375. Guess Number Higher or Lower II

    public int getMoneyAmount(int n) {
        int[][] res = new int[n][n];
        DP(res, 0, n-1);
        return res[0][n-1];
    }
    
    private int DP(int[][] res, int start, int end) {
        if(start >= end) {
            return 0;
        }
        if(res[start][end] != 0) {
            return res[start][end];
        }
        int minMax = Integer.MAX_VALUE;
        for(int i = start; i <= end; i++) {
            int cur = i + 1 + Math.max(DP(res, start, i - 1), DP(res, i + 1, end));
            minMax = Math.min(minMax, cur);
        }
        res[start][end] = minMax;
        return minMax;
    }