CodeForces 264C Choosing Balls dp（水

题目链接：

题意：

给定n q 表示有n个石头 q个询问

下面n个数字给出每个石头的价值

下面n个数字给出每个石头的颜色（用1-n表示）

选出一个子序列使得序列的权值和最大（序列权值计算方式：当这个点的颜色和前面那个点颜色相同时 贡献 value * a, otherwise 贡献 value * b）

下面q行，每行给出 a 和 b的值。

思路：

首先求dp方程 dp[i]表示颜色为i时的最大值 那么 this_point_value = max(dp[j] + b*v[i]) (i!=j)   this_point_value = max(dp[i] + a*v[i]) dp[color[i]] = this_point_value;

就是这样。

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 {
	int n, q, a, b;
	int[] v = new int[N], c = new int[N];
	long[] dp = new long[N];
	int[] pre = new int[N];
	long max1, max2;
	int col1, col2;
	void up(long val, int col){
		if(val>=max1){
			if(val>max1){
				if(col == col1){
					max1 = val;
				}
				else {
					max2 = max1; col2 = col1;
					max1 = val; col1 = col;
				}
			}
			else if(col!=col1){
				max2 = val; col2 = col;
			}
		}
		else if(val >= max2){
			if(col == col1)return;
			max2 = val; col2 = col;
		}
	}
	void work() throws Exception{
		n = Int(); q = Int();
		for(int i = 1; i <= n; i++)v[i] = Int();
		for(int i = 1; i <= n; i++)c[i] = Int();		

		while(q-->0){
			a = Int(); b = Int();
			long ans = 0;
			max1 = -inf64; max2 = -inf64;
			col1 = 0; col2 = 0;
			for(int i = 1; i <= n; i++)pre[i] = -1;
			for(int i = 1; i <= n; i++){
				long now = (long)v[i]*b;
				if(pre[c[i]]!=-1){
					now = max(now, dp[c[i]] + (long)a*v[i]);
			//		out.print("now1:"+now);
				}
				if(col1!=c[i] && col1!=0)now = max(now, max1 + (long)b*v[i]);
				else if(col2!=c[i] && col2!=0)now = max(now, max2 + (long)b*v[i]);
			//	out.println(" now2:"+now);

				up(now, c[i]);
				if(pre[c[i]] == -1)dp[c[i]] = now;
				else
				dp[c[i]] = max(dp[c[i]], now);
				pre[c[i]] = i;
				ans = max(ans, now);
			//	out.println(max1+" "+col1);	out.println(max2+" "+col2);	out.println(now+" "+ans+" ***");
			}
			out.println(ans);
		}
	}

    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 = 100000+5;
	static int M = 101;
	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 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);}
}