[ASSIGNMENT] 👉👉👉 A Man On Stairs of n Steps . 👤✏🔆

Question

A man can jump 1 or 2 steps at a time , find number of ways in which the man can climb n number of steps ?

/*
example ::: input :: 3
output :: 3 // because 3 ways
1st way) 3 times 1 step (1,1,1)
2nd way)1 time 2 steps together & then 1 step more(2,1)
3rd way) 1 step & then 1 time 2 steps together(1,2)
Remember man can take 1 or 2 steps at a time
*/

//level :: easy & interesting
//simple approach is welcome , with some explanation

HAPPY CODING ☺👍

Answer 1

//i can't mark more than 1 answer as best
https://code.sololearn.com/clieRlKMyz21/?ref=app
https://code.sololearn.com/cQwaDV55vIxl/?ref=app
https://code.sololearn.com/c621RzPeWuMn/?ref=app
https://code.sololearn.com/WC9QbGHc15Qk/?ref=app

Answer 2

After some observations,

if steps = 1: ways = 1
if steps = 2: ways = 2
if steps = 3: ways = 3
if steps = 4: ways = 5.....

And finally, I ended up with Fibonacci sequence
1, 2, 3, 5, 8, 13, 21.....

https://code.sololearn.com/cX917vOg9Mrl/?ref=app

Answer 3

thnx 😊😊 @river,bool1

Answer 4

Thank you for the challenge 👍
Here's my try :
https://code.sololearn.com/clieRlKMyz21/?ref=app

Answer 5

@tai
welcome to Sl

https://www.sololearn.com/Discuss/595802/?ref=app
u can start with language u want to learn
//happy coding☺

Answer 6

i will give a simple approach to this challenge later ☺

//just give it a try 👍

Answer 7

thnx 😊😊 swapnil,kartikey

Answer 8

My try -

https://code.sololearn.com/W4h1B7NEBnk0/?ref=app
By the way, @Gaurav congrats for cotd.

Answer 9

https://code.sololearn.com/ctBY7VYOQPLN/?ref=app

Answer 10

I tried to approach this problem by finding a mathematical pattern for the terms.

1 stair:
1
= 1 way

2 stairs:
11
2
= 2 ways

3 stairs:
111
12
21
= 3 ways

4 stairs:
1111
112
121
211
22
= 5 ways

5 stairs:
11111
1112
1121
1211
2111
122
212
221
= 8 ways

6 stairs:
111111
11112
11121
11211
12111
21111
1122
1212
1221
2112
2121
2211
222
= 13 ways

7 stairs:
1111111
111112
111121
111211
112111
121111
211111
11122
11212
11221
12112
12121
12211
21112
21121
21211
22111
1222
2122
2212
2221
= 21 ways

...

{1, 2, 3, 5, 8, 13, 21, ...} is the Fibonacci sequence starting from the third term (F2).

The Fibonacci sequence:
F0 = 0
F1 = 1
F2 = 1
F3 = 2
F4 = 3
F5 = 5
...

This means that to solve the initial problem one can use this equation:
<number of ways to climb the stairs> = F(<number of stairs>-1)

To simplify the task I rephrased the problem to "Given n, find the Fibonacci number of term F(n-1)"

Here are my codes (JavaScript and C++):
https://code.sololearn.com/Wc7Hle99U3JS/?ref=app
https://code.sololearn.com/cqYg2kTfY0wx/?ref=app

Answer 11

gaurav we can use a whole set of permutations & combinations here, i think 😰😰

Answer 12

i have done it!!!!!

https://code.sololearn.com/cbDIAsPOrQHp/?ref=app

Answer 13

Gaurav,great challenge,im lost!🤔🤔

Answer 14

Congrats for COTD

Answer 15

COT DAY
CONGRATS

Answer 16

not in that kind of state but i will try after a month

Answer 17

@Charan here is my Solotion
https://code.sololearn.com/cvNgxxjbX7sg

Answer 18

My try..
Doesn't work for more than 19 steps, any help very appreciated!

https://code.sololearn.com/cM1XQdLu5zm6/?ref=app

Answer 19

Since there's no answer in python yet, I'll post this clumsy one I made before any research (it works only up to 4, though hahaha)

https://code.sololearn.com/cno0PYFgy4tO/?ref=app

Answer 20

Congrats @ COTD Gaurav🍻🍺💓and cheeeeeers