0062-unique-paths.cpp

/*
 Given grid, return # of unique paths from top-left to bottom-right
 Ex. m = 3, n = 2 -> 3 unique paths (R->D->D, D->D->R, D->R->D)

 DP: edges have 1 unique path, inner cells consider where it comes from
 Recurrence relation: grid[i][j] = grid[i-1][j] + grid[i][j-1]

 Time: O(m x n)
 Space: O(m x n)
*/

classSolution {
public:
intuniquePaths(int m, int n) {
 vector<vector<int>> grid(m, vector<int>(n, 0));

for (int i = 0; i < m; i++) {
 grid[i][0] = 1;
 }
for (int j = 0; j < n; j++) {
 grid[0][j] = 1;
 }
for (int i = 1; i < m; i++) {
for (int j = 1; j < n; j++) {
 grid[i][j] = grid[i - 1][j] + grid[i][j - 1];
 }
 }

return grid[m - 1][n - 1];
 }
};