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| 1 | +/** |
| 2 | + * Title: Cat and Mouse |
| 3 | + * Description: A game on an undirected graph is played by two players, Mouse and Cat, who alternate turns. |
| 4 | + * Author: Hasibul Islam |
| 5 | + * Date: 06/05/2023 |
| 6 | + */ |
| 7 | + |
| 8 | +/** |
| 9 | + * @param {number[][]} graph |
| 10 | + * @return {number} |
| 11 | + */ |
| 12 | +var catMouseGame = function (graph) { |
| 13 | + const n = graph.length; |
| 14 | + //using anything less than n * 5 won't pass the 89 test cases since the June 2022. As test cases get harder will need to increase this value or fix this algorithm |
| 15 | + const state = new Array(n * 5) |
| 16 | + .fill(0) |
| 17 | + .map((el, i) => new Array(n).fill(0).map((el, i) => new Array(n).fill(-1))); |
| 18 | + |
| 19 | + function updateState(step, cat, mouse, value) { |
| 20 | + state[step][cat][mouse] = value; |
| 21 | + return state[step][cat][mouse]; |
| 22 | + } |
| 23 | + |
| 24 | + function dfs(step, cat, mouse) { |
| 25 | + if (step >= state.length) return 0; |
| 26 | + if (state[step][cat][mouse] !== -1) { |
| 27 | + return state[step][cat][mouse]; |
| 28 | + } |
| 29 | + let finalResult = -1; |
| 30 | + if (step & 1) { |
| 31 | + //cat's turn |
| 32 | + if (graph[cat].includes(mouse)) { |
| 33 | + return (state[step][cat][mouse] = 2); |
| 34 | + } |
| 35 | + for (const node of graph[cat]) { |
| 36 | + if (node !== 0) { |
| 37 | + let nextResult = dfs(step + 1, node, mouse, 0); |
| 38 | + if (nextResult === 2) { |
| 39 | + return (state[step][cat][mouse] = 2); |
| 40 | + } else if (nextResult === 1) { |
| 41 | + if (finalResult === -1) { |
| 42 | + finalResult = 1; |
| 43 | + } |
| 44 | + } else if (nextResult === 0) { |
| 45 | + finalResult = 0; |
| 46 | + } |
| 47 | + } |
| 48 | + } |
| 49 | + if (finalResult === -1) { |
| 50 | + finalResult = 1; |
| 51 | + } |
| 52 | + } else { |
| 53 | + //mouse's turn |
| 54 | + if (graph[mouse].includes(0)) { |
| 55 | + return (state[step][cat][mouse] = 1); |
| 56 | + } |
| 57 | + for (const node of graph[mouse]) { |
| 58 | + if (node !== cat && !graph[node].includes(cat)) { |
| 59 | + let nextResult = dfs(step + 1, cat, node, 1); |
| 60 | + if (nextResult === 1) { |
| 61 | + return (state[step][cat][mouse] = 1); |
| 62 | + } else if (nextResult === 2) { |
| 63 | + if (finalResult === -1) { |
| 64 | + finalResult = 2; |
| 65 | + } |
| 66 | + } else if (nextResult === 0) { |
| 67 | + finalResult = 0; |
| 68 | + } |
| 69 | + } |
| 70 | + } |
| 71 | + if (finalResult === -1) { |
| 72 | + finalResult = 2; |
| 73 | + } |
| 74 | + } |
| 75 | + return (state[step][cat][mouse] = finalResult); |
| 76 | + } |
| 77 | + return dfs(0, 2, 1); |
| 78 | +}; |
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