Given two n * m matrices A[][] and B[][] , the task is to make both the matrices strictly increasing (both rows and columns) only by swapping two elements in different matrices if they are located in the corresponding position i.e. A[i][j] can only be swapped with B[i][j] . If possible then print Yes otherwise, No .Examples:
Input:
A[][] = {{2, 10}, B[][] = {{9, 4},
{11, 5}} {3, 12}}
Output: Yes
Swap 2 with 9 and 5 with 12 then the resulting
matrices will be strictly increasing.
Input:
A[][] = {{1, 3}, B[][] = {{3, 1},
{2, 4}, {3, 6},
{5, 10}} {4, 8}}
Output: No
Approach: We can solve this problem using greedy technique . Swap A[i][j] with B[i][j] if A[i][j] > B[i][j] . At the end for every i and j we have A[i][j] ? B[i][j] . If the resultant matrices are strictly increasing then print Yes otherwise, print No . Below is the implementation of the above approach:
C++
#include<bits/stdc++.h>
using
namespace
std;
string Check(
int
a[][2],
int
b[][2],
int
n,
int
m)
{
for
(
int
i = 0; i < n; i++)
for
(
int
j = 0; j < m; j++)
if
(a[i][j] > b[i][j])
swap(a[i][j], b[i][j]);
for
(
int
i = 0; i < n; i++)
for
(
int
j = 0; j < m - 1; j++)
if
(a[i][j] >= a[i][j + 1] || b[i][j] >= b[i][j + 1])
return
"No"
;
for
(
int
i = 0; i < n - 1; i++)
for
(
int
j = 0; j < m ;j++)
if
(a[i][j] >= a[i + 1][j] || b[i][j] >= b[i + 1][j])
return
"No"
;
return
"Yes"
;
}
int
main()
{
int
n = 2, m = 2;
int
a[][2] = {{2, 10}, {11, 5}};
int
b[][2] = {{9, 4}, {3, 12}};
cout << (Check(a, b,n,m));
}
Java
class
GFG{
public
static
String Check(
int
a[][],
int
b[][],
int
n,
int
m)
{
for
(
int
i =
0
; i < n; i++)
for
(
int
j =
0
; j < m; j++)
if
(a[i][j] > b[i][j])
{
int
temp = a[i][j];
a[i][j] = b[i][j];
b[i][j] = temp;
}
for
(
int
i =
0
; i < n; i++)
for
(
int
j =
0
; j < m -
1
; j++)
if
(a[i][j] >= a[i][j +
1
] ||
b[i][j] >= b[i][j +
1
])
return
"No"
;
for
(
int
i =
0
; i < n -
1
; i++)
for
(
int
j =
0
; j < m ;j++)
if
(a[i][j] >= a[i +
1
][j] ||
b[i][j] >= b[i +
1
][j])
return
"No"
;
return
"Yes"
;
}
public
static
void
main(String[] args)
{
int
n =
2
, m =
2
;
int
a[][] = { {
2
,
10
}, {
11
,
5
} };
int
b[][] = { {
9
,
4
}, {
3
,
12
} };
System.out.print(Check(a, b, n, m));
}
}
Python3
def
Check(a, b):
for
i
in
range
(n):
for
j
in
range
(m):
if
a[i][j]>b[i][j]:
a[i][j], b[i][j]
=
b[i][j], a[i][j]
for
i
in
range
(n):
for
j
in
range
(m
-
1
):
if
(a[i][j]>
=
a[i][j
+
1
]
or
b[i][j]>
=
b[i][j
+
1
]):
return
"No"
for
i
in
range
(n
-
1
):
for
j
in
range
(m):
if
(a[i][j]>
=
a[i
+
1
][j]
or
b[i][j]>
=
b[i
+
1
][j]):
return
"No"
return
"Yes"
if
__name__
=
=
"__main__"
:
n, m
=
2
,
2
a
=
[[
2
,
10
], [
11
,
5
]]
b
=
[[
9
,
4
], [
3
,
12
]]
print
(Check(a, b))
C#
using
System;
using
System.Collections;
class
GfG{
static
string
Check(
int
[,]a,
int
[,]b,
int
n,
int
m)
{
for
(
int
i = 0; i < n; i++)
for
(
int
j = 0; j < m; j++)
if
(a[i, j] > b[i, j])
{
int
tmp = a[i, j];
a[i, j] = b[i, j];
b[i, j] = tmp;
}
for
(
int
i = 0; i < n; i++)
for
(
int
j = 0; j < m - 1; j++)
if
(a[i, j] >= a[i, j + 1] ||
b[i, j] >= b[i, j + 1])
return
"No"
;
for
(
int
i = 0; i < n - 1; i++)
for
(
int
j = 0; j < m ; j++)
if
(a[i, j] >= a[i + 1, j] ||
b[i, j] >= b[i + 1, j])
return
"No"
;
return
"Yes"
;
}
public
static
void
Main(
string
[]arg)
{
int
n = 2, m = 2;
int
[,]a = {{2, 10}, {11, 5}};
int
[,]b = {{9, 4}, {3, 12}};
Console.Write(Check(a, b, n, m));
}
}
PHP
<?php
function
Check(
$a
,
$b
,
$n
,
$m
)
{
for
(
$i
= 0;
$i
<
$n
;
$i
++)
{
for
(
$j
= 0;
$j
<
$n
;
$j
++)
{
if
(
$a
[
$i
][
$j
] >
$b
[
$i
][
$j
])
{
$temp
=
$a
[
$i
][
$j
];
$a
[
$i
][
$j
] =
$b
[
$i
][
$j
];
$b
[
$i
][
$j
] =
$temp
;
}
}
}
for
(
$i
= 0;
$i
<
$n
;
$i
++)
{
for
(
$j
= 0;
$j
<
$m
-1 ;
$j
++)
{
if
(
$a
[
$i
][
$j
] >=
$a
[
$i
][
$j
+ 1]
or
$b
[
$i
][
$j
] >=
$b
[
$i
][
$j
+ 1])
return
"No"
;
}
}
for
(
$i
= 0;
$i
<
$n
- 1;
$i
++)
{
for
(
$j
= 0;
$j
<
$m
;
$j
++)
{
if
(
$a
[
$i
][
$j
] >=
$a
[
$i
+ 1][
$j
]
or
$b
[
$i
][
$j
] >=
$b
[
$i
+ 1][
$j
])
return
"No"
;
}
}
return
"Yes"
;
}
$n
= 2;
$m
= 2;
$a
=
array
(
array
(2, 10),
array
(11, 5));
$b
=
array
(
array
(9, 4),
array
(3, 12));
print
(Check(
$a
,
$b
,
$n
,
$m
));
?>
Javascript
<script>
function
Check(a, b, n, m)
{
for
(let i = 0; i < n; i++)
for
(let j = 0; j < m; j++)
if
(a[i][j] > b[i][j])
{
let temp = a[i][j];
a[i][j] = b[i][j];
b[i][j] = temp;
}
for
(let i = 0; i < n; i++)
for
(let j = 0; j < m - 1; j++)
if
(a[i][j] >= a[i][j + 1] ||
b[i][j] >= b[i][j + 1])
return
"No"
;
for
(let i = 0; i < n - 1; i++)
for
(let j = 0; j < m ;j++)
if
(a[i][j] >= a[i + 1][j] ||
b[i][j] >= b[i + 1][j])
return
"No"
;
return
"Yes"
;
}
let n = 2, m = 2;
let a = [[ 2, 10 ], [ 11, 5 ]];
let b = [[ 9, 4 ], [3, 12 ]];
document.write(Check(a, b, n, m));
</script>
Time Complexity: O(N*M), as we are traversing over the matrix.
Auxiliary Space: O(1), as we are not using any extra space.
Last Updated :
22 Apr, 2022
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