Merge pull request ashutosh97#144 from rohitsh16/master

Added prime_subsequence

Author: ashutosh97

Prime_subsequence/question.txt

@@ -0,0 +1,10 @@
+
+Given a sequence of prime numbers A1,A2,…,AN. This sequence has exactly 2N subsequences.
+A subsequence of A is good if it does not contain any two identical numbers; in particular, the empty sequence is good.
+
+You to find the number of good subsequences which contain at most K numbers.
+This number could be very large, so compute it modulo 1,000,000,007.
+
+Constraints:
+1≤K≤N≤105
+2≤Ai≤8,000 for each valid i

Prime_subsequence/solution.cpp

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+#include<bits/stdc++.h>
+using namespace std;
+int main(){
+    ios_base::sync_with_stdio(false);
+    int n,k;cin>>n>>k;
+    int a[n];long long int mod=1000000007;
+    int max=0;
+    for(int i=0;i<n;i++){
+        cin>>a[i];
+        if(a[i]>max)
+            max=a[i];
+    }
+    long int f[max+1];
+    memset(f,0,sizeof(f));
+    for(int i=0;i<n;i++)
+        f[a[i]]++;
+    vector<long int>v;
+    for(int i=0;i<=max;i++)
+        if(f[i])
+            v.push_back(f[i]);
+    long int l=v.size();
+    k=k>l?l:k;
+    long int dpans[k+1][l],val;
+    val=v[0]+1;
+    memset(dpans,0,sizeof(dpans));
+    dpans[0][0]=1;
+    dpans[1][0]=val;
+    long int total=0;
+    for(int i=2;i<=k;i++)
+    	dpans[i][0]=val;
+    for(int i=1;i<l;i++)
+    	dpans[0][i]=1;
+    for(int i=1;i<l;i++)
+    	for(int j=1;j<=k;j++){
+    		total=((v[i]%mod)*(dpans[j-1][i-1])%mod)%mod;
+    		dpans[j][i]=(((dpans[j][i-1])%mod)+(total%mod))%mod;
+    	}
+    total=(dpans[k][l-1])%mod;
+    cout<<total<<endl;
+    return 0;
+}