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);}}