Data Structure Questions and Answers – Catalan Number using Dynamic Programming

This set of Data Structure Multiple Choice Questions & Answers focuses on “Catalan Number using Dynamic Programming”.

1. Which of the following is NOT a Catalan number?
a) 1
b) 5
c) 14
d) 43
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2. Which of the following numbers is the 6th Catalan number?
a) 14
b) 429
c) 132
d) 42
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3. Which of the following is not an application of Catalan Numbers?
a) Counting the number of Dyck words
b) Counting the number of expressions containing n pairs of parenthesis
c) Counting the number of ways in which a convex polygon can be cut into triangles by connecting vertices with straight lines
d) Creation of head and tail for a given number of tosses
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4. Which of the following methods can be used to find the nth Catalan number?
a) Recursion
b) Binomial coefficients
c) Dynamic programming
d) Recursion, Binomial Coefficients, Dynamic programming
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5. The recursive formula for Catalan number is given by Cn = ∑Ci*C(n-i).
Consider the following dynamic programming implementation for Catalan numbers:

#include<stdio.h>
int cat_number(int n)
{
     int i,j,arr[n],k;
     arr[0] = 1;
     for(i = 1; i < n; i++)
     {
         arr[i] = 0;
         for(j = 0,k = i - 1; j < i; j++,k--)
           ______________________;
     }
     return arr[n-1];
 
}
int main()
{
     int ans, n = 8;
     ans = cat_number(n);
     printf("%d\n",ans);
     return 0;
}

Which of the following lines completes the above code?
a) arr[i] = arr[j] * arr[k];
b) arr[j] += arr[i] * arr[k];
c) arr[i] += arr[j] * arr[k].
d) arr[j] = arr[i] * arr[k];
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6. Which of the following implementations of Catalan numbers has the smallest time complexity?
a) Dynamic programming
b) Binomial coefficients
c) Recursion
d) All have equal time complexity
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7. What is the output of the following code?

#include<stdio.h>
int cat_number(int n)
{
     int i,j,arr[n],k;
     arr[0] = 1;
     for(i = 1; i < n; i++)
     {
         arr[i] = 0;
         for(j = 0,k = i - 1; j < i; j++,k--)
         arr[i] += arr[j] * arr[k];
     }
     return arr[n-1];
}
int main()
{
     int ans, n = 8;
     ans = cat_number(n);
     printf("%d\n",ans);
     return 0;
}

a) 42
b) 132
c) 429
d) 1430
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8. Which of the following implementations of Catalan numbers has the largest space complexity(Don’t consider the stack space)?
a) Dynamic programming
b) Binomial coefficients
c) Recursion
d) All have equal space complexities
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9. What will be the value stored in arr[5] when the following code is executed?

#include<stdio.h>
int cat_number(int n)
{
     int i,j,arr[n],k;
     arr[0] = 1;
     for(i = 1; i < n; i++)
     {
         arr[i] = 0;
         for(j = 0,k = i - 1; j < i; j++,k--)
          arr[i] += arr[j] * arr[k];
     }
     return arr[n-1];
}
int main()
{
     int ans, n = 10;
     ans = cat_number(n);
     printf("%d\n",ans);
     return 0;
}

a) 14
b) 42
c) 132
d) 429
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10. Which of the following errors will occur when the below code is executed?

#include<stdio.h>
int cat_number(int n)
{
     int i,j,arr[n],k;
     arr[0] = 1;
     for(i = 1; i < n; i++)
     {
         arr[i] = 0;
         for(j = 0,k = i - 1; j < i; j++,k--)
           arr[i] += arr[j] * arr[k];
     }
     return arr[n-1];
}
int main()
{
     int ans, n = 100;
     ans = cat_number(n);
     printf("%d\n",ans);
     return 0;
}

a) Segmentation fault
b) Array size too large
c) Integer value out of range
d) Array index out of range
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