62. Unique Paths
A robot is located at the top-left corner of a m x n
grid (marked 'Start' in the diagram below).
The robot can only move either down or right at any point in time. The robot is trying to reach the bottom-right corner of the grid (marked 'Finish' in the diagram below).
How many possible unique paths are there?
Example 1:
Input: m = 3, n = 7 Output: 28
Example 2:
Input: m = 3, n = 2 Output: 3 Explanation: From the top-left corner, there are a total of 3 ways to reach the bottom-right corner: 1. Right -> Down -> Down 2. Down -> Down -> Right 3. Down -> Right -> Down
Example 3:
Input: m = 7, n = 3 Output: 28
Example 4:
Input: m = 3, n = 3 Output: 6
Constraints:
1 <= m, n <= 100
- It's guaranteed that the answer will be less than or equal to
2 * 109
.
the solution to the Above Question
class Solution {
public:
int dp[101][101];
int helper(int a,int b,int m,int n){
if(a==m-1 && b==n-1){
return 1;
}
if(a>m-1 || b>n-1){
return 0;
}
int ans=0;
{ if(dp[a+1][b]==-1){
dp[a+1][b]=helper(a+1,b,m,n);
}
if(dp[a][b+1]==-1){
dp[a][b+1]=helper(a,b+1,m,n);
}
ans=ans+dp[a+1][b]+ dp[a][b+1];
}
return ans;
}
int uniquePaths(int m, int n) {
for(int i=0; i<100; i++){
for(int j=0; j<100; j++){
dp[i][j]-=1;
}
}
int ans=0;
int a=0,b=0;
return helper(0,0,m,n);
}
};
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