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《算法》递归回溯最简单的题目

灵魂跑者 2022-02-17 阅读 76

1,2,2,3,4
9,8,0,1,5
3,6,1,1,2
3,3,4,4,5

例如一个二维数组,从任意一个点出发开始寻找出路径点总和大于等于2,小于等于4的路径集合,例如0-2 和 0-2-2满足条件。

递归回溯简单来说就是设置标记,向下递归,出来后还原标记和其他状态等,我这里做简单一点就只考虑4连通,8连通异曲同工而已。

直接上代码。

using System.Collections;
using System.Collections.Generic;
using System.Text;
using UnityEngine;

// 递归 回溯 标记
public class Dfs : MonoBehaviour
{
    public int[][] arr = new int[4][]
    {
       new int[5]{1,2,2,3,4},
       new int[5]{9,8,0,1,5},
       new int[5]{3,6,1,1,2},
       new int[5]{3,3,4,4,5},
    };
    public Vector2 begin = Vector2.zero;
    private List<List<int>> result = new List<List<int>>();
    private Stack<int> tmp = new Stack<int>();
    private int[][] dirty = new int[4][]
    {
        new int[5],
        new int[5],
        new int[5],
        new int[5],
    };
    // Start is called before the first frame update
    void Start()
    {
        // 从某个数开始寻找2,4总和之间的路径
        tmp.Clear();
        int row = (int)begin.x;
        int col = (int)begin.y;
        tmp.Push(arr[row][col]);
        dirty[row][col] = 1;
        dfs(row, col, ref arr[row][col]);
        if (result.Count > 0)
        {
            for (int i = 0; i < result.Count; i++)
            {
                StringBuilder sb = new StringBuilder();
                for (int j = 0; j < result[i].Count; j++)
                {
                    sb.Append(result[i][j] + " ");
                }
                Debug.LogError(sb.ToString());
            }
        }
    }

    private void dfs(int row, int col, ref int rNum)
    {
        // row-1 
        if (row - 1 >= 0 && dirty[row - 1][col] == 0)
        {
            if (rNum + arr[row - 1][col] > 4)
            {
            }
            else if (rNum + arr[row - 1][col] < 2)
            {
                tmp.Push(arr[row - 1][col]);
                rNum += arr[row - 1][col];
                dirty[row - 1][col] = 1;
                dfs(row - 1, col, ref rNum);
                rNum -= arr[row - 1][col];
                tmp.Pop();
                dirty[row - 1][col] = 0;
            }
            else
            {
                tmp.Push(arr[row - 1][col]);
                result.Add(StackToList(tmp));
                rNum += arr[row - 1][col];
                dirty[row - 1][col] = 1;
                dfs(row - 1, col, ref rNum);
                dirty[row - 1][col] = 0;
                rNum -= arr[row - 1][col];
                tmp.Pop();
            }
        }
        // row+1 
        if (row + 1 < 4 && dirty[row + 1][col] == 0)
        {
            if (rNum + arr[row + 1][col] > 4)
            {
            }
            else if (rNum + arr[row + 1][col] < 2)
            {
                tmp.Push(arr[row + 1][col]);
                rNum += arr[row + 1][col];
                dirty[row + 1][col] = 1;
                dfs(row + 1, col, ref rNum);
                dirty[row + 1][col] = 0;
                rNum -= arr[row + 1][col];
                tmp.Pop();
            }
            else
            {
                tmp.Push(arr[row + 1][col]);
                result.Add(StackToList(tmp));
                rNum += arr[row + 1][col];
                dirty[row + 1][col] = 1;
                dfs(row + 1, col, ref rNum);
                dirty[row + 1][col] = 0;
                rNum -= arr[row + 1][col];
                tmp.Pop();
            }
        }
        // col-1
        if (col - 1 >= 0&&dirty[row][col-1]==0)
        {
            if (rNum + arr[row][col - 1] > 4)
            {
            }
            else if (rNum + arr[row][col - 1] < 2)
            {
                tmp.Push(arr[row][col - 1]);
                rNum += arr[row][col - 1];
                dirty[row][col - 1] = 1;
                dfs(row, col - 1, ref rNum);
                dirty[row][col - 1] = 0;
                rNum -= arr[row][col - 1];
                tmp.Pop();
            }
            else
            {
                tmp.Push(arr[row][col - 1]);
                result.Add(StackToList(tmp));
                rNum += arr[row][col - 1];
                dirty[row][col - 1] = 1;
                dfs(row, col - 1, ref rNum);
                dirty[row][col - 1] = 0;
                rNum -= arr[row][col - 1];
                tmp.Pop();
            }
        }
        // col+1
        if (col + 1 < 5&&dirty[row][col+1]==0)
        {
            if (rNum + arr[row][col + 1] > 4)
            {
            }
            else if (rNum + arr[row][col + 1] < 2)
            {
                tmp.Push(arr[row][col + 1]);
                rNum += arr[row][col + 1];
                dirty[row][col + 1] = 1;
                dfs(row, col + 1, ref rNum);
                dirty[row][col + 1] = 0;
                rNum -= arr[row][col + 1];
                tmp.Pop();
            }
            else
            {
                tmp.Push(arr[row][col + 1]);
                result.Add(StackToList(tmp));
                rNum += arr[row][col + 1];
                dirty[row][col + 1] = 1;
                dfs(row, col + 1, ref rNum);
                dirty[row][col + 1] = 0;
                rNum -= arr[row][col + 1];
                tmp.Pop();
            }
        }
    }

    private List<int> StackToList(Stack<int> stack)
    {
        Stack<int> tmp = new Stack<int>();
        while (stack.Count > 0)
        {
            tmp.Push(stack.Pop());
        }
        List<int> list = new List<int>();
        while (tmp.Count > 0)
        {
            list.Add(tmp.Pop());
        }
        for (int i = 0; i < list.Count; i++)
        {
            stack.Push(list[i]);
        }
        return list;
    }
}

在这里插入图片描述

在这里插入图片描述

填入起始点,可以看到输出。

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