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| 1 | +/* |
| 2 | + * @lc app=leetcode id=980 lang=java |
| 3 | + * |
| 4 | + * [980] Unique Paths III |
| 5 | + * |
| 6 | + * https://leetcode.com/problems/unique-paths-iii/description/ |
| 7 | + * |
| 8 | + * algorithms |
| 9 | + * Hard (72.57%) |
| 10 | + * Likes: 453 |
| 11 | + * Dislikes: 55 |
| 12 | + * Total Accepted: 27.3K |
| 13 | + * Total Submissions: 37.7K |
| 14 | + * Testcase Example: '[[1,0,0,0],[0,0,0,0],[0,0,2,-1]]' |
| 15 | + * |
| 16 | + * On a 2-dimensional grid, there are 4 types of squares: |
| 17 | + * |
| 18 | + * |
| 19 | + * 1 represents the starting square. There is exactly one starting square. |
| 20 | + * 2 represents the ending square. There is exactly one ending square. |
| 21 | + * 0 represents empty squares we can walk over. |
| 22 | + * -1 represents obstacles that we cannot walk over. |
| 23 | + * |
| 24 | + * |
| 25 | + * Return the number of 4-directional walks from the starting square to the |
| 26 | + * ending square, that walk over every non-obstacle square exactly once. |
| 27 | + * |
| 28 | + * |
| 29 | + * |
| 30 | + * |
| 31 | + * Example 1: |
| 32 | + * |
| 33 | + * |
| 34 | + * Input: [[1,0,0,0],[0,0,0,0],[0,0,2,-1]] |
| 35 | + * Output: 2 |
| 36 | + * Explanation: We have the following two paths: |
| 37 | + * 1. (0,0),(0,1),(0,2),(0,3),(1,3),(1,2),(1,1),(1,0),(2,0),(2,1),(2,2) |
| 38 | + * 2. (0,0),(1,0),(2,0),(2,1),(1,1),(0,1),(0,2),(0,3),(1,3),(1,2),(2,2) |
| 39 | + * |
| 40 | + * |
| 41 | + * Example 2: |
| 42 | + * |
| 43 | + * |
| 44 | + * Input: [[1,0,0,0],[0,0,0,0],[0,0,0,2]] |
| 45 | + * Output: 4 |
| 46 | + * Explanation: We have the following four paths: |
| 47 | + * 1. (0,0),(0,1),(0,2),(0,3),(1,3),(1,2),(1,1),(1,0),(2,0),(2,1),(2,2),(2,3) |
| 48 | + * 2. (0,0),(0,1),(1,1),(1,0),(2,0),(2,1),(2,2),(1,2),(0,2),(0,3),(1,3),(2,3) |
| 49 | + * 3. (0,0),(1,0),(2,0),(2,1),(2,2),(1,2),(1,1),(0,1),(0,2),(0,3),(1,3),(2,3) |
| 50 | + * 4. (0,0),(1,0),(2,0),(2,1),(1,1),(0,1),(0,2),(0,3),(1,3),(1,2),(2,2),(2,3) |
| 51 | + * |
| 52 | + * |
| 53 | + * Example 3: |
| 54 | + * |
| 55 | + * |
| 56 | + * Input: [[0,1],[2,0]] |
| 57 | + * Output: 0 |
| 58 | + * Explanation: |
| 59 | + * There is no path that walks over every empty square exactly once. |
| 60 | + * Note that the starting and ending square can be anywhere in the |
| 61 | + * grid. |
| 62 | + * |
| 63 | + * |
| 64 | + * |
| 65 | + * |
| 66 | + * |
| 67 | + * |
| 68 | + * |
| 69 | + * Note: |
| 70 | + * |
| 71 | + * |
| 72 | + * 1 <= grid.length * grid[0].length <= 20 |
| 73 | + * |
| 74 | + */ |
| 75 | + |
| 76 | +// @lc code=start |
| 77 | +class Solution { |
| 78 | + int n, m; |
| 79 | + HashMap<Integer, Integer> dp; |
| 80 | + |
| 81 | + int p(int x, int y){ return x*m+y; } |
| 82 | + |
| 83 | + int callme(int x, int y, int[][] grid, int cur){ |
| 84 | + if(x<0 || y<0 || x>=grid.length || y>=grid[0].length || grid[x][y] == -1) |
| 85 | + return 0; |
| 86 | + if(grid[x][y] == 2) |
| 87 | + return cur == 0 ? 1 : 0; |
| 88 | + if((cur&(1<<p(x, y))) == 0) |
| 89 | + return 0; |
| 90 | + |
| 91 | + if( dp.containsKey(cur*n*m + p(x, y)) ) |
| 92 | + return dp.get(cur*n*m + p(x, y)); |
| 93 | + |
| 94 | + int ret = 0; |
| 95 | + cur ^= (1<<p(x, y)); |
| 96 | + |
| 97 | + //left |
| 98 | + ret += callme(x, y-1, grid, cur); |
| 99 | + //right |
| 100 | + ret += callme(x, y+1, grid, cur); |
| 101 | + //up |
| 102 | + ret += callme(x-1, y, grid, cur); |
| 103 | + //down |
| 104 | + ret += callme(x+1, y, grid, cur); |
| 105 | + |
| 106 | + cur ^= (1<<p(x, y)); |
| 107 | + |
| 108 | + dp.put(cur*n*m + p(x, y), ret); |
| 109 | + return ret; |
| 110 | + } |
| 111 | + |
| 112 | + public int uniquePathsIII(int[][] grid) { |
| 113 | + int cur = 0, x = 0, y = 0; n = grid.length; m = grid[0].length; |
| 114 | + dp = new HashMap<Integer, Integer>(); |
| 115 | + |
| 116 | + for(int i=0; i<n; i++) |
| 117 | + for(int j=0; j<m; j++){ |
| 118 | + if(grid[i][j] == 0) //free |
| 119 | + cur ^= (1<<p(i, j)); |
| 120 | + else if(grid[i][j] == 1){ |
| 121 | + x = i; |
| 122 | + y = j; |
| 123 | + } |
| 124 | + } |
| 125 | + |
| 126 | + grid[x][y] = -1; |
| 127 | + return callme(x+1, y, grid, cur)+callme(x-1, y, grid, cur)+callme(x, y-1, grid, cur)+callme(x, y+1, grid, cur); |
| 128 | + |
| 129 | + } |
| 130 | +} |
| 131 | +// @lc code=end |
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