WEEK:6 PROGRAMMING ASSIGNMENT 1 SOLUTION (Jan 2020-Apr2020) An Introduction to Programming through C++ NPTEL 2020

  

               An Introduction To Programming Through C++

IIT Bombay.

Week 6- Programming Assignment 1:

Suppose I have a red block (R) of height 1, a blue block (B) of height 2, and a green block (G) of height 3.  I can stack the blocks one above the other to build a tower.  For example, I can stack in the order RBG and I would get a tower of height 6.  I wish to compute how many different towers of a given height n can be built if there are ample blocks of each colour.

Let T(n) denote the number of towers of height n.

Write a program that prints T(n) given n.

Sample Test Cases

Input Output

Test Case 1

1

1

Test Case 2

2

2

Test Case 3

3

4

Test Case 4

4

7

Test Case 5

5

13

Test Case 6

-10

0

Test Case 7

29

29249425

WRITE/COPY THESE CODE DIRECTLY IN NPTEL TERMINAL AND COMPILE AND RUN THEN SUBMIT.

PROGRAM:

#include <iostream>

using namespace std;

long int Tower(int w, int x, int w_x, int y, int w_y, int z, int w_z){
    if(w < 0){
  return 0;
    } else if(w==0){
  return 1;
    }
   
    return Tower(w-w_x,x-1,w_x,y,w_y,z,w_z) + Tower(w-w_y,x,w_x,y-1,w_y,z,w_z) + Tower(w-w_z,x,w_x,y,w_y,z-1,w_z);
}

int main(){

    int G=3, B=2, R=1;
    int h;
    
    cin>>h;

    int w_g = h / G; // maximum G can be used
    int w_b = h / B; // maximum B can be used
    int w_r = h / R; // maximum B can be used
    
    int counts = 0; 
    if(h > 0){
        counts = Tower(h,w_g,G,w_b,B,w_r,R);
    }

   
    cout<< counts<<"\n";

    return 0;
}

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