How Can I Solve My Dynamic Programming Problem? - c++

Question

Here is my code:
#include<bits/stdc++.h>
using namespace std;
typedef long long int lli;
#define M 1000000007
#define INF 1000000007
typedef pair<lli,lli> ll;
#define mem(a,x) memset(a,x,sizeof(a))
lli n,k,m;
lli dist[507][507];
lli path1[207][207];
vector<int> v2(1005,1);
vector<double> v;
lli x,y,c,z,t,q,u,d,a1,b;
struct edge
{
lli a,b,cost;
};
/*void djkstra(int x,vector<ll> v[])
{
mem(vis,0);
dist[x]=0;
s2.insert({0,x});
while(!s2.empty())
{
ll p=*s2.begin();
s2.erase(s2.begin());
x=p.second;
if(vis[x])
continue;
vis[x]=1;
for(int j=0;j<v[x].size();j++)
{
if(dist[v[x][j].second]>dist[x]+v[x][j].first)
{
dist[v[x][j].second]=dist[x]+v[x][j].first;
s2.insert({dist[v[x][j].second],v[x][j].second});
a[v[x][j].second]=x;
}
}
}
}*/
lli parent[100007];
lli find(lli a)
{
return a==parent[a]?a:parent[a]=find(parent[a]);
}
void dset(lli n)
{
for(int j=0;j<=n;j++)
parent[j]=j;
}
void unio(lli a,lli b,lli rank[])
{
if(rank[find(a)]>rank[find(b)])
parent[find(b)]=find(a);
else if(rank[find(b)]>rank[find(a)])
parent[find(a)]=find(b);
else
{
parent[find(a)]=find(b);
rank[find(b)]++;
}
}
bool check(lli a)
{
if((a1*a*m+b*(a-1)+d)>=x)
return true;
return false;
}
/*bool valid(int i,int x)
{
for(int j=1;j<x;j++)
{
if((abs(b[j-1]-i)==abs(j-x))||(i==b[j-1])||(j==x))
return false;
}
return true;
}*/
lli p[10007];
lli dp[301][301][301];
map<ll,ll> pat;
map<ll,lli> p2;
lli pr[200007],we[200007];
lli a[100005];
map<lli,lli> m4;
vector<int> v4;
int f=0;
lli tot=1;
lli vis[1001][1001];
lli p1;
lli s[10001];
lli n1;
lli solve(lli n,lli i,lli c)
{
//cout<<n<<" "<<i<<" "<<a[i]<<" "<<dp[n][i]<<endl;
if(i>n1)
return 0;
if(c==0&&n>0)
return 0;
if(c==0&&n==0)
return 1;
if(n<0)
return 0;
if(dp[n][i][c]!=-1)
return dp[n][i][c];
dp[n][i][c]=solve(n-i,i,c-1);
dp[n][i][c]+=solve(n,i+1,c);
return dp[n][i][c];
}
int main()
{
while(1)
{
string s="\0";
getline(cin,s);
if(s.size()==0)
return 0;
string d[3];
d[0]="\0";
d[1]="\0";
d[2]="\0";
int c=0;
for(int i=0;i<=300;i++)
{
for(int j=1;j<=300;j++)
{
for(int k=1;k<=300;k++)
dp[i][j][k]=-1;
}
}
for(int j=0;j<s.length();j++)
{
if(s[j]!=' ')
d[c]+=s[j];
else
c++;
}
int f;
stringstream ss(d[0]);
ss>>f;
n1=f;
lli d1=0;
for(int i=1;i<=f;i++)
d1+=solve(f,1,i);
for(int i=0;i<=300;i++)
{
for(int j=0;j<=300;j++)
dp[0][i][j]=1;
}
lli sum[f+1];
mem(sum,0);
sum[0]=1;
for(int i=1;i<=f;i++)
{
if(i==1)
sum[i]=dp[f][1][i];
else
sum[i]=sum[i-1]+dp[f][1][i];
}
if(c==0)
{
if(f!=0)
cout<<d1<<endl;
else
cout<<1<<endl;
}
else if(c==1)
{
int f1;
stringstream ss1(d[1]);
ss1>>f1;
if(f1>f)
f1=f;
cout<<sum[f1]<<endl;
}
else
{
int f1,f2;
stringstream ss1(d[1]);
ss1>>f1;
stringstream ss2(d[2]);
ss2>>f2;
if(f1>f)
cout<<0<<endl;
else
{
if(f2>f)
f2=f;
cout<<sum[f2]-sum[f1]+dp[f][1][f1]<<endl;
}
}
}
}
In the following function:
lli solve(lli n,lli i,lli c)
My solution is O(N^3), and it should pass the test cases (N=300), but still time limit exceeds for it.
How can I solve this problem?
Here is the problem link.

Answer 1

Ok so the point the dynamic programming is being able to reuse what was already done.
So how to reuse your code?
Here's my idea:
let say the total amount is 6$ and we know we have a total of 3 pieces maximum totalize that amount. You can begin to try by beginning with by finding the way to make a total of 1$, than 2$, 3$, .. alway reusing what you done before.
Example
1 $ total
only way 1x1$ (keep that in memory)
2 $ total
-decompose in all possible 2 pieces you can add: 1+1, 2
-to find other possibilities, reuse what you done before recursivly (the recursion at this level stops after only the first iteration because 1$ is the minimum dollar value)
-keep that in memory
... (continue like that with 3 $ total, 4 $ total, 5$ total ...)
6$ total
-decompose in all possible 2 pieces you can add: 6, 1+5, 2+4 3+3 (always (n intDiv 2) +1 possibilities) possibilites
-to find other possibilities, reuse what you done before recursivly:
example: for the 3+3 possibility, go look at all the possibilities found at 3$ total to find all possibilities.
- Remove all possibilites that used too much pieces.
You finished by finding all possibilities as an answer: 1+1+4, 1+2+3, 3+3 and 2+2+2.
Hope it helps :)