FatMouse and Cheese
Problem Description
FatMouse has stored some cheese in a city. The city can be considered as a square grid of dimension n: each grid location is labelled (p,q) where 0 <= p < n and 0 <= q < n. At each grid location Fatmouse has hid between 0 and 100 blocks of cheese in a hole. Now he's going to enjoy his favorite food.
FatMouse begins by standing at location (0,0). He eats up the cheese where he stands and then runs either horizontally or vertically to another location. The problem is that there is a super Cat named Top Killer sitting near his hole, so each time he can run at most k locations to get into the hole before being caught by Top Killer. What is worse -- after eating up the cheese at one location, FatMouse gets fatter. So in order to gain enough energy for his next run, he has to run to a location which have more blocks of cheese than those that were at the current hole.
Given n, k, and the number of blocks of cheese at each grid location, compute the maximum amount of cheese FatMouse can eat before being unable to move.
FatMouse begins by standing at location (0,0). He eats up the cheese where he stands and then runs either horizontally or vertically to another location. The problem is that there is a super Cat named Top Killer sitting near his hole, so each time he can run at most k locations to get into the hole before being caught by Top Killer. What is worse -- after eating up the cheese at one location, FatMouse gets fatter. So in order to gain enough energy for his next run, he has to run to a location which have more blocks of cheese than those that were at the current hole.
Given n, k, and the number of blocks of cheese at each grid location, compute the maximum amount of cheese FatMouse can eat before being unable to move.
Input
There are several test cases. Each test case consists of
a line containing two integers between 1 and 100: n and k
n lines, each with n numbers: the first line contains the number of blocks of cheese at locations (0,0) (0,1) ... (0,n-1); the next line contains the number of blocks of cheese at locations (1,0), (1,1), ... (1,n-1), and so on.
The input ends with a pair of -1's.
a line containing two integers between 1 and 100: n and k
n lines, each with n numbers: the first line contains the number of blocks of cheese at locations (0,0) (0,1) ... (0,n-1); the next line contains the number of blocks of cheese at locations (1,0), (1,1), ... (1,n-1), and so on.
The input ends with a pair of -1's.
Output
For each test case output in a line the single integer giving the number of blocks of cheese collected.
Sample Input
3 1
1 2 5
10 11 6
12 12 7
-1 -1
Sample Output
37
本题使用了一个dp数组来记录所走过的路径，通过记忆化的方法来优化代码，是一种高效的方法。
不过要注意本题有个值得注意的地方：
int xx=x+dirx[j]*i; int yy=y+diry[j]*i;
这里的i表示走了多少步，其中（1<=i<=k）,因为题目说最多走k步
1 #include<iostream> 2 #include<cstdio> 3 #include<cstring> 4 using namespace std; 5 #define N 106 6 int mp[N][N]; 7 int dp[N][N]; 8 int n,k; 9 int dirx[]={0,0,-1,1}; 10 int diry[]={-1,1,0,0}; 11 int dfs(int x,int y) 12 { 13 if(dp[x][y]!=0) return dp[x][y]; 14 int maxn=0; 15 for(int i=1;i<=k;i++) 16 for(int j=0;j<4;j++) 17 { 18 int xx=x+dirx[j]*i; 19 int yy=y+diry[j]*i; 20 if(xx<0 || xx>=n || yy<0 || yy>=n) 21 continue; 22 if(mp[xx][yy]<=mp[x][y]) 23 continue; 24 int cnt=dfs(xx,yy); 25 if(maxn<cnt) 26 maxn=cnt; 27 28 } 29 dp[x][y]=mp[x][y]+maxn; 30 return dp[x][y]; 31 } 32 int main() 33 { 34 while(scanf("%d%d",&n,&k)==2 && n+k!=-2) 35 { 36 37 for(int i=0;i<n;i++) 38 { 39 for(int j=0;j<n;j++) 40 { 41 scanf("%d",&mp[i][j]); 42 } 43 } 44 memset(dp,0,sizeof(dp)); 45 int ans=dfs(0,0); 46 printf("%d ",ans); 47 } 48 return 0; 49 }