
}
// Sort the copied array
Array.Sort(b);
// Find maximum submatrix size.
for (int k = 0; k < C; ++k) {
ans = Math.Max(ans, b[k] * (C - k));
}
}
return ans;
}
static void findMax1s(int [,]mat) {
int [,]ryt = new int[R + 2,C + 2];
int [,]dwn = new int[R + 2,C + 2];
precompute(mat, ryt, dwn);
// Solving for row swap and column swap
int rswap = solveRowSwap(ryt);
int cswap = solveColumnSwap(dwn);
// Comparing both.
if (rswap > cswap) {
Console.WriteLine("Row Swap\n" + rswap);
} else {
Console.WriteLine("Column Swap\n" + cswap);
}
}
// Driven Program
public static void Main() {
int [,]mat = {{0, 0, 0},
{1, 1, 0},
{1, 1, 0},
{0, 0, 0},
{1, 1, 0}};
findMax1s(mat);
}
}
/* This C# code is contributed by PrinciRaj1992*/输出：
Row Swap
6