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  • [LC] 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?

    Solution:

    Space: O(M * N)

    class Solution {
        public int uniquePaths(int m, int n) {
            int [] paths = new int[m][n];
            for (int i = 0; i < m; i++) {
                paths[i][0] = 1;
            }
            for (int i = 0; i < n; i++) {
                paths[0][i] = 1;
            }
            for (int i = 1; i < m; i++) {
                for (int j = 1; j < n; j++) {
                    paths[i][j] = paths[i - 1][j] + paths[i][j - 1];
                }
            }
            return paths[m - 1][n - 1];
        }
    }

    Optimized Space to O(N)

    class Solution {
        public int uniquePaths(int m, int n) {
            if (m == 0 || n == 0) {
                return 0;
            }
            if (m == 1 ||n == 1) {
                return 1;
            }
            int [] paths = new int[n];
            Arrays.fill(paths, 1);
            for (int i = 1; i < m; i++) {
                for (int j = 1; j < n; j++) {
                    paths[j] += paths[j - 1];
                }
            }
            return paths[n - 1];
        }
    }
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  • 原文地址:https://www.cnblogs.com/xuanlu/p/12047185.html
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