Travelling Salesman Problem

Teacher Mai is in a maze with n rows and m columns. There is a non-negative number in each cell. Teacher Mai wants to walk from the top left corner (1,1) to the bottom right corner (n,m). He can choose one direction and walk to this adjacent cell. However, he can‘t go out of the maze, and he can‘t visit a cell more than once.

Teacher Mai wants to maximize the sum of numbers in his path. And you need to print this path.

There are multiple test cases.

For each test case, the first line contains two numbers n,m(1≤n,m≤100,n?m≥2).

In following n lines, each line contains m numbers. The j-th number in the i-th line means the number in the cell (i,j). Every number in the cell is not more than 104.

For each test case, in the first line, you should print the maximum sum.

In the next line you should print a string consisting of "L","R","U" and "D", which represents the path you find. If you are in the cell (x,y), "L" means you walk to cell (x,y?1), "R" means you walk to cell (x,y+1), "U" means you walk to cell (x?1,y), "D" means you walk to cell (x+1,y).

3 3
2 3 3
3 3 3
3 3 2

25
RRDLLDRR

当n,m有一个奇数时，‘S形’可全取。

否则至少要少取一个，

假设少取(mx,my) ，当mx+my为偶数时，必定有一个与(mx,my)相邻的不能取

否则必能全取剩下的。（‘S形’+特判2行‘长城形’)

#include<bits/stdc++.h> 
using namespace std;
#define For(i,n) for(int i=1;i<=n;i++)
#define Fork(i,k,n) for(int i=k;i<=n;i++)
#define Rep(i,n) for(int i=0;i<n;i++)
#define ForD(i,n) for(int i=n;i;i--)
#define RepD(i,n) for(int i=n;i>=0;i--)
#define Forp(x) for(int p=pre[x];p;p=next[p])
#define Forpiter(x) for(int &p=iter[x];p;p=next[p])  
#define Lson (x<<1)
#define Rson ((x<<1)+1)
#define MEM(a) memset(a,0,sizeof(a));
#define MEMI(a) memset(a,127,sizeof(a));
#define MEMi(a) memset(a,128,sizeof(a));
#define INF (2139062143)
#define F (100000007)
#define MAXN (100+10)
typedef long long ll;
ll mul(ll a,ll b){return (a*b)%F;}
ll add(ll a,ll b){return (a+b)%F;}
ll sub(ll a,ll b){return (a-b+llabs(a-b)/F*F+F)%F;}
void upd(ll &a,ll b){a=(a%F+b%F)%F;}
int n,m;
ll a[MAXN][MAXN];
int main()
{
//	freopen("Travelling.in","r",stdin);
	
	while(cin>>n>>m) {
		ll sum=0,mi=INF;int mx,my;
		For(i,n) For(j,m) {
			scanf("%lld",&a[i][j]),sum+=a[i][j];
			if (mi>a[i][j]&&(i+j)%2==1)
				mi=min(mi,a[i][j]),mx=i,my=j;
		}
		if (n%2==0&&m%2==0)
		{
			cout<<sum-mi<<endl;	
			
			if (mx%2==1) {
				For(i,mx-1) 
				{
					if (i&1) {For(j,m-1) putchar('R');}
					else {For(j,m-1) putchar('L'); }
					if (i<n) putchar('D');
				}

				int tx=mx,ty=1;
				int p=0;
				For(j,m)
				{
					if (my==j) {if (j<m) putchar('R');continue;}
					if (p==0) printf("D");
					else printf("U");
					p^=1;
					if (j<m) putchar('R');
				}
				Fork(i,mx+2,n) 
				{
					putchar('D');
					if ((i&1)^1) {For(j,m-1) putchar('R');}
					else {For(j,m-1) putchar('L'); }
				}
			}
			
			if (my%2==1) {
				For(i,my-1) 
				{
					if (i&1) {For(j,n-1) putchar('D'); }
					else {For(j,n-1) putchar('U'); }
					if (i<m) putchar('R');
				}
			
				int tx=1,ty=my;
				int p=0;
				For(j,n)
				{
					if (mx==j) {if (j<n) putchar('D');continue;}
					if (p==0) printf("R");
					else printf("L");
					p^=1;
					if (j<n) putchar('D');
				}
				
				Fork(i,my+2,m) 
				{
					putchar('R');
					if ((i&1)^1) {For(j,n-1) putchar('D'); }
					else {For(j,n-1) putchar('U'); }
				}
			}
			
			
		} 
		else {
			cout<<sum<<endl;
			if (n%2) {
				For(i,n) 
				{
					if (i&1) {For(j,m-1) putchar('R');}
					else {For(j,m-1) putchar('L'); }
					if (i<n) putchar('D');
				}
			} else {
				For(i,m) 
				{
					if (i&1) {For(j,n-1) putchar('D'); }
					else {For(j,n-1) putchar('U'); }
					if (i<m) putchar('R');
				}
			}
		}
		cout<<endl;
	}
	
	return 0;
}