Measure one litre using two vessels and infinite water supplys in C++

In this problem, we are given two vessels with capacities x and y and a supply of infinite water. Our task is to create a program that will be able to calculate exactly 1 liter in one vessel. Given the condition that x and y are co-primes. Co-primes also is known as relatively prime, mutually prime are numbers two numbers that have 1 as their only common divisor. So, this implies that their gcd(greatest common divisor) is 1.

Here, let’s suppose we have two vessels V1 with capacity x and V2 with capacity y. To measure 1 liter using these two vessels we will fill first vessels from water supply and then pour it to the second one. Do this process continues until the vessel V1 contains 1 litre of water.

Let’s take an example to understand the problem,

Input −

V1 = 5, V2 = 8
V1 = 5 ; V2 = 0 -> pour water from V1 to V2 and refill it.
V1 = 5 ; V2 = 5 -> pour water from V1 to V2 and refill it.
V1 = 2 ; V2 = 0 -> pour water from V1 to V2. Now, V2 is filled, empty it.
V1 = 5 ; V2 = 2 -> pour water from V1 to V2 and refill it.
V1 = 5 ; V2 = 7 -> pour water from V1 to V2 and refill it.
V1 = 4 ; V2 = 0 -> pour water from V1 to V2. Now, V2 is filled, empty it.
V1 = 1 ; V2 = 0 -> pour water from V1 to V2 and refill it.
Here, V1 measures 1 litre of water.

Example

Program to illustrate the solution,

Live Demo

#include <iostream>
using namespace std;
int x, y, V1, V2 = 0;
int transferWater(int amt1, int amt2) {
   if (amt1 + amt2 < y){
      V2 += V1;
      return V1;
   }
   int transferred = y - V2;
   V2 = 0;
   return transferred;
}
void measure1Litre() {
   while(V1 != 1){
      if (V1 == 0)
         V1 = x;
      cout<<"Vessel 1: "<<V1<<" | Vessel 2: "<<V2<<endl;
      V1 = V1 - transferWater(V1, V2);
   }
   cout<<"Vessel 1: "<<V1<<" | Vessel 2: "<<V2<<endl;
}
int main() {
   x= 5, y = 8;
   measure1Litre();
   return 0;
}

Output

Vessel 1: 5 | Vessel 2: 0
Vessel 1: 5 | Vessel 2: 5
Vessel 1: 2 | Vessel 2: 0
Vessel 1: 5 | Vessel 2: 2
Vessel 1: 5 | Vessel 2: 7
Vessel 1: 4 | Vessel 2: 0
Vessel 1: 5 | Vessel 2: 4
Vessel 1: 1 | Vessel 2: 0

Narendra Kumar

Updated on 03-Jun-2020 07:26:25

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