# C++ Program to find out if a palindromic matrix can be made from a given matrix

Suppose, we are given a matrix with dimensions h x w. The matrix contains English letters. We have to create another matrix that will contain palindromic rows and columns, i.e. each row and column would be palindromes. To do that, any arrangement of rows and columns can be done from the given matrix; but no element can be changed, i.e. an 'a' cannot be changed to a 'b'. If that is possible to make a palindromic matrix from the given matrix, we return true; or otherwise, we return false.

So, if the input is like h = 4, w = 4, mat = {"xxyy", "xyxx", "yxxy", "xyyy"}, then the output will be true.

## Steps

To solve this, we will follow these steps −

Define one map mp
Define an array count of size 4.
for initialize i := 0, when i < h, update (increase i by 1), do:
for initialize j := 0, when j < w, update (increase j by 1), do:
(increase tp[mat[i, j]] by 1)
for each value val in tp, do:
increase count[second value of val mod 4] by 1
check := true
if h mod 2 is same as 0 and w mod 2 is same as 0, then:
if count + count + count > 0, then:
check := false
otherwise when h mod 2 is same as 1 and w mod 2 is same as 1, then:
if count + count > 1, then:
check := false
otherwise when count > h / 2 + w / 2, then:
check := false
Otherwise
if count + count > 0, then:
check := false
otherwise when h mod 2 is same as 1 and count > w / 2, then:
check := false
otherwise when w mod 2 is same as 1 and count > h / 2, then:
check := false
return check

## Example

Let us see the following implementation to get better understanding −

#include <bits/stdc++.h>
using namespace std;
const int INF = 1e9;

bool solve(int h, int w, vector<string> mat){
map<char, int> tp;
vector<int> count(4);
for (int i = 0; i < h; ++i) {
for (int j = 0; j < w; ++j)
tp[mat[i][j]]++;
}
for (auto val : tp)
count[val.second % 4]++;
bool check = true;
if (h % 2 == 0 && w % 2 == 0) {
if (count + count + count > 0)
check = false;
}
else if (h % 2 == 1 && w % 2 == 1) {
if (count+count > 1)
check = false;
else if (count > h / 2 + w / 2)
check = false;
} else {
if (count + count > 0)
check = false;
else if (h % 2 == 1 && count > w / 2)
check = false;
else if (w % 2 == 1 && count > h / 2)
check = false;
}
return check;
}
int main() {
int h = 4, w = 4;
vector<string> mat = {"xxyy", "xyxx", "yxxy", "xyyy"};
cout<< solve(h, w, mat);
return 0;
}

## Input

4, 4, {"xxyy", "xyxx", "yxxy", "xyyy"}

## Output

1