Maximum size square Sub | C ++ program for the above approach ; Function to find the maximum size of matrix with sum <= K ; N size of rows and M size of cols ; To store the prefix sum of matrix ; Create Prefix Sum ; Traverse each rows ; Update the prefix sum till index i x j ; To store the maximum size of matrix with sum <= K ; Traverse the sum matrix ; Index out of bound ; Maximum possible size of matrix ; Binary Search ; Find middle index ; Check whether sum <= K or not If Yes check for other half of the search ; Else check it in first half ; Update the maximum size matrix ; Print the final answer ; Driver Code ; Given target sum ; Function Call
#include <bits/stdc++.h> NEW_LINE using namespace std ; void findMaxMatrixSize ( vector < vector < int > > arr , int K ) { int i , j ; int n = arr . size ( ) ; int m = arr [ 0 ] . size ( ) ; int sum [ n + 1 ] [ m + 1 ] ; for ( int i = 0 ; i <= n ; i ++ ) { for ( int j = 0 ; j <= m ; j ++ ) { if ( i == 0 j == 0 ) { sum [ i ] [ j ] = 0 ; continue ; } sum [ i ] [ j ] = arr [ i - 1 ] [ j - 1 ] + sum [ i - 1 ] [ j ] + sum [ i ] [ j - 1 ] - sum [ i - 1 ] [ j - 1 ] ; } } int ans = 0 ; for ( i = 1 ; i <= n ; i ++ ) { for ( j = 1 ; j <= m ; j ++ ) { if ( i + ans - 1 > n j + ans - 1 > m ) break ; int mid , lo = ans ; int hi = min ( n - i + 1 , m - j + 1 ) ; while ( lo < hi ) { mid = ( hi + lo + 1 ) / 2 ; if ( sum [ i + mid - 1 ] [ j + mid - 1 ] + sum [ i - 1 ] [ j - 1 ] - sum [ i + mid - 1 ] [ j - 1 ] - sum [ i - 1 ] [ j + mid - 1 ] <= K ) { lo = mid ; } else { hi = mid - 1 ; } } ans = max ( ans , lo ) ; } } cout << ans << endl ; } int main ( ) { vector < vector < int > > arr ; arr = { { 1 , 1 , 3 , 2 , 4 , 3 , 2 } , { 1 , 1 , 3 , 2 , 4 , 3 , 2 } , { 1 , 1 , 3 , 2 , 4 , 3 , 2 } } ; int K = 4 ; findMaxMatrixSize ( arr , K ) ; return 0 ; }