Codeforces 212E IT Restaurants 树形dp（水

题目链接：点击打开链接

题意：

给定n个点的树，染两种颜色，不同颜色不能相邻且要给尽可能多的节点染色。求颜色A和颜色B可能的染色节点个数。（copy from figo）

而且至少一个点染A，至少一个点染B

dp[i][j]=1表示i点染j个A色是可行的 =0表示不可行。

import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.text.DecimalFormat;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collection;
import java.util.Collections;
import java.util.Comparator;
import java.util.Deque;
import java.util.HashMap;
import java.util.Iterator;
import java.util.LinkedList;
import java.util.Map;
import java.util.PriorityQueue;
import java.util.Scanner;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;
import java.util.Queue;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.FileOutputStream;

public class Main {
	ArrayList<Integer> L = new ArrayList(), R = new ArrayList();
	int[][] dp = new int[N][N];//表示i点的子树 染j个红色时能得到最多几个蓝色
	int[] siz = new int[N], ans = new int[N];
	int n;
	void dfs(int u, int fa){
		for(int i = 2; i <= n; i++)dp[u][i] = 0;
		dp[u][0] = 1;
		siz[u] = 1;
		for(int i = head[u]; i!=-1; i = edge[i].nex){
			int v = edge[i].to; if(v == fa)continue;
			dfs(v, u);
			siz[u] += siz[v];
			for(int j = n-1; j >= 0; j--)
				if(dp[u][j]>0)
					dp[u][j+siz[v]] = 1;
		}
		int s = n-siz[u];
		for(int i = n-1; i >= 0; i--)
			if(dp[u][i]>0)dp[u][i+s] = 1;

		for(int i = 1; i < n-1; i++)
			if(dp[u][i]>0)ans[i] = 1;
	}
	void work() throws Exception {
		init_edge();
		n = Int();
		for(int i = 0; i <= n; i++)ans[i] = 0;
		for(int i = 1, u, v; i< n; i++){
			u =Int(); v = Int();
			add(u,v,1); add(v,u,1);
		}
		dfs(1,-1);
		int len = 0;
		for(int i = 1; i < n-1; i++)len += ans[i];
		out.println(len);
		for(int i = 1; i < n-1; i++)
			if(ans[i]>0){
				out.println(i+" "+(n-1-i));
			}
	}

	public static void main(String[] args) throws Exception {
		Main wo = new Main();
		in = new BufferedReader(new InputStreamReader(System.in));
		out = new PrintWriter(System.out);
		// in = new BufferedReader(new InputStreamReader(new FileInputStream(new
		// File("input.txt"))));
		// out = new PrintWriter(new File("output.txt"));
		wo.work();
		out.close();
	}

	static int N = 5050;
	static int M = N * 2;
	DecimalFormat df = new DecimalFormat("0.0000");
	static int inf = (int) 1e9;
	static long inf64 = (long) 1e18;
	static double eps = 1e-8;
	static double Pi = Math.PI;
	static int mod = (int) 1e9 + 7;

	private String Next() throws Exception {
		while (str == null || !str.hasMoreElements())
			str = new StringTokenizer(in.readLine());
		return str.nextToken();
	}

	private int Int() throws Exception {
		return Integer.parseInt(Next());
	}

	private long Long() throws Exception {
		return Long.parseLong(Next());
	}

	private double Double() throws Exception {
		return Double.parseDouble(Next());
	}

	StringTokenizer str;
	static Scanner cin = new Scanner(System.in);
	static BufferedReader in;
	static PrintWriter out;

	class Edge{
		int from, to, dis, nex;
		Edge(){}
		Edge(int from, int to, int	 dis, int nex)
		{
		this.from = from; this.to = to; this.dis = dis; this.nex =	nex;
		}
	}
	Edge[] edge = new Edge[M<<1];
	int[] head = new int[N]; int edgenum;
	void init_edge(){ for(int i = 0; i < N; i++)head[i] = -1; edgenum = 0;}
	void add(int u, int v, int dis){
		edge[edgenum] = new Edge(u, v, dis, head[u]);
		head[u] = edgenum++;
	}
	 /*
	 */
	int upper_bound(int[] A, int l, int r, int val) {// upper_bound(A+l,A+r,val)-A;
		int pos = r;
		r--;
		while (l <= r) {
			int mid = (l + r) >> 1;
			if (A[mid] <= val) {
				l = mid + 1;
			} else {
				pos = mid;
				r = mid - 1;
			}
		}
		return pos;
	}

	int lower_bound(int[] A, int l, int r, int val) {// upper_bound(A+l,A+r,val)-A;
		int pos = r;
		r--;
		while (l <= r) {
			int mid = (l + r) >> 1;
			if (A[mid] < val) {
				l = mid + 1;
			} else {
				pos = mid;
				r = mid - 1;
			}
		}
		return pos;
	}

	int Pow(int x, int y) {
		int ans = 1;
		while (y > 0) {
			if ((y & 1) > 0)
				ans *= x;
			y >>= 1;
			x = x * x;
		}
		return ans;
	}

	double Pow(double x, int y) {
		double ans = 1;
		while (y > 0) {
			if ((y & 1) > 0)
				ans *= x;
			y >>= 1;
			x = x * x;
		}
		return ans;
	}

	int Pow_Mod(int x, int y, int mod) {
		int ans = 1;
		while (y > 0) {
			if ((y & 1) > 0)
				ans *= x;
			ans %= mod;
			y >>= 1;
			x = x * x;
			x %= mod;
		}
		return ans;
	}

	long Pow(long x, long y) {
		long ans = 1;
		while (y > 0) {
			if ((y & 1) > 0)
				ans *= x;
			y >>= 1;
			x = x * x;
		}
		return ans;
	}

	long Pow_Mod(long x, long y, long mod) {
		long ans = 1;
		while (y > 0) {
			if ((y & 1) > 0)
				ans *= x;
			ans %= mod;
			y >>= 1;
			x = x * x;
			x %= mod;
		}
		return ans;
	}

	int gcd(int x, int y) {
		if (x > y) {
			int tmp = x;
			x = y;
			y = tmp;
		}
		while (x > 0) {
			y %= x;
			int tmp = x;
			x = y;
			y = tmp;
		}
		return y;
	}

	int max(int x, int y) {
		return x > y ? x : y;
	}

	int min(int x, int y) {
		return x < y ? x : y;
	}

	double max(double x, double y) {
		return x > y ? x : y;
	}

	double min(double x, double y) {
		return x < y ? x : y;
	}

	long max(long x, long y) {
		return x > y ? x : y;
	}

	long min(long x, long y) {
		return x < y ? x : y;
	}

	int abs(int x) {
		return x > 0 ? x : -x;
	}

	double abs(double x) {
		return x > 0 ? x : -x;
	}

	long abs(long x) {
		return x > 0 ? x : -x;
	}

	boolean zero(double x) {
		return abs(x) < eps;
	}

	double sin(double x) {
		return Math.sin(x);
	}

	double cos(double x) {
		return Math.cos(x);
	}

	double tan(double x) {
		return Math.tan(x);
	}

	double sqrt(double x) {
		return Math.sqrt(x);
	}
}