lec10_35.cpp

class Solution {
    public:
       
    
        int minFallingPathSum(vector<vector<int>>& matrix) {
            int n = matrix.size();
            int m = matrix[0].size();
            int mini = 1e8;  // Initialize to a large value
    
            vector<vector<int>>dp(n , vector<int> (m , -1));
    
            vector<int>prev( m , 0) , cur(m ,0);
    
            for(int j = 0 ; j<m;j++) prev[j] = matrix[0][j];
            for(int i = 1 ; i<n; i++){
                for(int j = 0 ; j<m; j++){
                    int u = matrix[i][j] +prev[j];
                    int ld = matrix[i][j] ;
                    if(j-1>=0) ld+= prev[j-1];
                    else ld +=1e8;
                    int rd =  matrix[i][j];
                    if(j+1<m) rd+= prev[j+1];
                    else rd += 1e8;
    
                    cur[j] = min({u , ld , rd});
                }
                prev = cur;
            } 
            for (int j = 0; j < m; j++) {
                mini = min(mini, prev[j]);  // Start from the last row
            }
    
            return mini;
        }
    };