CodeForces 148E Porcelain dp+背包(水

题目链接：点击打开链接

题意：

给定1个n层书架，1共取m本书。

下面n行给出每层书的价值。

每次可以取任意1层的最左端或最右真个1本书。

问能取得的最大价值。

思路：

1、明显是先求出对每层任取任意本书能取得的最大价值。

2、然后背包1下。

1：

对1层书任意j本，那末1定是从左端取k本，右端取 j-k本，求个前缀和然后枚举 j和k便可。每层n^2的dp

2：

分组背包。

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 m,n; int[] sum = new int[N],num = new int[N]; int[][] dp = new int[N][N],h = new int[2][M]; void work() throws Exception{ n = Int(); m = Int(); for(int i = 1; i <= n; i++){ num[i] = Int(); sum[0] = 0; for(int j = 1; j <= num[i]; j++){ sum[j] = sum[j⑴]+Int(); } dp[i][0] = 0; for(int j = 1; j <= num[i]; j++){ dp[i][j] = 0; for(int k = 0; k <= j; k++) dp[i][j] = max(dp[i][j],sum[k] + sum[num[i]] - sum[num[i]-j+k]); } } int cur = 0,old = 1; for(int i = 0; i <= m; i++)h[cur][i] = 0; for(int i = 1; i <= n; i++) { cur ^= 1; old ^= 1; for(int j = 0; j <= m; j++)h[cur][j] = h[old][j]; for(int j = 0; j <= num[i]; j++) { for(int k = j; k <= m; k++) h[cur][k] = max(h[cur][k],h[old][k-j]+dp[i][j]); } } out.println(h[cur][m]); } 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 = 101; static int M = 10001; DecimalFormat df=new DecimalFormat(0.0000); static int inf = (int)1e9; static long inf64 = (long) 1e18; static double eps = 1e⑻; 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] = ⑴; edgenum = 0;} void add(int u,int v,int dis){ edge[edgenum] = new Edge(u,v,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);} }