Recursion Practice.md

A. Print from 1 to N

You will be given a number N. Print from 1 to N in separate lines using recursion.

Input You will be given a number N ( 1 ≤ N ≤ 10³ )

Output Print N lines contain number from 1 to N.

Example

5

1
2
3
4
5

B. Print from N to 1

You will be given a number N. Print from N to 1 separated by a single space using recursion.

Input You will be given a number N ( 1 ≤ N ≤ 10³ )

Output Print from N to 1 separated by a single space.

Example

4

4 3 2 1

C. Factorial

You will be given a number N. Using recursion get the factorial of N.

Input You will be given a number N ( 1 ≤ N ≤ 20 )

Output Print the factorial of the number N.

Example

5

120

D. Max number

You will be given an array of size N. Using recursion get the maximum value in this array.

Input You will be given a number N ( 1 ≤ N ≤ 10³ ). Next line will contain N numbers ( x_i ≤ |10⁹| )

Output print a maximum value in this array.

Example

5
1 -3 5 4 -6

5

E. Combination

You will be given two number n and r. Your are asked to print the value nCr using recursion.

Input The input consists of two numbers n and r ( 0 ≤ r, n ≤ 30 ).

Output Print the value _nC_r.

Examples

4 2

6

3 3

1

F. GCD

You will be given two numbers X and Y. You are asked to print the Greatest Common Divisor between X and Y using recursion.

Input Input will consist of two integers, X and Y ( -10⁹ ≤ A, B ≤ 10⁹ ) in one line. The input will not contain 2 zeros.

Output Print the GCD between X and Y.

Examples

4 16

4

5 13

1

G. Base Conversion

In this problem, you need to convert a decimal number into a binary number.

Input The first line of input contains an integer, T, which denotes the number of input you have to handle. Each of the next T lines contains an integer N (0<N<10000000).

Output For each input number you have to print the converted binary number.

Example

2
10
3

1010
11

H. Count Vowels

In this problem, you just need to count the number of vowels contain in an input string using recursion.

Input Input file contains a single line of string S. 1< |S| <200

Output Print the number of vowels contained in the input string.

Example

Data Structure Lab

6

I. Fibonacci

Given an integer N, print the value of N_th Fibonacci number using recursion. Note that, F₀ = 0 and F₁ = 1. Also, F_n = F_n - 1 + F_n - 2.

Input Input will consist of an integer, N (0 <= N <= 30) in one line.

Output Output will consist of 1 line: Value of Nth Fibonacci.

Example

5

5

J. Sum of a Matrix

Given two same size matrices find its summation.

Input Input will consist of two integers R and C, (0 < R, C <101). Next there will be R rows each with C integers A_ijs (-100 < A_ijs < 100), the first matrix. Next there will be R rows each with C integers B_ij (-100 < B_ij < 100), the second matrix.

Output Output will consist of Result matrix.

Example

2 3
1 2 3
4 5 6
1 3 5
7 9 11

2 5 8
11 14 17

K. Multiplication of Matrices

Given two matrices find its multiplication using recursion.

Input Input will consist of two integers R_a and C_a, (0 < R_a, C_as <101). Next there will be R_a rows each with C_a integers A_ij (-100 < A_ij < 100), the first matrix. Next two integers R_b and C_b, (0 < R_b, C_b <101). Next there will be R_b rows each with C_b integers B_ij (-100 < B_ij < 100), the first matrix. You can always assume that C_a is equal to R_b.

Output Output will consist of Result matrix.

2 2
1 2
2 1
2 2
3 4
4 3

11 10
10 11

L. Print Even Indices

Given an integer N, and N integers, print the numbers in even indices in reverse order using recursion. Assume 0-based indexing.

Input Input will consist of an integer, N (1 <= N <= 10³) in the first line. The next line contains N integers Xi (Xi <= |10⁹|).

Output The output will consist of numbers in even indices in reverse order

Examples

4
1 4 2 7

2 1

7
1 5 8 2 3 9 11

11 3 8 1

M. Sum of an Array using Recursion

Given an integer N, and N integers, find the sum of the N integers using recursion.

Input Input will consist of an integer, N (1 <= N <= 10³) in the first line. The next line contains N integers X_i (X_i <= |10⁹|).

Output The output will consist of 1 line: Value of sum.

Examples

4
1 4 2 7

14

4
5 5 5 5

20

N. Print Digits using Recursion

In this problem, you need to separate and print the digits of a given input number using recursion. You are not allowed to input the integer number as a string.

Input The first line of input contains an integer, T, which denotes the number of input you have to handle. Each of the next T lines contains an integer N (0<=N<=10000000).

Output For each input number, you have to print the digits separated by space.

Example

3
121
39
123456

1 2 1
3 9
1 2 3 4 5 6