leetcode -- Unique Paths

public int uniquePaths(int m, int n) {
// Start typing your Java solution below
// DO NOT write main() function
int[][] steps = new int[m+2][n+2];
for(int i = 0; i < n + 2; i++){
steps[m+1][i] = 0;
}
for(int i = 0; i < m + 2; i++){
steps[i][n+1] = 0;
}
steps[m][n+1] = 1;
for(int i = m; i >= 1; i--){
for(int j = n; j >= 1; j--){
steps[i][j] = steps[i+1][j] + steps[i][j+1];
}
}
return steps[1][1];
}

public int uniquePaths(int m, int n) {
// Start typing your Java solution below
// DO NOT write main() function
int[][] matrix = new int[m+2][n+2];
for(int i = 0; i < m+2; i++){
for(int j = 0; j < n+2; j++){
matrix[i][j] = -1;
}
}

return dp(1, 1, m, n, matrix);
}

public int dp(int r, int c, int m, int n, int[][] matrix){
if(r > m || c > n){
return 0;
}
if(r == m && c == n){
return 1;
}
if(matrix[r+1][c] == -1){
matrix[r+1][c] = dp(r+1, c, m, n, matrix);
}
if(matrix[r][c+1] == -1){
matrix[r][c+1] = dp(r, c+1, m, n, matrix);
}

return matrix[r+1][c] + matrix[r][c+1];
}