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?
Above is a 7 x 3 grid. How many possible unique paths are there?
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| Example 1:
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 -> Right -> Down
2. Right -> Down -> Right
3. Down -> Right -> Right
Example 2:
Input: m = 7, n = 3
Output: 28
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Constraints:
- 1 <= m, n <= 100
- It’s guaranteed that the answer will be less than or equal to 2 * 10 ^ 9.
Solution:
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| class Solution {
public int uniquePaths(int m, int n) {
int[][] dp = new int[n][m];
Arrays.fill(dp[0], 1);
for (int i = 1; i < n; i++) {
for (int j = 0; j < m; j++) {
dp[i][j] += dp[i - 1][j];
if (j > 0) {
dp[i][j] += dp[i][j - 1];
}
}
}
return dp[n-1][m-1];
}
}
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Solution 2#
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| class Solution {
public int uniquePaths(int m, int n) {
int[][] dp = new int[m][n];
dp[0][0] = 1;
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
if (i == 0 && j == 0) continue;
if (i > 0) {
dp[i][j] += dp[i - 1][j];
}
if (j > 0) {
dp[i][j] += dp[i][j - 1];
}
}
}
return dp[m-1][n-1];
}
}
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