62. Unique Paths (Medium)
https://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).
How many possible unique paths are there?
Above is a 7 x 3 grid. How many possible unique paths are there?
Note: m and n will be at most 100.
Example 1:
Input: m = 3, n = 2 Output: 3 Explanation: From the top-left corner, there are a total of 3 ways to reach the bottom-right corner: 1. Right -> Right -> Down 2. Right -> Down -> Right 3. Down -> Right -> Right
Example 2:
Input: m = 7, n = 3 Output: 28
Solutions
1.
class Solution {
int[][] pathCount;
public int uniquePaths(int m, int n) {
pathCount = new int[m][n];
for (int i = 0; i < m; i++) {
Arrays.fill(pathCount[i], -1);
}
return walkThrough(m - 1, n - 1);
}
public int walkThrough(int m, int n) {
if (m == 0 && n == 0) {
return 1;
}
if (m < 0 || n < 0) {
return 0;
}
if (pathCount[m][n] >= 0) {
return pathCount[m][n];
}
int p1 = walkThrough(m - 1, n);
int p2 = walkThrough(m, n - 1);
pathCount[m][n] = p1 + p2;
return p1 + p2;
}
}
2.
class Solution {
public int uniquePaths(int m, int n) {
int[][] pathCount = new int[m][n];
return getCount(pathCount, m, n);
}
private int getCount(int[][] pathCount, int m, int n) {
int row = pathCount.length;
int col = pathCount[0].length;
// only one pathway to (0,0) when col.no=0
for (int i = 0; i < row; i++) {
pathCount[i][0] = 1;
}
// only one pathway to (0,0) when row.no=0
for (int i = 0; i < col; i++) {
pathCount[0][i] = 1;
}
for (int i = 1; i < row; i++) {
for (int j = 1; j < col; j++) {
pathCount[i][j] = pathCount[i - 1][j] + pathCount[i][j - 1];
}
}
return pathCount[m - 1][n - 1];
}
}