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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

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Problem C

Longest Run on a Snowboard

Input: standard input

Output: standard output

Time Limit: 5 seconds

Memory Limit: 32 MB

 

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 22 21 8 
13 12 11 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 be24-17-16-1 (start at 24, end at 1). Of course if you would go25-24-23-...-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 rowsR and the number of columns C. After that followR lines with C numbers each, defining the heights.R and C won‘t be bigger than 100, N not bigger than15 and the heights are always in the range from 0 to100.

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 72 77 43 10 
38 50 59 84 81 
5 23 37 71 77 
96 10 93 53 82 
94 15 96 69 9 
74 0 62 38 96 
37 54 55 82 38 
Spiral 5 5 
1 2 3 4 5 
16 17 18 19 6 
15 24 25 20 7 
14 23 22 21 8 
13 12 11 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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UVA - 10285 Longest Run on a Snowboard