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

 

 

public int uniquePaths(int m, int n) {
  int[][] map = new int[m][n];
  for (int i = 0; i < m; i++)
    map[i][0] = 1;
  for (int j = 0; j < n; j++)
    map[0][j]=1;
  for (int i = 1; i < m; i++) {
    for (int j = 1; j < n; j++)
      map[i][j] = map[i - 1][j] + map[i][j - 1]; //每一格路线的和都是其左格和上格的和
  }
  return map[m - 1][n - 1];
}