gs gs122 Number Theory - Generating Partitions - Quiz No.1
gs gs122 Data Communication and Computer Network Quiz
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Question 1: What is meant by integer partition?
representing an integer as sum of positive and negative real numbers
representing an integer as sum of positive and negative integers
representing an integer as sum of positive integers
representing an integer as sum of positive real numbers
Question 3: What is meant by number theory?
study of integers
study of complex numbers
numerology
theory of origination of mathematics
Question 4: Which of the following is true according to Ramanujan’s congruence?
No. of partitions are divisible by 5 for a number 3 more than a multiple of 5
No. of partitions are divisible by 5 for a number 4 more than a multiple of 5
No. of partitions are divisible by 5 for a number 2 more than a multiple of 5
No. of partitions are divisible by 5 for a number 1 more than a multiple of 5
Question 8: What is the approach implemented in the following code?
#include<iostream> using namespace std; void printArray(int p[], int n) { for (int i = 0; i <= n-1; i++) cout << p[i] << " "; cout << endl; } void func1(int n) { int p[n]; int k = 0; p[k] = n; while (true) { printArray(p, k+1); int rem_val = 0; while (k >= 0 && p[k] == 1) { rem_val += p[k]; k--; } if (k < 0) return; p[k]--; rem_val++; while (rem_val > p[k]) { p[k+1] = p[k]; rem_val = rem_val - p[k]; k++; } p[k+1] = rem_val; k++; } } int main() { int n; cin>>n; func1(n); return 0; }
greedy approach
dynamic programming
recursion(divide and conquer)
backtracking
Question 9: What will be the output of the following code?
#include<iostream> using namespace std; int list[200]; void func(int n, int m = 0) { int i; if(n == 0) { for(i = 0; i < m; ++i) printf("%d ", list[i]); printf("\n"); return; } for(i = n; i > 0; --i) { if(m == 0 || i <= list[m - 1]) { list[m] = i; func(n - i, m + 1); } } } int main() { int n=3; func(n,0); return 0; } 3 2 1 1 1 1 1 1 1 2 1 3 1 1 1 1 2 3 3 1 2 1 1 1
Question 10: Which of the following correctly represents the code to print partitions of a number?
#include<iostream> using namespace std; int print[200]; void partitn(int n,int k,int idx) { if(n==0) { for(int i=0;i<idx;i++) cout<<print[i]<<" "; cout<<endl; return ; } for(int i=k;i>0;i--) { if(i>n)continue; print[idx]=i; partitn(n-i,i,idx+1); } } int main() { int n; cin>>n; partitn(n,n,0); return 0; } #include<iostream> using namespace std; int print[200]; void partitn(int n,int k,int idx) { if(n==0) { for(int i=0;i<idx;i++) cout<<print[i]<<" "; cout<<endl; return ; } for(int i=k;i>0;i--) { if(i>n)continue; print[idx]=i; partitn(n-i,i,idx+1); } } int main() { int n; cin>>n; partitn(n,0,0); return 0; } #include<iostream> using namespace std; int print[200]; void partitn(int n,int k,int idx) { if(n==0) { for(int i=0;i<idx;i++) cout<<print[i]<<" "; cout<<endl; return ; } for(int i=k;i>0;i--) { print[idx]=i; partitn(n-i,i,idx+1); } } int main() { int n; cin>>n; partitn(n,0,0); return 0; } #include<iostream> using namespace std; int print[200]; void partitn(int n,int k,int idx) { if(n==0) { for(int i=0;i<idx;i++) cout<<print[i]<<" "; cout<<endl; return ; } for(int i=k;i>0;i--) { print[idx]=i; partitn(n-i,i,idx+1); } } int main() { int n; cin>>n; partitn(n,n,0); return 0; } Online Quizzes of gs122 Data Communication and Computer Network
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