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  • 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.

    题目:机器人从左上角到右下角,每次只能往右或者下走一格,问有多少种走法?

    思路:DP问题,构造一个m*n矩阵,用step[row][col]代表走到(i,j)节点的多种线路数,因为只能往右或者下移动,所以矩阵的第一行(只能往右移动)和第一列(只能往下移动)为1.其它节点的线路数为

     steps[i][j] = steps[i - 1][j] + steps[i][j - 1];
     1     public int uniquePaths(int m, int n) {
     2          if (m == 0 || n == 0) return 0;
     3          if (m == 1 || n == 1) return 1;
     4          int[][] steps = new int[m][n];
     5          for (int i = 0; i < m; i++)
     6              for (int j = 0; j < n; j++) {
     7                  if (i==0 || j==0)  steps[i][j] = 1;
     8                  else steps[i][j] = steps[i - 1][j] + steps[i][j - 1];
     9              }
    10          return steps[m - 1][n - 1];
    11     }
     
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  • 原文地址:https://www.cnblogs.com/wzj4858/p/7675910.html
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