题解 | #矩阵最长递增路径#

感觉陷入思维定势了，一心想着怎么只用动态规划解题，没想到使用dfs+动态规划的结合方法。。。

class Solution {
  public:
    //记录四个方向
    int dirs[4][2] = {{-1, 0}, {1, 0}, {0, -1}, {0, 1}};
    int n, m;
    //深度优先搜索，返回最大单元格数
    int dfs(vector<vector<int> >& matrix, vector<vector<int> >& dp, int i, int j) {
        if (dp[i][j] != 0)
            return dp[i][j];
        dp[i][j]++;
        for (int k = 0; k < 4; k++) {
            int nexti = i + dirs[k][0];
            int nextj = j + dirs[k][1];
            //判断条件
            if (nexti >= 0 && nexti < n && nextj >= 0 && nextj < m &&
                    matrix[nexti][nextj] > matrix[i][j])
                dp[i][j] = max(dp[i][j], dfs(matrix, dp, nexti, nextj) + 1);
        }
        return dp[i][j];
    }
    int solve(vector<vector<int> >& matrix) {
        //矩阵不为空
        if (matrix.size() == 0 || matrix[0].size() == 0)
            return 0;
        int res = 0;
        n = matrix.size();
        m = matrix[0].size();
        //i，j处的单元格拥有的最长递增路径
        vector<vector<int> > dp (n, vector <int> (m));
        for (int i = 0; i < n; i++)
            for (int j = 0; j < m; j++)
                //更新最大值
                res = max(res, dfs(matrix, dp, i, j));
        return res;
    }
};