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Program to find k where given matrix has k by k square of same value in C++
Suppose we have a 2d matrix, we have to find the largest k × k submatrix where all of its elements are containing the same value, then find the value of k.
So, if the input is like
| 1 | 1 | 8 | 3 |
| 1 | 5 | 5 | 5 |
| 2 | 5 | 5 | 5 |
| 4 | 5 | 5 | 5 |
then the output will be 3, as there is a 3 × 3 square matrix of value 5.
To solve this, we will follow these steps −
n := row count of matrix
m := column count of matrix
Define one 2D array dp of size (n x m) and fill with 1
ret := 1
for initialize i := n - 1, when i >= 0, update (decrease i by 1), do −
for initialize j := m - 1, when j >= 0, update (decrease j by 1), do −
val := inf
if i + 1 < n and v[i + 1, j] is same as v[i, j], then −
val := minimum of dp[i + 1, j] and val
Otherwise
val := 0
if j + 1 < m and v[i, j + 1] is same as v[i, j], then −
val := minimum of dp[i, j + 1] and val
Otherwise
val := 0
if i + 1 < n and j + 1 < m and v[i + 1, j + 1] is same as v[i, j], then −
val := minimum of dp[i + 1, j + 1] and val
Otherwise
val := 0
if val is same as inf, then −
Ignore following part, skip to the next iteration
dp[i, j] := dp[i, j] + val
ret := maximum of ret and dp[i, j]
return ret
Example
Let us see the following implementation to get better understanding −
#include <bits/stdc++.h>
using namespace std;
class Solution {
public:
int solve(vector<vector<int>>& v) {
int n = v.size();
int m = v[0].size();
vector<vector<int>> dp(n, vector<int>(m, 1));
int ret = 1;
for (int i = n - 1; i >= 0; i--) {
for (int j = m - 1; j >= 0; j--) {
int val = INT_MAX;
if (i + 1 < n && v[i + 1][j] == v[i][j]) {
val = min(dp[i + 1][j], val);
}
else {
val = 0;
}
if (j + 1 < m && v[i][j + 1] == v[i][j]) {
val = min(dp[i][j + 1], val);
}
else {
val = 0;
}
if (i + 1 < n && j + 1 < m && v[i + 1][j + 1] == v[i][j]) {
val = min(dp[i + 1][j + 1], val);
}
else {
val = 0;
}
if (val == INT_MAX)
continue;
dp[i][j] += val;
ret = max(ret, dp[i][j]);
}
}
return ret;
}
};
int solve(vector<vector<int>>& matrix) {
return (new Solution())->solve(matrix);
}
int main(){
vector<vector<int>> matrix = {
{1, 1, 8, 3},
{1, 5, 5, 5},
{2, 5, 5, 5},
{4, 5, 5, 5}
};
cout << solve(matrix);
}Input
{ {1, 1, 8, 3}, {1, 5, 5, 5}, {2, 5, 5, 5}, {4, 5, 5,
5} };Output
3
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