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## Data Structure Questions and Answers-Catalan Number using Dynamic Programming

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Question 1 [CLICK ON ANY CHOICE TO KNOW MCQ multiple objective type questions RIGHT ANSWER] |

Which of the following is NOT a Catalan number?

1 | |

5 | |

14 | |

43 |

Question 1 Explanation:

Catalan numbers are given by: (2n!)/((n+1)!n!).

For n = 0, we get C0 = 1.

For n = 3, we get C3 = 5.

For n = 4, we get C4 = 14.

For n = 5, we get C3 = 42.

Question 2 [CLICK ON ANY CHOICE TO KNOW MCQ multiple objective type questions RIGHT ANSWER] |

Which of the following numbers is the 6th Catalan number?

14 | |

429 | |

132 | |

None of the mentioned |

Question 2 Explanation:

Catalan numbers are given by: (2n!)/((n+1)!n!).

First Catalan number is given by n = 0.

So the 6th Catalan number will be given by n = 5, which is 42.

Question 3 [CLICK ON ANY CHOICE TO KNOW MCQ multiple objective type questions RIGHT ANSWER] |

Which of the following is/are applications of Catalan numbers?

Counting the number of Dyck words | |

Counting the number of expressions containing n pairs of parenthesis | |

Counting the number of ways in which a convex polygon can be cut into triangles by connecting vertices with straight lines | |

All of the mentioned |

Question 3 Explanation:

Catalan numbers are used in all of the above applications.

Question 4 [CLICK ON ANY CHOICE TO KNOW MCQ multiple objective type questions RIGHT ANSWER] |

Which of the following methods can be used to find the nth Catalan number?

Recursion | |

Binomial coefficients | |

Dynamic programming | |

All of the mentioned |

Question 4 Explanation:

All of the mentioned methods can be used to find the nth Catalan number.

Question 5 [CLICK ON ANY CHOICE TO KNOW MCQ multiple objective type questions RIGHT ANSWER] |

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?

arr[i] = arr[j] * arr[k]; | |

arr[j] += arr[i] * arr[k]; | |

arr[i] += arr[j] * arr[k]. | |

arr[j] = arr[i] * arr[k]; |

Question 5 Explanation:

The line arr[i] += arr[j] * arr[k] reflects the recursive formula Cn = ∑Ci*C(n-i).

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