Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
Minimum possible final health of the last monster in a game in C++
Problem statement
Given N monsters, each monster has initial health h[i] which is an integer. A monster is alive if its health is greater than 0.
In each turn a random monster kills another random monster, the monster which is attacked, its health reduces by the amount of health of the attacking monster. This process is continued until a single monster is left. What will be the minimum possible health of the last remained monster.
Example
If input array is {2, 14, 28, 56} then output will be 2 because When only the first monster keeps on attacking the remaining 3 monsters, the final health of the last monster will be 2, which is minimum.
Algorithm
We can obtain final answer using below GCD formula −
H(min) = gcd(h1, h2, …, hn)
Example
#include <iostream>
using namespace std;
int gcd(int a, int b) {
if (a == 0)
return b;
return gcd(b % a, a);
}
int getPossibleHealth(int* health, int n) {
int currentGcd = gcd(health[0], health[1]);
for (int i = 2; i < n; ++i) {
currentGcd = gcd(currentGcd, health[i]);
}
return currentGcd;
}
int main() {
int health[] = { 4, 6, 8, 12 };
int n = sizeof(health) / sizeof(health[0]);
cout << "Possible final health = " << getPossibleHealth(health, n) << endl;
return 0;
}Output
When you compile and execute above program. It generates following output −
Possible final health = 2
309 Views
