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如果是非递归情况
如果当前点(方格)为出口,则成功退出 (否则)
如果可继续走(向相邻点试探),存在某个可前进 的相邻点(分支)则:
1、将当前点保存,以便回退
2、将相邻点作为当前点继续(该分支)
如果不能前进则:
1、取出最近保存的点,回退作为当前点
2、如果无法取出,则无通路,失败退出
接下来考虑递归情况
#include <iostream>
using namespace std;
typedef struct ElemType{int x;int y;
};
typedef struct StackNode { //栈元素结点定义ElemType data; //结点数据StackNode* next; //结点链接指针
}*LinkStack; //链式栈
void InitStack(LinkStack& S) { //栈初始化S = NULL; //栈顶(链头)指针置空
}
int IsEmpty(const LinkStack& S) { //判栈空否return S == NULL;
}
int Push(LinkStack& S, ElemType& e) { //进栈StackNode* s = new StackNode;if (!s) exit(1); //可省略s->data = e; //结点赋值s->next = S; S = s; //链入栈顶return 1;
}
int Pop(LinkStack& S, ElemType& e) { //出栈if (IsEmpty(S)) return 0;StackNode* q = S;S = q->next; e = q->data; //摘下原栈顶delete q; return 1; //释放原栈顶结点
}
void ReTraverse(const LinkStack& S) {if (S) {ReTraverse(S->next);cout << "("<<S->data.x<<","<<S->data.y<<")"<<endl;}
}
void Go(ElemType start, ElemType end,int map[][10],LinkStack &S) {ElemType e; ElemType a;if (map[start.x][start.y] == 0) {if (start.x == end.x && start.y == end.y) { Push(S, start); ReTraverse(S); }else {map[start.x][start.y] = 1;Push(S, start);ElemType startA; startA.x = start.x - 1; startA.y = start.y;ElemType startL; startL.y = start.y - 1; startL.x = start.x;ElemType startV; startV.x = start.x + 1; startV.y = start.y;ElemType startR; startR.y = start.y + 1; startR.x = start.x;Go(startA, end,map,S);Go(startL, end, map, S);Go(startV, end, map, S);Go(startR, end, map, S);map[start.x][start.y] = 2;Pop(S, e);}}
}
int main(){LinkStack S; InitStack(S);ElemType start; ElemType end;start.x = 1; start.y = 1;end.x = 8; end.y = 8;int map[10][10] =//用二维数组表示地图:9代表墙,0代表通路{{ 9,9,9,9,9,9,9,9,9,9 },{ 9,0,0,9,0,0,0,9,0,9 },{ 9,0,0,9,0,0,0,9,0,9 },{ 9,0,0,0,0,9,9,0,0,9 },{ 9,0,9,9,9,0,0,0,0,9 },{ 9,0,0,0,9,9,0,0,0,9 },{ 9,0,9,0,0,0,9,0,9,9 },{ 9,0,9,9,9,0,9,9,0,9 },{ 9,9,0,0,0,0,0,0,0,9 },{ 9,9,9,9,9,9,9,9,9,9 }};Go(start, end, map, S);
}
用二维数组表示地图,
Go函数内部设计思路见图:
首先该位置必须为0,即不能为"墙"才能行走,其次如果该位置是终点,则为递归的“出口”,则结束
否则进入递归最小问题:该位置从0标记为1记为走过的路,但因为不能再次走所以不能为0,入栈,之后分别计算上下左右的临近点坐标,挨个调用进行递归,若都失败弹出,则说明进入到了死胡同,标记出栈的位置为2,即为回退的路,与走过的路“1”做区分,然后出栈
完成以上步骤即可得出最终路径: