10520 - Determine it

[Alexander Kozlov]

Dear friends!
I have just got AC for this problem.
I consider j >= 1. That is 1 <= i,j <= n and

.......................| max(aik + ank),...j > 1
aij = ........ + <...................................i >= j
.......................| 0, .......................j = 1

[Larry]

Can you post some examples?

[Lars Hellsten]

Maybe he means that the j = 0 (j > 0) condition in the problem statement should actually be j = 1 (j > 1). You'll never actually consider j = 0 because k always starts at 1. If you implement this in the obvious way, your loop condition will probably do this check implicitly though.

Anyway, this problem is straightforward, aside from the not-quite-obvious-without-testing fact answers can be larger than 2^32.

[Larry]

I used long long and got WA, is this enough or do I need bigint?

[Alexander Kozlov]

Input:

5 10
4 1
6 13
10 36
11 243
14 67
15 198
16 325
17 423
19 499

Output:

1140
42
3770
313416
4728294
13721734
87589260
308839050
859374414
4578345958

[Larry]

Thanks. Stupid mistake, I changed my stuff from int to long long and didn't remember to change one of the intermediate variables..

[shihabbd81]

the coditions should be j>1 and j=1 not j>0 and j=0
it was my mistake.
sorry.

Shihab Uddin
problemsetter of 10520

[Examiner]

Then the formula implies a[n, 1] is always 0; this contradicts the input, unless the second number is also 0.

[asif_rahman0]

can someone check my following Input/output.
my code gives the following answer:

Code: Select all

Input:
1 2
1 1
1 9
1 15
15 1
9 1
2 1
10 10
13 6
15 105
15 350
15 450
19 450
17 319
17 400
11 411
17 411
19 19

Output:
2
1
9
15
442370
3842
4
87060
565260
46448850
154829500
199066500
4128768900
648086142
812647200
7997238
834994998
174325798

Output is now corrected.

rabbi

[mf]

I get a different output only for 19 450 -- 4128768900.

[asif_rahman0]

thnx mf.
Got accepted.
It should be 64 bit data type.

[Martin Macko]

thnx mf.
Got accepted.
It should be 64 bit data type.

Please, fix the output to the 19 450 case in your very first post in this thread, so people won't get confused by the incorrect output.

[mhayter1]

Hi, I've past all test cases on the forum, and I use a 64 bit data type without success. Could anyone help?

Code: Select all

#include<iostream>
#include<algorithm>
using namespace std;

const unsigned long long SIZE=500;
unsigned long long memo[SIZE][SIZE];
bool found[SIZE][SIZE];
unsigned long long n;

inline void update(unsigned long long i,unsigned long long j,unsigned long long v)
{
    memo[i][j]=v;
    found[i][j]=true;
}
inline unsigned long long  mx(unsigned long long &a,unsigned long long &b)
{
    if(a>=b)return a;
    else return b;
}

unsigned long long zzz;

unsigned long long a(unsigned long long i,unsigned long long j)
{
    if(found[i][j]) return memo[i][j];
    if(i>=j)
    {
        unsigned long long s1=0;
        unsigned long long s2=0;
        if(i<n)
        {
            for(unsigned long long k=i+1;k<=n;k++)
            {
                unsigned long long ak1=a(k,1);
                update(k,1,ak1);
                
                unsigned long long akj=a(k,j);
                update(k,j,akj);
                
                unsigned long long sum=ak1+akj;
                s1=mx(s1,sum);
            }
        }
        else if(i==n)
        {
            s1=0;
        }
        if(j>1)
        {
            for(unsigned long long k=1;k<j;k++)
            {
                unsigned long long aik=a(i,k);
                update(i,k,aik);
                
                unsigned long long ank=a(n,k);
                update(n,k,ank);
                
                unsigned long long sum=aik+ank;
                s2=mx(s2,sum);
            }
        }
        else if(j==1)
        {
            s2=0;
        }
        unsigned long long aij=s1+s2;
        update(i,j,aij);
        return memo[i][j];
    }
    else
    {
        unsigned long long s1=0;
        for(unsigned long long k=i;k<j;k++)
        {
            unsigned long long aik=a(i,k);
            update(i,k,aik);
            
            unsigned long long akonej=a(k+1,j);
            update(k+1,j,akonej);
            
            unsigned long long sum=aik+akonej;
            s1=mx(s1,sum);
        }
        update(i,j,s1);
        return memo[i][j];
    }
}
        
int main()
{
    while(cin>>n>>memo[n][1])
    {
        memset(found,0,sizeof(found));
        found[n][1]=true;
        cout<<(unsigned long long)a(1,n)<<endl;
    }
    unsigned long long z;
    cin>>z;
    return 0;
}
    

[smilitude]

i checked your program in my pc with all possible inputs. and after comparing with my ac program's output, my judge program printed

Code: Select all

Total Case 9481; passed 9481; failed 0

which astonished me! i am not sure why its not working in judge.
i used devcpp, and it works fine in my pc.

[andmej]

I solved this using top-down dynamic programming (memoization). I was wondering, is it possible to solve this in a bottom-up approach? Thanks.