[CareerCup] 9.2 Robot Moving 机器人移动

9.2 Imagine a robot sitting on the upper left corner of an X by Y grid. The robot can only move in two directions: right and down. How many possible paths are there for the robot to go from (0,0) to (X,Y)?
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 Imagine certain spots are "off limits," such that the robot cannot step on them. Design an algorithm to find a path for the robot from the top left to the bottom right.

LeetCode上的原题，请参见我之前的博客Unique Paths 不同的路径和Unique Paths II 不同的路径之二。

解法一：

class Solution {
public:
    int getPath(int x, int y) {
        vector<int> dp(y + 1, 1);
        for (int i = 1; i <= x; ++i) {
            for (int j = 1; j <= y; ++j) {
                dp[j] += dp[j - 1];
            }
        }
        return dp[y];
    }
};

解法二：

class Solution {
public:
    int getPath(int x, int y) {
        double num = 1, denom = 1;
        int small = x < y ? x : y;
        for (int i = 1; i <= small; ++i) {
            num *= x + y - i + 1;
            denom *= i;
        }
        return (int)(num / denom);
    }
};