62. Unique Paths

There is a robot on an `m x n` grid. The robot is initially located at the top-left corner (i.e., `grid[0][0]`). The robot tries to move to the bottom-right corner (i.e., `grid[m - 1][n - 1]`). The robot can only move either down or right at any point in time.

Given the two integers `m` and `n`, return the number of possible unique paths that the robot can take to reach the bottom-right corner.

The test cases are generated so that the answer will be less than or equal to `2 * 109`.

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
``````

Constraints:

• `1 <= m, n <= 100`

``````class Solution {
public:
int uniquePaths(int m, int n) {
vector<vector<int>> dp(m, vector<int>(n, 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];
}
};
``````

``````class Solution {
public:
int uniquePaths(int m, int n) {
vector<int> dp(n, 1);
for (int i = 1; i < m; ++i) {
for (int j = 1; j < n; ++j) {
dp[j] += dp[j - 1];
}
}
return dp[n - 1];
}
};
``````

``````class Solution {
public:
int uniquePaths(int m, int n) {
double num = 1, denom = 1;
int small = m > n ? n : m;
for (int i = 1; i <= small - 1; ++i) {
num *= m + n - 1 - i;
denom *= i;
}
return (int)(num / denom);
}
};
``````

Github 同步地址：

https://github.com/grandyang/leetcode/issues/62

Unique Paths II

Minimum Path Sum

Dungeon Game

Minimum Path Cost in a Grid

Minimum Cost Homecoming of a Robot in a Grid

Number of Ways to Reach a Position After Exactly k Steps

Paths in Matrix Whose Sum Is Divisible by K

https://leetcode.com/problems/unique-paths/

https://leetcode.com/problems/unique-paths/discuss/22981/My-AC-solution-using-formula

https://leetcode.com/problems/unique-paths/discuss/22954/0ms-5-lines-DP-Solution-in-C%2B%2B-with-Explanations

LeetCode All in One 题目讲解汇总(持续更新中…)

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