博弈论[leetocde913]

class Solution {
    static final int MOUSE_WIN = 1;
    static final int CAT_WIN = 2;
    static final int DRAW = 0;

    int n;
    int[][][] dp;   // dp[mouse][cat][turns]：表示在经历turns轮次，老鼠在mouse位置，猫在cat位置时游戏的状态
    int[][] graph;

    public int catMouseGame(int[][] graph) {
        this.n = graph.length;
        this.graph = graph;
        this.dp = new int[n][n][n*2];

        // 初始化
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                Arrays.fill(dp[i][j], -1);
            }
        }

        return getResult(1, 2, 0);
    }

    private int getResult(int mouse, int cat, int turns) {
        if (turns == 2*n) {
            return DRAW;
        }

        // 未分出比赛状态
        if (dp[mouse][cat][turns] == -1) {
            if (mouse == 0) {
                dp[mouse][cat][turns] = MOUSE_WIN;
            } else if (mouse == cat) {
                dp[mouse][cat][turns] = CAT_WIN;
            } else {
                getNextResult(mouse, cat, turns);
            }
        }

        return dp[mouse][cat][turns];
    }

    private void getNextResult(int mouse, int cat, int turns) {
        // turns 为偶数时，老鼠先走
        int curMove = turns % 2 == 0? mouse: cat;
        int notHopeResult = curMove == mouse?  CAT_WIN: MOUSE_WIN;

        int result = notHopeResult;
        int[] nextNodes = graph[curMove];
        for (int next: nextNodes) {
            if (curMove == cat && next == 0) continue;  // 猫无法移动到0
            int nextCat = curMove == cat? next: cat;
            int nextMouse = curMove == mouse? next: mouse;
            int nextResult = getResult(nextMouse, nextCat, turns + 1);

            if (nextResult != notHopeResult) {  // 对于老鼠来说：他不希望nextResult为猫赢
                result = nextResult;
                if (result != DRAW) break;  // 已经分出胜负，则无需再比赛；若为平局则一直试探下一个next
            }
        }

        dp[mouse][cat][turns] = result;
    }
}

题解见官方