public class Solution {
    /*
     * @param : a vector of integers
     * @return: a boolean which equals to true if the first player will win
     */
    //set X(Alice) and Y(Bob) are the total value each player get
    //so when X got to move first, it wants the difference to be max Sx = X - Y
    //   when Y got to move first, it wants the difference to be max Sy = Y - X
    //   therefore after the next move X make, Sx = -Sy + m
    //set f[i][j] represents a[i, j] one side first move the max difference
    //f[i][j] = max{a[i] - f[i + 1][j], a[j] - f[i][j - 1]}
    public boolean firstWillWin(int[] values) {
        // write your code here
        if (values == null && values.length == 0) {
            return false;
        }

        int n = values.length;
        int[][] f = new int[n][n];
        //init
        //if there is only one number the first hand got the item value
        int i, j, len;
        for (i = 0; i < n; i++) {
            f[i][i] = values[i];
        }


        for (len = 2; len <= n; len++) {
            for (i = 0; i <= n - len; i++) {
                j = i + len - 1;
                f[i][j] = Math.max(values[i] - f[i + 1][j], values[j] - f[i][j - 1]);
            }
        }

        return f[0][n - 1] >= 0;
    }
};