CodeForces 173C Spiral Maximum dp 矩阵降次

题目链接：点击打开链接

题意：

给定n*m的矩阵，可以在矩阵中画出题目图片里黑色的线条。

任选一个点，左下右上的顺序走，走出图里的情况。使得走过的数字和最大，问最大的和。

思路：

点击打开链接

题解比较详细了

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, m;
	int[][] a = new int[N][N], sum = new int[N][N];
	int[][][] s;
	void work() throws Exception {
		n = Int(); m = Int();
		for(int i = 1; i<= n; i++)
			for(int j = 1; j <= m; j++){
				sum[i][j] = a[i][j] = Int();
				if(i>0)
					sum[i][j] += sum[i-1][j];
				if(j>0)
					sum[i][j] += sum[i][j-1];
				if(i>0&&j>0)
					sum[i][j] -= sum[i-1][j-1];
			}
		s = new int[n+1][][];
		for(int i = 1; i <= n; i++)s[i] = new int[m+1][];
		for(int i = 1; i <= n; i++)for(int j = 1; j <= m; j++){
			s[i][j] = new int[min(n+2-i,m+2-j)/2];
			s[i][j][0] = a[i][j];
		}
		int ans = -inf;
		for(int k = 1; k <= 250; k++)
			for(int i = 1; i+2*k <= n; i++)
				for(int j = 1; j + 2*k <= m; j++)
				{
		s[i][j][k] = sum[i+2*k][j+2*k]-sum[i-1][j+2*k]-sum[i+2*k][j-1]+sum[i-1][j-1]-s[i+1][j+1][k-1]-a[i+1][j];

					ans = max(ans, s[i][j][k]);
				}
		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 = 505;
	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);
	}
}