衣橱整理
难度:
标签:
题目描述
English description is not available for the problem. Please switch to Chinese.
代码结果
运行时间: 76 ms, 内存: 15.5 MB
/*
* Problem: Given an m x n grid representing a wardrobe, we need to count the number of cells that a cleaner can organize. The cleaner starts at grid[0][0] and can only move right or down. A cell can be organized only if the sum of the digits of the row index and the column index is less than or equal to cnt.
*
* Solution Approach using Java Stream API:
* 1. Use a helper function to calculate the sum of the digits of a number.
* 2. Use nested IntStream to iterate over each cell.
* 3. Filter out cells that cannot be organized.
* 4. Count the remaining cells.
*/
import java.util.stream.IntStream;
public class SolutionStream {
public int digitSum(int x) {
int sum = 0;
while (x > 0) {
sum += x % 10;
x /= 10;
}
return sum;
}
public long organizeCells(int m, int n, int cnt) {
return IntStream.range(0, m)
.boxed()
.flatMap(i -> IntStream.range(0, n)
.filter(j -> digitSum(i) + digitSum(j) <= cnt)
.boxed())
.count();
}
public static void main(String[] args) {
SolutionStream sol = new SolutionStream();
System.out.println(sol.organizeCells(4, 7, 5)); // Output: 18
}
}
解释
方法:
本题解采用深度优先搜索(DFS)的方法。从矩阵的左上角开始,递归地向右和向下进行搜索,同时跟踪已访问的节点以避免重复计算。搜索过程中,首先判断当前位置是否有效(即坐标在矩阵内,且各数位之和不超过给定的阈值k,且未被访问过),如果有效,则递归地探索当前位置的右侧和下方位置。每访问一个有效格子,就计算当前格子和其递归得到的格子数之和,最终返回总的可访问格子数。
时间复杂度:
O(m*n)
空间复杂度:
O(m*n)
代码细节讲解
🦆
为什么选择深度优先搜索(DFS)而不是广度优先搜索(BFS)来解决这个问题?
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在实际实现中DFS如何确保不会因为递归过深而导致栈溢出?
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在计算数位之和的函数中,是否有更高效的方法,尤其是对于大矩阵中的较大数值?
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