int minPathSumHelper(int m, int n, const vector<vector<int>>& grid, vector<vector<int>>& rec)
{
if(m == m_rows - 1 && n == m_cols - 1){
rec[m][n] = grid[m][n];
return grid[m][n];
}
if(rec[m][n] == -1) {
int cur = grid[m][n];
rec[m][n] = cur + min(m < (m_rows - 1) ? minPathSumHelper(m+1, n, grid, rec) : INT_MAX,
n < (m_cols - 1) ? minPathSumHelper(m, n+1, grid, rec) : INT_MAX);
}
return rec[m][n];
}
void minPathSumHelper(int row, int col, vector<vector<int>> &grid, int &sum, int &res) {
if (sum > res) return;
if (row == 0 && col == 0) {
res = min(res, sum + grid[row][col]);
}
sum += grid[row][col];
if (row) {
minPathSumHelper(row - 1, col, grid, sum, res);
}
if (col) {
minPathSumHelper(row, col - 1, grid, sum, res);
}
sum -= grid[row][col];
}
int minPathSum(vector<vector<int>>& grid) {
m_rows = (int)grid.size();
m_cols = (int)grid[0].size();
if(m_rows == 0 || m_cols == 0) return 0;
if(m_rows == 1 && m_cols == 1) return grid[0][0];
int s = max(m_rows, m_cols);
vector<vector<int>> rec;
for(int i = 0; i < s; i++){
rec.push_back(vector<int>(s, -1));
}
return minPathSumHelper(0, 0, grid, rec);
}
int minPathSum(vector<vector<int>>& grid) {
int res = INT_MAX;
int sum = 0;
minPathSumHelper(grid.size() - 1, grid[0].size() - 1, grid, sum, res);
return res;
}
