uniquePaths.java

// Source : https://oj.leetcode.com/problems/unique-paths/
// Inspired by : http://www.jiuzhang.com/solutions/unique-paths/
// Author : Lei Cao
// Date   : 2015-10-11

/**********************************************************************************
 *
 * 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).
 *
 *
 *    start                                                  
 *    +---------+----+----+----+----+----+
 *    |----|    |    |    |    |    |    |
 *    |----|    |    |    |    |    |    |
 *    +----------------------------------+
 *    |    |    |    |    |    |    |    |
 *    |    |    |    |    |    |    |    |
 *    +----------------------------------+
 *    |    |    |    |    |    |    |----|
 *    |    |    |    |    |    |    |----|
 *    +----+----+----+----+----+---------+
 *                                   finish
 *
 *
 * How many possible unique paths are there?
 *
 * Above is a 3 x 7 grid. How many possible unique paths are there?
 *
 * Note: m and n will be at most 100.
 *
 **********************************************************************************/

package dynamicProgramming.uniquePaths;

public class uniquePaths {
    /**
     * @param n, m: positive integer (1 <= n ,m <= 100)
     * @return an integer
     */
    public int uniquePaths(int m, int n) {
        // write your code here
        int[][] matrix = new int[m][n];
        for (int i = 0; i < m; i++) {
            matrix[i][0] = 1;
        }
        for (int i = 0; i < n; i++) {
            matrix[0][i] = 1;
        }

        for (int i = 1; i < m; i++)  {
            for (int j = 1; j < n; j++) {
                matrix[i][j] = matrix[i-1][j] + matrix[i][j-1];
            }
        }
        return matrix[m-1][n-1];
    }
}