【leetcode】62.63 Unique Paths

62. Unique Paths

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).

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.

Tips：机器人从左上一直走到右下，（只能走右与下）直到走到FInish的位置。

package medium;

import java.util.Arrays;

public class L62UniquePaths {
	public int uniquePaths(int m, int n) {
		int[][] visited = new int[m][n];
		for (int i = 0; i < m; i++) {
			for (int j = 0; j < n; j++) {
				visited[i][j] = -1;
				System.out.println(i + "," + j + ">" + visited[i][j]);
			}
		}
		int count = movingCount(m, n, 0, 0, visited);
		return count;
	}
	public int movingCount(int m, int n, int row, int col, int[][] visited) {
		int count = 0;
		if (row < 0 || col < 0 || row >= m || col >= n)
			return 0;
		if (row == m - 1 && col == n - 1)
			return 1;
		if (visited[row][col] != -1)
			return visited[row][col];
		count = movingCount(m, n, row + 1, col, visited) + movingCount(m, n, row, col + 1, visited);
		visited[row][col] = count;
		return count;
	}

        //另外一种很快地方法。当前状态依赖于前一种状态
	public int Solution2(int m, int n) {
		int[] row = new int[n];
		Arrays.fill(row,1);
		for (int i = 1; i < m; i++) {
			for (int j = 1; j < n; j++) {
				row[j]+=row[j-1];
			}
		}
		return row[n-1];
	}

	public static void main(String[] args) {
		L62UniquePaths cc = new L62UniquePaths();
		int count = cc.uniquePaths(3, 4);
		System.out.println(count);
	}
}

 63. Unique Paths II

Follow up for "Unique Paths":

Now consider if some obstacles are added to the grids. How many unique paths would there be?

An obstacle and empty space is marked as 1 and 0 respectively in the grid.

For example,

There is one obstacle in the middle of a 3x3 grid as illustrated below.

[
  [0,0,0],
  [0,1,0],
  [0,0,0]
]

The total number of unique paths is 2.

Note: m and n will be at most 100.

Tips:本题目是根据62题，稍作改变得来的，数组中1的位置不能走。

package medium;

public class L63UniquePaths2 {

	public int uniquePathsWithObstacles(int[][] obstacleGrid) {
		if (obstacleGrid == null)
			return 0;
		int m = obstacleGrid.length;
		int n = obstacleGrid[0].length;
		int[][] visited = new int[m][n];
		for (int i = 0; i < m; i++) {
			for (int j = 0; j < n; j++) {
				visited[i][j] = -1;
				System.out.println(i + "," + j + ">" + visited[i][j]);
			}
		}
		int count = movingCount(m, n, 0, 0, visited, obstacleGrid);
		return count;

	}

	public int movingCount(int m, int n, int row, int col, int[][] visited, int[][] obstacleGrid) {
		int count = 0;
		if (row < 0 || col < 0 || row >= m || col >= n)
			return 0;
		if (obstacleGrid[row][col] == 0) {
			if (row == m - 1 && col == n - 1)
				return 1;
			if (visited[row][col] != -1)
				return visited[row][col];
			count = movingCount(m, n, row + 1, col, visited, obstacleGrid)
					+ movingCount(m, n, row, col + 1, visited, obstacleGrid);
			visited[row][col] = count;
		}

		return count;
	}

	public static void main(String[] args) {
		L63UniquePaths2 l63 = new L63UniquePaths2();
		int[][] obstacleGrid = { { 0, 0, 0 }, { 0, 1, 0 }, { 0, 0, 0 } };
		int[][] aa = { { 1 } };
		int count = l63.uniquePathsWithObstacles(aa);
		System.out.println(count);

	}
}