给定一个二元矩阵，任务是找出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，我们可以交换任意两列。输出“行交换”或“列交换”和最大大小。
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
这个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。
要找到允许行交换的最大大小的二进制子矩阵，请创建一个二维数组，例如 dp[i][j]。 dp[i][j] 的每个值都包含第 i 行 (i,j) 右侧连续 1 的个数。现在，将一维临时数组中的每一列一一存储，比如说 b[] 并排序，并找到最大的 b[i] * (n – i)，因为 b[i] 表示子矩阵宽度和(n – i) 是子矩阵高度。
类似地，要找到允许列交换的最大大小二进制子矩阵，请找到 dp[i][j]，其中每个值包含第 j 列中 (i, j) 下方的连续 1 的数量。类似地，将每一行一维临时数组中的每一行都一一存储，比如说 b[] 并排序。找到最大值 b[i] * (m – i)，因为 b[i] 表示子矩阵高度，而 (n – i) 是子矩阵宽度。
下面是这个方法的实现：
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
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