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11 | 11 | * @param {number} mouseJump |
12 | 12 | * @return {boolean} |
13 | 13 | */ |
14 | | -function canMouseWin(grid, catJump, mouseJump) { |
15 | | - const dirs = [ |
16 | | - [1, 0], |
17 | | - [-1, 0], |
18 | | - [0, 1], |
19 | | - [0, -1], |
20 | | - ]; |
21 | | - const m = grid.length; |
22 | | - const n = grid[0].length; |
23 | | - let mouse_pos = null; |
24 | | - let cat_pos = null; |
25 | | - let available = 0; // available steps for mouse and cat |
| 14 | +var canMouseWin = function (A, maxC, maxM) { |
| 15 | + let n = A.length, |
| 16 | + m = A[0].length, |
| 17 | + seen = {}, |
| 18 | + pos = [ |
| 19 | + [0, 1], |
| 20 | + [0, -1], |
| 21 | + [1, 0], |
| 22 | + [-1, 0], |
| 23 | + ], |
| 24 | + xM, |
| 25 | + yM, |
| 26 | + xC, |
| 27 | + yC, |
| 28 | + xF, |
| 29 | + yF; |
| 30 | + for (let i = 0; i < n; i++) |
| 31 | + for (let j = 0; j < m; j++) |
| 32 | + if (A[i][j] === "M") [xM, yM] = [i, j]; |
| 33 | + else if (A[i][j] === "C") [xC, yC] = [i, j]; |
| 34 | + else if (A[i][j] === "F") [xF, yF] = [i, j]; |
26 | 35 |
|
27 | | - // Search the start pos of mouse and cat |
28 | | - for (let i = 0; i < m; i++) { |
29 | | - for (let j = 0; j < n; j++) { |
30 | | - if (grid[i][j] !== "#") { |
31 | | - available++; |
32 | | - } |
33 | | - if (grid[i][j] === "M") { |
34 | | - mouse_pos = [i, j]; |
35 | | - } else if (grid[i][j] === "C") { |
36 | | - cat_pos = [i, j]; |
37 | | - } |
38 | | - } |
39 | | - } |
| 36 | + let invalid = ([x, y]) => |
| 37 | + x < 0 || x >= n || y < 0 || y >= m ? true : A[x][y] === "#"; |
40 | 38 |
|
41 | | - const dp = function (turn, mouse_pos, cat_pos) { |
42 | | - // if (turn === m * n * 2) { |
43 | | - // We already search the whole grid (9372 ms 74.3 MB) |
44 | | - if (turn === available * 2) { |
45 | | - // We already search the whole touchable grid (5200 ms 57.5 MB) |
46 | | - return false; |
47 | | - } |
48 | | - if (turn % 2 === 0) { |
49 | | - // Mouse |
50 | | - const [i, j] = mouse_pos; |
51 | | - for (let [di, dj] of dirs) { |
52 | | - for (let jump = 0; jump <= mouseJump; jump++) { |
53 | | - // Note that we want to do range(mouseJump + 1) instead of range(1, mouseJump + 1) |
54 | | - // considering the case that we can stay at the same position for next turn. |
55 | | - const new_i = i + di * jump; |
56 | | - const new_j = j + dj * jump; |
| 39 | + //returns whether the current player ( determined by level -odd/even) can win the game while on the current state |
| 40 | + let recursion = ([[xM, yM], [xC, yC]], level) => { |
| 41 | + let whoPlays = Boolean(level % 2), |
| 42 | + state = [ |
| 43 | + [ |
| 44 | + [xM, yM], |
| 45 | + [xC, yC], |
| 46 | + ], |
| 47 | + level, |
| 48 | + ].toString(), |
| 49 | + maxAllowable = whoPlays ? maxC : maxM; |
| 50 | + if (seen[state] === undefined) { |
| 51 | + //memoization |
| 52 | + //end states |
| 53 | + if ((xC === xF && yC === yF) || (xC === xM && yC === yM) || level >= 70) |
| 54 | + // level>=70 makes this pass |
| 55 | + return (seen[state] = whoPlays); |
| 56 | + if (xM === xF && yM === yF) return (seen[state] = !whoPlays); |
| 57 | + //try staying still first |
| 58 | + if ( |
| 59 | + recursion( |
| 60 | + [ |
| 61 | + [xM, yM], |
| 62 | + [xC, yC], |
| 63 | + ], |
| 64 | + level + 1 |
| 65 | + ) === false |
| 66 | + ) |
| 67 | + return (seen[state] = true); |
| 68 | + //then try moving |
| 69 | + for (let [dx, dy] of pos) |
| 70 | + for (let k = 1; k <= maxAllowable; k++) { |
| 71 | + let newState = whoPlays |
| 72 | + ? [xC + dx * k, yC + dy * k] |
| 73 | + : [xM + dx * k, yM + dy * k]; |
| 74 | + if (invalid(newState) || seen[state]) break; |
57 | 75 | if ( |
58 | | - 0 <= new_i && |
59 | | - new_i < m && |
60 | | - 0 <= new_j && |
61 | | - new_j < n && |
62 | | - grid[new_i][new_j] !== "#" |
63 | | - ) { |
64 | | - // Valid pos |
65 | | - if ( |
66 | | - dp(turn + 1, [new_i, new_j], cat_pos) || |
67 | | - grid[new_i][new_j] === "F" |
68 | | - ) { |
69 | | - return true; |
70 | | - } |
71 | | - } else { |
72 | | - // Stop extending the jump since we cannot go further |
73 | | - break; |
74 | | - } |
| 76 | + recursion( |
| 77 | + whoPlays ? [[xM, yM], newState] : [newState, [xC, yC]], |
| 78 | + level + 1 |
| 79 | + ) === false |
| 80 | + ) |
| 81 | + return (seen[state] = true); |
75 | 82 | } |
76 | | - } |
77 | | - return false; |
78 | | - } else { |
79 | | - // Cat |
80 | | - const [i, j] = cat_pos; |
81 | | - for (let [di, dj] of dirs) { |
82 | | - for (let jump = 0; jump <= catJump; jump++) { |
83 | | - const new_i = i + di * jump; |
84 | | - const new_j = j + dj * jump; |
85 | | - if ( |
86 | | - 0 <= new_i && |
87 | | - new_i < m && |
88 | | - 0 <= new_j && |
89 | | - new_j < n && |
90 | | - grid[new_i][new_j] !== "#" |
91 | | - ) { |
92 | | - if ( |
93 | | - !dp(turn + 1, mouse_pos, [new_i, new_j]) || |
94 | | - (new_i === mouse_pos[0] && new_j === mouse_pos[1]) || |
95 | | - grid[new_i][new_j] === "F" |
96 | | - ) { |
97 | | - // This condition will also handle the case that the cat cannot jump through the mouse |
98 | | - return false; |
99 | | - } |
100 | | - } else { |
101 | | - break; |
102 | | - } |
103 | | - } |
104 | | - } |
105 | | - return true; |
| 83 | + seen[state] = false; |
106 | 84 | } |
| 85 | + return seen[state]; |
107 | 86 | }; |
108 | | - |
109 | | - return dp(0, mouse_pos, cat_pos); |
110 | | -} |
| 87 | + return recursion( |
| 88 | + [ |
| 89 | + [xM, yM], |
| 90 | + [xC, yC], |
| 91 | + ], |
| 92 | + 0 |
| 93 | + ); |
| 94 | +}; |
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