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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