/**
 * 计算二项式系数 <br/>
 * 动态规划
 * O(nk)
 * 
 * @author chenxuegui
 * 
 */
public class BinomialCoefficient
{
	public static void main(String[] args)
	{
		int n = 4;
		int k = 3;
		System.out.println(binomial(new int[n+1][n+1], n, k));

	}

	/**
	 * 计算二项式系数
	 * @param recode
	 * @param n
	 * @param k
	 * @return
	 */
	public static int binomial(int[][] recode, int n, int k)
	{
		for (int i = 0; i <= n; i++)
		{
			for (int j = 0; j <= Math.min(k, i); j++)
			{
				if (j == i || j == 0)
				{
					recode[i][j] = 1;
				}
				else
				{
					recode[i][j] = recode[i - 1][j] + recode[i - 1][j - 1];
				}
			}
		}
		
		return recode[n][k];

	}

}

动态规划——1 计算二项式系数