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);
}
}