Integer Partition

import java.util.LinkedList;
import java.util.Queue;


public class PartitionNumber {

    static int n;
    static int[][] memo;
    public static void main(String[] args) {
        int n = 5;
        memo = new int[n+10][n+10];
        for (int i = 0 ; i <= n; i++) {
            for (int j = 0; j <= n ; j++) {
                memo[i][j] = -1;
            }
        }

        System.out.println("Numbers of Number: " + dp(n,1));
        System.out.println("list all those numbers: ");
        generate(n);
    }

    public static int dp(int n, int k) {
        if (n == 0 || k > n) return 0;
        if (n == k) return 1;
        if (memo[n][k] != -1) return memo[n][k];
        if (n > k) return memo[n][k] = dp(n-k,k) + dp(n,k+1);
        else return memo[n][k] = dp(n, k+1);
    }

    public static void generate(int n) {
        Queue<Node> queue = new LinkedList<PartitionNumber.Node>();
        for (int i = 1; i <= n; i++) {
            queue.add(new Node(i + "", i, n - i));
        }
        while (!queue.isEmpty()) {
            Node node = queue.poll();
            if (node.remain == 0) System.out.println(node.val);
            for (int i = node.min; i <= node.remain; i++) {
                queue.add(new Node(node.val + i, i, node.remain - i));
            }
        }
    }

    public static class Node {
        String val;
        int min, remain;
        public Node(String val, int min, int remain) {
            this.val = val;
            this.min = min;
            this.remain = remain;
        }
    }
}