迷宫问题,求最短路径长度、最短路径条数、所有最短路径,DFS+BFS+栈+队列
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一组测试数据得到的结果
8 8 3
3 3
4 5
6 6
2 1
7 7
最短路径 1 :
(2, 1) (3, 1) (4, 1) (5, 1) (6, 1) (7, 1) (7, 2) (7, 3) (7, 4) (7, 5) (7, 6) (7, 7)
最短路径 2 :
(2, 1) (3, 1) (4, 1) (5, 1) (6, 1) (6, 2) (7, 2) (7, 3) (7, 4) (7, 5) (7, 6) (7, 7)
最短路径 3 :
(2, 1) (3, 1) (4, 1) (5, 1) (6, 1) (6, 2) (6, 3) (7, 3) (7, 4) (7, 5) (7, 6) (7, 7)
最短路径 4 :
(2, 1) (3, 1) (4, 1) (5, 1) (6, 1) (6, 2) (6, 3) (6, 4) (7, 4) (7, 5) (7, 6) (7, 7)
最短路径 5 :
(2, 1) (3, 1) (4, 1) (5, 1) (6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (7, 5) (7, 6) (7, 7)
最短路径 6 :
(2, 1) (3, 1) (4, 1) (5, 1) (5, 2) (6, 2) (7, 2) (7, 3) (7, 4) (7, 5) (7, 6) (7, 7)
最短路径 7 :
(2, 1) (3, 1) (4, 1) (5, 1) (5, 2) (6, 2) (6, 3) (7, 3) (7, 4) (7, 5) (7, 6) (7, 7)
最短路径 8 :
(2, 1) (3, 1) (4, 1) (5, 1) (5, 2) (6, 2) (6, 3) (6, 4) (7, 4) (7, 5) (7, 6) (7, 7)
最短路径 9 :
(2, 1) (3, 1) (4, 1) (5, 1) (5, 2) (6, 2) (6, 3) (6, 4) (6, 5) (7, 5) (7, 6) (7, 7)
最短路径 10 :
(2, 1) (3, 1) (4, 1) (5, 1) (5, 2) (5, 3) (6, 3) (7, 3) (7, 4) (7, 5) (7, 6) (7, 7)
最短路径 11 :
(2, 1) (3, 1) (4, 1) (5, 1) (5, 2) (5, 3) (6, 3) (6, 4) (7, 4) (7, 5) (7, 6) (7, 7)
最短路径 12 :
(2, 1) (3, 1) (4, 1) (5, 1) (5, 2) (5, 3) (6, 3) (6, 4) (6, 5) (7, 5) (7, 6) (7, 7)
最短路径 13 :
(2, 1) (3, 1) (4, 1) (5, 1) (5, 2) (5, 3) (5, 4) (6, 4) (7, 4) (7, 5) (7, 6) (7, 7)
最短路径 14 :
(2, 1) (3, 1) (4, 1) (5, 1) (5, 2) (5, 3) (5, 4) (6, 4) (6, 5) (7, 5) (7, 6) (7, 7)
最短路径 15 :
(2, 1) (3, 1) (4, 1) (5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (6, 5) (7, 5) (7, 6) (7, 7)
最短路径 16 :
(2, 1) (3, 1) (4, 1) (5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6) (5, 7) (6, 7) (7, 7)
最短路径 17 :
(2, 1) (3, 1) (4, 1) (4, 2) (5, 2) (6, 2) (7, 2) (7, 3) (7, 4) (7, 5) (7, 6) (7, 7)
最短路径 18 :
(2, 1) (3, 1) (4, 1) (4, 2) (5, 2) (6, 2) (6, 3) (7, 3) (7, 4) (7, 5) (7, 6) (7, 7)
最短路径 19 :
(2, 1) (3, 1) (4, 1) (4, 2) (5, 2) (6, 2) (6, 3) (6, 4) (7, 4) (7, 5) (7, 6) (7, 7)
最短路径 20 :
(2, 1) (3, 1) (4, 1) (4, 2) (5, 2) (6, 2) (6, 3) (6, 4) (6, 5) (7, 5) (7, 6) (7, 7)
最短路径 21 :
(2, 1) (3, 1) (4, 1) (4, 2) (5, 2) (5, 3) (6, 3) (7, 3) (7, 4) (7, 5) (7, 6) (7, 7)
最短路径 22 :
(2, 1) (3, 1) (4, 1) (4, 2) (5, 2) (5, 3) (6, 3) (6, 4) (7, 4) (7, 5) (7, 6) (7, 7)
最短路径 23 :
(2, 1) (3, 1) (4, 1) (4, 2) (5, 2) (5, 3) (6, 3) (6, 4) (6, 5) (7, 5) (7, 6) (7, 7)
最短路径 24 :
(2, 1) (3, 1) (4, 1) (4, 2) (5, 2) (5, 3) (5, 4) (6, 4) (7, 4) (7, 5) (7, 6) (7, 7)
最短路径 25 :
(2, 1) (3, 1) (4, 1) (4, 2) (5, 2) (5, 3) (5, 4) (6, 4) (6, 5) (7, 5) (7, 6) (7, 7)
最短路径 26 :
(2, 1) (3, 1) (4, 1) (4, 2) (5, 2) (5, 3) (5, 4) (5, 5) (6, 5) (7, 5) (7, 6) (7, 7)
最短路径 27 :
(2, 1) (3, 1) (4, 1) (4, 2) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6) (5, 7) (6, 7) (7, 7)
最短路径 28 :
(2, 1) (3, 1) (4, 1) (4, 2) (4, 3) (5, 3) (6, 3) (7, 3) (7, 4) (7, 5) (7, 6) (7, 7)
最短路径 29 :
(2, 1) (3, 1) (4, 1) (4, 2) (4, 3) (5, 3) (6, 3) (6, 4) (7, 4) (7, 5) (7, 6) (7, 7)
最短路径 30 :
(2, 1) (3, 1) (4, 1) (4, 2) (4, 3) (5, 3) (6, 3) (6, 4) (6, 5) (7, 5) (7, 6) (7, 7)
最短路径 31 :
(2, 1) (3, 1) (4, 1) (4, 2) (4, 3) (5, 3) (5, 4) (6, 4) (7, 4) (7, 5) (7, 6) (7, 7)
最短路径 32 :
(2, 1) (3, 1) (4, 1) (4, 2) (4, 3) (5, 3) (5, 4) (6, 4) (6, 5) (7, 5) (7, 6) (7, 7)
最短路径 33 :
(2, 1) (3, 1) (4, 1) (4, 2) (4, 3) (5, 3) (5, 4) (5, 5) (6, 5) (7, 5) (7, 6) (7, 7)
最短路径 34 :
(2, 1) (3, 1) (4, 1) (4, 2) (4, 3) (5, 3) (5, 4) (5, 5) (5, 6) (5, 7) (6, 7) (7, 7)
最短路径 35 :
(2, 1) (3, 1) (4, 1) (4, 2) (4, 3) (4, 4) (5, 4) (6, 4) (7, 4) (7, 5) (7, 6) (7, 7)
最短路径 36 :
(2, 1) (3, 1) (4, 1) (4, 2) (4, 3) (4, 4) (5, 4) (6, 4) (6, 5) (7, 5) (7, 6) (7, 7)
最短路径 37 :
(2, 1) (3, 1) (4, 1) (4, 2) (4, 3) (4, 4) (5, 4) (5, 5) (6, 5) (7, 5) (7, 6) (7, 7)
最短路径 38 :
(2, 1) (3, 1) (4, 1) (4, 2) (4, 3) (4, 4) (5, 4) (5, 5) (5, 6) (5, 7) (6, 7) (7, 7)
最短路径 39 :
(2, 1) (3, 1) (3, 2) (4, 2) (5, 2) (6, 2) (7, 2) (7, 3) (7, 4) (7, 5) (7, 6) (7, 7)
最短路径 40 :
(2, 1) (3, 1) (3, 2) (4, 2) (5, 2) (6, 2) (6, 3) (7, 3) (7, 4) (7, 5) (7, 6) (7, 7)
最短路径 41 :
(2, 1) (3, 1) (3, 2) (4, 2) (5, 2) (6, 2) (6, 3) (6, 4) (7, 4) (7, 5) (7, 6) (7, 7)
最短路径 42 :
(2, 1) (3, 1) (3, 2) (4, 2) (5, 2) (6, 2) (6, 3) (6, 4) (6, 5) (7, 5) (7, 6) (7, 7)
最短路径 43 :
(2, 1) (3, 1) (3, 2) (4, 2) (5, 2) (5, 3) (6, 3) (7, 3) (7, 4) (7, 5) (7, 6) (7, 7)
最短路径 44 :
(2, 1) (3, 1) (3, 2) (4, 2) (5, 2) (5, 3) (6, 3) (6, 4) (7, 4) (7, 5) (7, 6) (7, 7)
最短路径 45 :
(2, 1) (3, 1) (3, 2) (4, 2) (5, 2) (5, 3) (6, 3) (6, 4) (6, 5) (7, 5) (7, 6) (7, 7)
最短路径 46 :
(2, 1) (3, 1) (3, 2) (4, 2) (5, 2) (5, 3) (5, 4) (6, 4) (7, 4) (7, 5) (7, 6) (7, 7)
最短路径 47 :
(2, 1) (3, 1) (3, 2) (4, 2) (5, 2) (5, 3) (5, 4) (6, 4) (6, 5) (7, 5) (7, 6) (7, 7)
最短路径 48 :
(2, 1) (3, 1) (3, 2) (4, 2) (5, 2) (5, 3) (5, 4) (5, 5) (6, 5) (7, 5) (7, 6) (7, 7)
最短路径 49 :
(2, 1) (3, 1) (3, 2) (4, 2) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6) (5, 7) (6, 7) (7, 7)
最短路径 50 :
(2, 1) (3, 1) (3, 2) (4, 2) (4, 3) (5, 3) (6, 3) (7, 3) (7, 4) (7, 5) (7, 6) (7, 7)
最短路径 51 :
(2, 1) (3, 1) (3, 2) (4, 2) (4, 3) (5, 3) (6, 3) (6, 4) (7, 4) (7, 5) (7, 6) (7, 7)
最短路径 52 :
(2, 1) (3, 1) (3, 2) (4, 2) (4, 3) (5, 3) (6, 3) (6, 4) (6, 5) (7, 5) (7, 6) (7, 7)
最短路径 53 :
(2, 1) (3, 1) (3, 2) (4, 2) (4, 3) (5, 3) (5, 4) (6, 4) (7, 4) (7, 5) (7, 6) (7, 7)
最短路径 54 :
(2, 1) (3, 1) (3, 2) (4, 2) (4, 3) (5, 3) (5, 4) (6, 4) (6, 5) (7, 5) (7, 6) (7, 7)
最短路径 55 :
(2, 1) (3, 1) (3, 2) (4, 2) (4, 3) (5, 3) (5, 4) (5, 5) (6, 5) (7, 5) (7, 6) (7, 7)
最短路径 56 :
(2, 1) (3, 1) (3, 2) (4, 2) (4, 3) (5, 3) (5, 4) (5, 5) (5, 6) (5, 7) (6, 7) (7, 7)
最短路径 57 :
(2, 1) (3, 1) (3, 2) (4, 2) (4, 3) (4, 4) (5, 4) (6, 4) (7, 4) (7, 5) (7, 6) (7, 7)
最短路径 58 :
(2, 1) (3, 1) (3, 2) (4, 2) (4, 3) (4, 4) (5, 4) (6, 4) (6, 5) (7, 5) (7, 6) (7, 7)
最短路径 59 :
(2, 1) (3, 1) (3, 2) (4, 2) (4, 3) (4, 4) (5, 4) (5, 5) (6, 5) (7, 5) (7, 6) (7, 7)
最短路径 60 :
(2, 1) (3, 1) (3, 2) (4, 2) (4, 3) (4, 4) (5, 4) (5, 5) (5, 6) (5, 7) (6, 7) (7, 7)
最短路径 61 :
(2, 1) (2, 2) (3, 2) (4, 2) (5, 2) (6, 2) (7, 2) (7, 3) (7, 4) (7, 5) (7, 6) (7, 7)
最短路径 62 :
(2, 1) (2, 2) (3, 2) (4, 2) (5, 2) (6, 2) (6, 3) (7, 3) (7, 4) (7, 5) (7, 6) (7, 7)
最短路径 63 :
(2, 1) (2, 2) (3, 2) (4, 2) (5, 2) (6, 2) (6, 3) (6, 4) (7, 4) (7, 5) (7, 6) (7, 7)
最短路径 64 :
(2, 1) (2, 2) (3, 2) (4, 2) (5, 2) (6, 2) (6, 3) (6, 4) (6, 5) (7, 5) (7, 6) (7, 7)
最短路径 65 :
(2, 1) (2, 2) (3, 2) (4, 2) (5, 2) (5, 3) (6, 3) (7, 3) (7, 4) (7, 5) (7, 6) (7, 7)
最短路径 66 :
(2, 1) (2, 2) (3, 2) (4, 2) (5, 2) (5, 3) (6, 3) (6, 4) (7, 4) (7, 5) (7, 6) (7, 7)
最短路径 67 :
(2, 1) (2, 2) (3, 2) (4, 2) (5, 2) (5, 3) (6, 3) (6, 4) (6, 5) (7, 5) (7, 6) (7, 7)
最短路径 68 :
(2, 1) (2, 2) (3, 2) (4, 2) (5, 2) (5, 3) (5, 4) (6, 4) (7, 4) (7, 5) (7, 6) (7, 7)
最短路径 69 :
(2, 1) (2, 2) (3, 2) (4, 2) (5, 2) (5, 3) (5, 4) (6, 4) (6, 5) (7, 5) (7, 6) (7, 7)
最短路径 70 :
(2, 1) (2, 2) (3, 2) (4, 2) (5, 2) (5, 3) (5, 4) (5, 5) (6, 5) (7, 5) (7, 6) (7, 7)
最短路径 71 :
(2, 1) (2, 2) (3, 2) (4, 2) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6) (5, 7) (6, 7) (7, 7)
最短路径 72 :
(2, 1) (2, 2) (3, 2) (4, 2) (4, 3) (5, 3) (6, 3) (7, 3) (7, 4) (7, 5) (7, 6) (7, 7)
最短路径 73 :
(2, 1) (2, 2) (3, 2) (4, 2) (4, 3) (5, 3) (6, 3) (6, 4) (7, 4) (7, 5) (7, 6) (7, 7)
最短路径 74 :
(2, 1) (2, 2) (3, 2) (4, 2) (4, 3) (5, 3) (6, 3) (6, 4) (6, 5) (7, 5) (7, 6) (7, 7)
最短路径 75 :
(2, 1) (2, 2) (3, 2) (4, 2) (4, 3) (5, 3) (5, 4) (6, 4) (7, 4) (7, 5) (7, 6) (7, 7)
最短路径 76 :
(2, 1) (2, 2) (3, 2) (4, 2) (4, 3) (5, 3) (5, 4) (6, 4) (6, 5) (7, 5) (7, 6) (7, 7)
最短路径 77 :
(2, 1) (2, 2) (3, 2) (4, 2) (4, 3) (5, 3) (5, 4) (5, 5) (6, 5) (7, 5) (7, 6) (7, 7)
最短路径 78 :
(2, 1) (2, 2) (3, 2) (4, 2) (4, 3) (5, 3) (5, 4) (5, 5) (5, 6) (5, 7) (6, 7) (7, 7)
最短路径 79 :
(2, 1) (2, 2) (3, 2) (4, 2) (4, 3) (4, 4) (5, 4) (6, 4) (7, 4) (7, 5) (7, 6) (7, 7)
最短路径 80 :
(2, 1) (2, 2) (3, 2) (4, 2) (4, 3) (4, 4) (5, 4) (6, 4) (6, 5) (7, 5) (7, 6) (7, 7)
最短路径 81 :
(2, 1) (2, 2) (3, 2) (4, 2) (4, 3) (4, 4) (5, 4) (5, 5) (6, 5) (7, 5) (7, 6) (7, 7)
最短路径 82 :
(2, 1) (2, 2) (3, 2) (4, 2) (4, 3) (4, 4) (5, 4) (5, 5) (5, 6) (5, 7) (6, 7) (7, 7)
最短路径 83 :
(2, 1) (2, 2) (2, 3) (2, 4) (3, 4) (4, 4) (5, 4) (6, 4) (7, 4) (7, 5) (7, 6) (7, 7)
最短路径 84 :
(2, 1) (2, 2) (2, 3) (2, 4) (3, 4) (4, 4) (5, 4) (6, 4) (6, 5) (7, 5) (7, 6) (7, 7)
最短路径 85 :
(2, 1) (2, 2) (2, 3) (2, 4) (3, 4) (4, 4) (5, 4) (5, 5) (6, 5) (7, 5) (7, 6) (7, 7)
最短路径 86 :
(2, 1) (2, 2) (2, 3) (2, 4) (3, 4) (4, 4) (5, 4) (5, 5) (5, 6) (5, 7) (6, 7) (7, 7)
最短路径 87 :
(2, 1) (2, 2) (2, 3) (2, 4) (3, 4) (3, 5) (3, 6) (4, 6) (5, 6) (5, 7) (6, 7) (7, 7)
最短路径 88 :
(2, 1) (2, 2) (2, 3) (2, 4) (3, 4) (3, 5) (3, 6) (4, 6) (4, 7) (5, 7) (6, 7) (7, 7)
最短路径 89 :
(2, 1) (2, 2) (2, 3) (2, 4) (3, 4) (3, 5) (3, 6) (3, 7) (4, 7) (5, 7) (6, 7) (7, 7)
最短路径 90 :
(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (3, 5) (3, 6) (4, 6) (5, 6) (5, 7) (6, 7) (7, 7)
最短路径 91 :
(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (3, 5) (3, 6) (4, 6) (4, 7) (5, 7) (6, 7) (7, 7)
最短路径 92 :
(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (3, 5) (3, 6) (3, 7) (4, 7) (5, 7) (6, 7) (7, 7)
最短路径 93 :
(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6) (3, 6) (4, 6) (5, 6) (5, 7) (6, 7) (7, 7)
最短路径 94 :
(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6) (3, 6) (4, 6) (4, 7) (5, 7) (6, 7) (7, 7)
最短路径 95 :
(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6) (3, 6) (3, 7) (4, 7) (5, 7) (6, 7) (7, 7)
最短路径 96 :
(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6) (2, 7) (3, 7) (4, 7) (5, 7) (6, 7) (7, 7)
最短路径长度: 11
最短路径条数: 96
#include <iostream>#include <string>#include <cstdio>#include <cstring>#include <cstdlib>#include <queue>#include <stack>using namespace std;const int SIZE = 102;//边界数组,四个方向,按照下、右、上、左的顺序int coordinate[4][2] = {1,0, 0,1, -1,0, 0,-1};stack<int> sx;stack<int> sy;stack<int> sxCopy;stack<int> syCopy;int mazeBfs[SIZE][SIZE]; //广搜用的迷宫int mazeDfs[SIZE][SIZE]; //深搜用的迷宫int oddEven[SIZE][SIZE]; //奇偶剪枝状态数组int n; //迷宫行数int m; //迷宫列数int k; //封闭房间数int kr, kl; //每个封闭房间的行号和列号int p, q; //小鼠a的行号和列号int r, s; //小鼠b的行号和列号int ShortestPathLength; //最短路径的长度int ShortestPahtNumber; //最短路径的条数int ans = 1; //输出第ans条最短路径//广搜求最短路径长度//int BFS(int p, int q, int r, int s, int len, int n, int m);int BFS();//深搜求最短路径条数//void DFS(int x, int y, int r, int s, int len, int n, int m, int shortlength);void DFS(int x, int y, int len);int main(){ while (scanf("%d%d%d", &n, &m, &k) != EOF) { memset(mazeBfs, 0, sizeof(mazeBfs)); //初始化迷宫 memset(mazeDfs, 0, sizeof(mazeDfs)); //奇偶剪枝数组初始化 for (int i=0; i<=n; i++) { if (i%2 == 1) { for (int j=0; j<=m; j++) { if (j%2 == 1) { oddEven[i][j] = 1; } else { oddEven[i][j] = 0; } } } else { for (int j=0; j<=m; j++) { if (j%2 == 1) { oddEven[i][j] = 0; } else { oddEven[i][j] = 1; } } } } for (int i=1; i<=k; i++) { scanf("%d%d", &kr, &kl); //输入封闭房间的坐标 //存入迷宫中,迷宫中,1代表封闭房间,0代表可以走 mazeBfs[kr][kl] = 1; mazeDfs[kr][kl] = 1; } scanf("%d%d", &p, &q); //小鼠a的坐标 scanf("%d%d", &r, &s); //小鼠b的坐标 //求最短路径长度 ShortestPathLength = BFS(); if (ShortestPathLength == -1) //没路可走时 { printf("No Solution!\n"); continue; } //求最短路径条数及输出所有的最短路径 ShortestPahtNumber = 0; sx.push(p); sy.push(q); DFS(p, q, 0); //输出结果 printf("最短路径长度: %d\n\n", ShortestPathLength); printf("最短路径条数: %d\n\n", ShortestPahtNumber); } return 0;}int BFS(){ queue<int> qx; //存横坐标的队列 queue<int> qy; //存纵坐标的队列 queue<int> qlen; //存长度的队列 int xa, ya; //当前节点坐标 int length; //到达当前节点长度 qx.push(p); qy.push(q); qlen.push(0); mazeBfs[p][q] = 1; while (!qx.empty()) { if ((qx.front()==r) && (qy.front()==s)) //判断是否到达小鼠b { return qlen.front(); } //临时保存队头值 int xx, yy ,ll; xx = qx.front(); yy = qy.front(); ll = qlen.front(); //保存完之后,出队 qx.pop(); qy.pop(); qlen.pop(); for (int i=0; i<4; i++) { //算第i方向上的新值 xa = xx + coordinate[i][0]; ya = yy + coordinate[i][1]; length = ll; //新的点在迷宫内,且没有走过 if ((xa>=1) && (xa<=n) && (ya>=1) && (ya<=m) && (mazeBfs[xa][ya]==0)) { //入队 qx.push(xa); qy.push(ya); length += 1; qlen.push(length); //标记新点 mazeBfs[xa][ya] = 1; } } } return -1; //如果没有路,返回0}void DFS(int x, int y, int len){ if ((x==r) && (y==s) && (len==ShortestPathLength)) //找到一条最短路径 { ShortestPahtNumber++; //输出最短路径 printf("最短路径 %3d :\n", ans++); int j = sx.size(); for (int i=1; i<=j; i++) { sxCopy.push(sx.top()); sx.pop(); syCopy.push(sy.top()); sy.pop(); } for (int i=1; i<=j; i++) { printf("(%d, %d) ", sxCopy.top(), syCopy.top()); sx.push(sxCopy.top()); sxCopy.pop(); sy.push(syCopy.top()); syCopy.pop(); } printf("\n\n"); return ; } //一般剪枝 int theoryShortestLength; //当前节点到终点的理论最小值 theoryShortestLength = (abs(x-r)) + (abs(y-s)); if ((len+theoryShortestLength) > ShortestPathLength) //当前长度+理论最小值>最短路径长度 { return ; } //奇偶剪枝 if ((ShortestPathLength-len)%2 != ((abs(oddEven[x][y]-oddEven[r][s])) % 2)) { return ; } for (int i=0; i<4; i++) { int xx, yy; xx = x + coordinate[i][0]; yy = y + coordinate[i][1]; if ((xx>=1) && (xx<=n) && (yy>=1) && (yy<=m) && (mazeDfs[xx][yy]==0)) { sx.push(xx); sy.push(yy); mazeDfs[xx][yy] = 1; DFS(xx, yy, len+1); //回溯 sx.pop(); sy.pop(); mazeDfs[xx][yy] = 0; } }}
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