There are only 2 directions to reach a given cell[i][j], either from above it or from left,

dp[i][j  1] (paths from its left)

dp[i  1][j] (paths from its above)
Total path = Sum of path from its left + Sum of path from its above
dp[i][j] = dp[i][j  1] + dp[i  1][j];
class Solution {
public:
int uniquePaths(int m, int n) {
vector<vector<int>>dp(m, vector<int>(n));
for(int i = 0; i < m; i++) dp[i][0] = 1;
for(int i = 0; i < n; i++) dp[0][i] = 1;
for(int i = 1; i < m; i++)
for(int j = 1; j < n; j++)
dp[i][j] = dp[i  1][j] + dp[i][j  1];
return dp[m  1][n  1];
}
};