//62. 不同路径

func uniquePaths(m int, n int) int {

  dp := make([][]int, m)

  // 行赋初始值为1

  for i := range dp {

    dp[i] = make([]int, n)

    dp[i][0] = 1

  }

  // 列赋初始值为1

  for j := 0; j < n; j++ {

    dp[0][j] = 1

  }

  for i := 1; i < m; i++ {

    for j := 1; j < n; j++ {

      dp[i][j] = dp[i-1][j] + dp[i][j-1]

    }

  }

  return dp[m-1][n-1]

}

//63. 不同路径 II

func uniquePathsWithObstacles(obstacleGrid [][]int) int {

  m := len(obstacleGrid)

  n := len(obstacleGrid[0])

  //如果在起点或终点出现了障碍，直接返回0

  if obstacleGrid[m-1][n-1] == 1 || obstacleGrid[0][0] == 1 {

    return 0

  }

  dp := make([][]int, m)

  for i := range dp {

    dp[i] = make([]int, n)

  }

  // 行赋初始值为1，有障碍物停止

  for i := 0; i < m && obstacleGrid[i][0] == 0; i++ {

    dp[i][0] = 1

  }

 // 列赋初始值为1，有障碍物停止

  for j := 0; j < n && obstacleGrid[0][j] == 0; j++ {

    dp[0][j] = 1

  }

  for i := 1; i < m; i++ {

    for j := 1; j < n; j++ {

      //有障碍物跳过

      if obstacleGrid[i][j] != 1 {

        dp[i][j] = dp[i-1][j] + dp[i][j-1]

      }

    }

  }

  return dp[m-1][n-1]

}