UVA - 10285 Longest Run on a Snowboard

从任意点出发，走出一条严格递减的序列出来，看最长序列是多长

#include<iostream>
#include<map>
#include<string>
#include<cstring>
#include<cstdio>
#include<cstdlib>
#include<cmath>
#include<queue>
#include<vector>
#include<algorithm>
using namespace std;
int a[110][110];
int dp[110][110];
int dx[4]={0,0,-1,1};
int dy[4]={-1,1,0,0};
int r,c;
int dfs(int x,int y)
{
int i,tx,ty;
if(dp[x][y]!=0)
return dp[x][y];
dp[x][y]=1;
for(i=0;i<4;i++)
{
tx=x+dx[i];
ty=y+dy[i];
if(tx>-1&&tx<r&&ty>-1&&ty<c&&a[tx][ty]<a[x][y])
dp[x][y]=max(dp[x][y],dfs(tx,ty)+1);
}
return dp[x][y];
}
int main()
{
string s;
int T,i,j,ans;
cin>>T;
while(T--)
{
cin>>s>>r>>c;
for(i=0;i<r;i++)
for(j=0;j<c;j++)
cin>>a[i][j];
memset(dp,0,sizeof(dp));
ans=0;
for(i=0;i<r;i++)
for(j=0;j<c;j++)
ans=max(ans,dfs(i,j));
cout<<s<<": "<<ans<<endl;
}
return 0;
}

Longest Run on a Snowboard

Time Limit: 3000MS

Memory Limit: Unknown

64bit IO Format: %lld & %llu

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Description





Problem C
Longest Run on a Snowboard
Input: standard input
Output: standard output
Time Limit: 5 seconds
Memory Limit: 32MB
 

Michael likes snowboarding. That's not very surprising, since snowboarding is really great. The bad thing is that in order to gain speed, the area must slide downwards. Another disadvantage is that when you've reached the bottom of the hill you have to walk
up again or wait for the ski-lift.

Michael would like to know how long the longest run in an area is. That area is given by a grid of numbers, defining the heights at those points. Look at this example:

 1  2  3  4 5 

16 17 18 19 6

15 24 25 20 7

14 23 2221 8 

13 1211 10 9 

One can slide down from one point to a connected other one if and only if the height decreases. One point is connected to another if it's at left, at right, above or below it. In the sample map, a possible slide would be
24-17-16-1 (start at 24, end at 1). Of course if you would go
25-24-23-...-3-2-1, it would be a much longer run. In fact, it's the longest possible.

Input

The first line contains the number of test cases N. Each test case starts with a line containing the name (it's a single string), the number of rows
R and the number of columns C. After that follow
R lines with C numbers each, defining the heights.
R and C won't be bigger than 100, N not bigger than
15 and the heights are always in the range from 0 to
100.

For each test case, print a line containing the name of the area, a colon, a space and the length of the longest run one can slide down in that area.

Sample Input 

2

Feldberg 10 5

56 14 51 58 88

26 94 24 39 41

24 16 8 51 51

76 7277 43 10 

38 50 59 84 81

5 23 37 71 77

96 10 93 53 82

94 15 96 69 9

74 0 6238 96 

37 54 55 8238 

Spiral 5 5

1 23 4 5 

16 17 18 19 6

15 24 25 20 7

14 23 2221 8 

13 1211 10 9 

 

Sample Output

Feldberg: 7

Spiral: 25

(Math Lovers’ Contest, Problem Setter: Stefan Pochmann)

 

Source

Root :: AOAPC I: Beginning Algorithm Contests (Rujia Liu) ::
Volume 5. Dynamic Programming

Root :: Competitive Programming: Increasing the Lower Bound of Programming Contests (Steven & Felix Halim) :: Chapter 3. Problem Solving Paradigms :: Complete Search ::

Recursive Backtracking

Root :: Competitive Programming 2: This increases the lower bound of Programming Contests. Again (Steven & Felix Halim) :: Graph :: Special Graph (Directed Acyclic Graph) ::

Single-Source Shortest/Longest Paths on DAG

Root :: AOAPC II: Beginning Algorithm Contests (Second Edition) (Rujia Liu) :: Chapter 9. Dynamic Programming ::

Exercises

Root :: Competitive Programming 3: The New Lower Bound of Programming Contests (Steven & Felix Halim) :: Graph :: Special Graph (Directed Acyclic Graph) ::

Single-Source Shortest/Longest Paths on DAG

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