62. Unique Paths

    /*
     * 62. Unique Paths
     * 2016-5-8 by Mingyang
     * 简单的DP
     */
    public static int uniquePaths(int m, int n) {
        if (m == 0 || n == 0)
            return 0;
        if (m == 1 || n == 1)
            return 1;
        int[][] dp = new int[m][n];
        // 只有一行时，到终点每个格子只有一种走法
        for (int i = 0; i < n; i++)
            dp[0][i] = 1;
        // 只有一列时，到终点每个格子只有一种走法
        for (int i = 0; i < m; i++)
            dp[i][0] = 1;
        // for each body node, number of path = paths from top + paths from left
        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];
    }