POJ-3176 Cow Bowling【基础DP】

刺骨的言语ヽ痛彻心扉 2022-09-24 06:25 134阅读 0赞

Cow Bowling

<table> 
 <tbody> 
  <tr> 
   <td><strong>Time Limit:</strong>&nbsp;1000MS</td> 
   <td>&nbsp;</td> 
   <td><strong>Memory Limit:</strong>&nbsp;65536K</td> 
  </tr> 
  <tr> 
   <td><strong>Total Submissions:</strong>&nbsp;17284</td> 
   <td>&nbsp;</td> 
   <td><strong>Accepted:</strong>&nbsp;11538</td> 
  </tr> 
 </tbody> 
</table>

Description

The cows don't use actual bowling balls when they go bowling. They each take a number (in the range 0..99), though, and line up in a standard bowling-pin-like triangle like this:

7
    
    
    
            3   8
    
    
    
          8   1   0
    
    
    
        2   7   4   4
    
    
    
      4   5   2   6   5

Then the other cows traverse the triangle starting from its tip and moving "down" to one of the two diagonally adjacent cows until the "bottom" row is reached. The cow's score is the sum of the numbers of the cows visited along the way. The cow with the highest score wins that frame.  
  
Given a triangle with N (1 <= N <= 350) rows, determine the highest possible sum achievable.

Input

Line 1: A single integer, N  
  
Lines 2..N+1: Line i+1 contains i space-separated integers that represent row i of the triangle.

Output

Line 1: The largest sum achievable using the traversal rules

Sample Input

5
    7
    3 8
    8 1 0
    2 7 4 4
    4 5 2 6 5

Sample Output

Hint

Explanation of the sample:

7
    
             *
    
            3   8
    
           *
    
          8   1   0
    
           *
    
        2   7   4   4
    
           *
    
      4   5   2   6   5

The highest score is achievable by traversing the cows as shown above.

#include<stdio.h>
    #include<string.h>
    #include<algorithm>
    
    using namespace std;
    int map[400][400];
    int wcn[400][400];
    int main()
    {
    	int n;
    	while(scanf("%d",&n)!=EOF)
    	{
    		int wc=1;
    		for(int i=1;i<=n;i++)
    		{
    			for(int j=1;j<=wc;j++)
    			{
    				int nn;
    				scanf("%d",&nn);
    				map[i][j]=wcn[i][j]=nn;
    			}
    			wc++;
    		}
    		wc=1;
    		for(int i=1;i<n;i++){
    			for(int j=1;j<=wc;j++){
    				if(j==1){
    					map[i+1][j]+=map[i][j];
    					map[i+1][j+1]+=map[i][j];
    				}
    				else if(j==wc&&wc!=1){
    					map[i+1][j+1]+=map[i][j];
    					if((wcn[i+1][j]+map[i][j])>map[i+1][j]){
    						map[i+1][j]=wcn[i+1][j]+map[i][j];
    					}
    				}
    				else{
    					if((wcn[i+1][j]+map[i][j])>map[i+1][j]){
    						map[i+1][j]=wcn[i+1][j]+map[i][j];
    					}
    					if((wcn[i+1][j+1]+map[i][j])>map[i+1][j+1]){
    						map[i+1][j+1]=wcn[i+1][j+1]+map[i][j];
    					}
    				}
    			}
    			wc++;
    		}
    		int ans=0;
    		for(int i=1;i<=n;i++)
    		{
    			if(map[n][i]>ans)
    			{
    				ans=map[n][i];
    			}
    		}
    		printf("%d\n",ans);
    	}
    	return 0;
    }