Skip to main content

Number of paths Recursion Basic Problem

Number of paths Recursion Basic Problem-

Problem Statement-

The problem is to count all the possible paths from top left to bottom right of a MxN matrix with the constraints that from each cell you can either move to right or down.

The first line of input contains an integer T, denoting the number of test cases. The first line of each test case is M and N, M is number of rows and N is number of columns.

For each test case, print the number of paths.

1 ≤ T ≤ 30
1 ≤ M,N ≤ 10

3 3
2 8


Testcase 1:
 Let the given input 3*3 matrix is filled as such:

The possible paths which exists to reach 'I' from 'A' following above conditions are as follows:

This is Strongly recommended that You should try This question to your own before jumping to direct solution

Try this question Yourself Practice here-gfg

Number of paths Rat in a maze Recursion Basic Problem
Rat in A mace

Now My Solution-

We can solve this question  recusively 

There can be 2 type of problems here one we have to print path(needed 2d array) and one we have to tell number of total path.

In this question I will focus only number of total path If you want print the Number of paths also 

i will write solution for that too comment below this post for that printing path .

now Lets jump to Solution 

My Approach -

let's think about base condition 

if we have only one element then we have only one path (return 1) and if we go out of m,n then we don't have any solution so we will return 0 in that case.


        return 0;



        return 1;


See recustion is  a topic where you have to think about sub problem what i am thinking now  if i am standing at a generic position lets say at index i,j  i have 2 choices form my poison either i can go to right j+1th poison where j  denoting column index or i can go down at i+1th row.

So here i got my induction step -

return solution(i+1,j,m,n)+solution(i,j+1,m,n);

according to these concept i can write my code . Here is my solution -


Popular posts from this blog

Vaccine Distribution Codechef December Long challenge solution 2020

 Vaccine Distribution  Codechef December Long challenge solution 2020- This Problem vaccine distribution is taken from December long challenge 2020. lets read problem statement. Problem statement- Finally, a COVID vaccine is out on the market and the Chefland government has asked you to form a plan to distribute it to the public as soon as possible. There are a total of  N N  people with ages  a 1 , a 2 , … , a N a 1 , a 2 , … , a N . There is only one hospital where vaccination is done and it is only possible to vaccinate up to  D D  people per day. Anyone whose age is  ≥ 80 ≥ 80  or  ≤ 9 ≤ 9  is considered to be  at risk . On each day, you may not vaccinate both a person who is at risk and a person who is not at risk. Find the smallest number of days needed to vaccinate everyone. Input The first line of the input contains a single integer  T T  denoting the number of test cases. The description of  T T  test cases follows. The first line of each test case contains two space-separ

Codechef February long challenge solution 2021

   Codechef February  long challenge solution 2021- Hey guys Welcome Again, A small update CodeChef February  long challenge solution 2021 starting from 1st week of beb  2021 . Codechef long challenge is one of the popular contests of CodeChef you should participate in codechef Feb  long challenge.This is first contest of codechef in 2021 so good luck. And wish you happy new year. Contest link- I will post the solution after Contest.Stay tuned. About CodeChef  February  long challenge solution 2021: CodeChef Long Challenge is a 10-day monthly coding contest where you can show off your computer programming skills. The significance being - it gives you enough time to think about a problem, try different ways of attacking the problem, read the concepts etc. If you’re usually slow at solving problems and have ample time at hand, this is ideal for you. We also put in a lot of efforts in getting quality problems, w

Merge Two sorted array Without Extra Space

Problem statement-  Given two sorted arrays arr1[] and arr2[] of sizes N and M in non-decreasing order. Merge them in sorted order without using any extra space. Modify arr1 so that it contains the first N elements and modify arr2 so that it contains the last M elements.    Example 1: Input:  N = 4, arr1[] = [1 3 5 7]  M = 5, arr2[] = [0 2 6 8 9] Output:  arr1[] = [0 1 2 3] arr2[] = [5 6 7 8 9] Explanation: After merging the two  non-decreasing arrays, we get,  0 1 2 3 5 6 7 8 9.   Example 2: Input:  N = 2, arr1[] = [10, 12]  M = 3, arr2[] = [5 18 20] Output:  arr1[] = [5 10] arr2[] = [12 18 20] Explanation: After merging two sorted arrays  we get 5 10 12 18 20. Your Task: You don't need to read input or print anything. You only need to complete the function merge() that takes arr1, arr2, N and M as input parameters and modifies them in-place so that they look like the sorted merged array when concatenated. Expected Time Complexity:  O((n+m) log(n+m)) Expected Auxilliary Space: O(1