import java.util.Arrays;
/**
* Source : https://oj.leetcode.com/problems/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).
*
*
* 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.
*
*/
public class UniquePaths {
/**
* 相当于走迷宫,不过只可以向前或者向下,两个方向
*
* 使用深度优先,递归查找
*
* @param x
* @param y
* @param m
* @param n
* @param result
* @return
*/
public int walk (int x, int y, int m, int n, int result) {
if (x == n - 1 && y == m - 1) {
return result + 1;
}
if (x < n - 1) {
result = walk(x+1, y, m, n, result);
}
if (y < m - 1) {
result = walk(x, y+1, m, n, result);
}
return result;
}
public int finAllUniquePaths (int m, int n) {
if (m <= 0 || n <= 0) {
return 0;
}
return walk(0, 0, m, n, 0);
}
/**
* 使用动态规划
* dp[i][j] = dp[i][j-1] + do[i-1][j]
*
* 边界条件
* 如果i = 0或者 j = 0,dp[0][j] = 1;
*
* @param m
* @param n
*/
public int finAllUniquePathsByDP (int m, int n) {
int[][] maze = new int[m][n];
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
if (i == 0 || j == 0) {
maze[i][j] = 1;
} else {
maze[i][j] = maze[i-1][j] + maze[i][j-1];
}
}
}
return maze[m-1][n-1];
}
/**
* 动态规划,使用滚动数组
*
* @param m
* @param n
* @return
*/
public int finAllUniquePathsByDPAndScrollArray (int m, int n) {
int[] scrollArray = new int[n];
Arrays.fill(scrollArray, 1);
for (int i = 1; i < m; i++) {
for (int j = 1; j < n; j++) {
scrollArray[j] += scrollArray[j-1];
}
}
return scrollArray[n -1];
}
public static void main(String[] args) {
UniquePaths uniquePaths = new UniquePaths();
System.out.println(uniquePaths.finAllUniquePaths(1,1));
System.out.println(uniquePaths.finAllUniquePaths(1,2));
System.out.println(uniquePaths.finAllUniquePaths(1,3));
System.out.println(uniquePaths.finAllUniquePaths(2,2));
System.out.println(uniquePaths.finAllUniquePaths(2,3));
System.out.println(uniquePaths.finAllUniquePaths(3,3));
System.out.println("======dp=======");
System.out.println(uniquePaths.finAllUniquePathsByDP(1,1));
System.out.println(uniquePaths.finAllUniquePathsByDP(1,2));
System.out.println(uniquePaths.finAllUniquePathsByDP(1,3));
System.out.println(uniquePaths.finAllUniquePathsByDP(2,2));
System.out.println(uniquePaths.finAllUniquePathsByDP(2,3));
System.out.println(uniquePaths.finAllUniquePathsByDP(3,3));
System.out.println("======dp use scroll array=======");
System.out.println(uniquePaths.finAllUniquePathsByDPAndScrollArray(2,2));
System.out.println(uniquePaths.finAllUniquePathsByDPAndScrollArray(2,3));
System.out.println(uniquePaths.finAllUniquePathsByDPAndScrollArray(3,3));
}
}