C_Stable_Groups.cpp

#include<bits/stdc++.h>
using namespace std ; 

# define int long long int 
# define vi vector<int> 
# define vs vector<string> 
# define vv vector<vector<int>>
# define f(i,a,b) for(int i=a;i<b;i++)
# define in cin>>
# define out cout<<
# define nl <<endl;
# define input(arr) fr(0,arr.size()) in arr[i] 
# define output(arr) fr(0,arr.size()) out arr[i]<<' ' 
# define mod 1e9+7
# define ps(x,y) fixed<<setprecision(y)<<x
# define setbits(x) __builtin_popcountll(x)
# define zrobits(x) __builtin_ctzll(x)
# define inf 1e18
# define sortv(a) sort(a.begin(),a.end())
                                        
int gcd(int a, int b){return b == 0 ? a : gcd(b, a % b);}
bool isprime(int x){for(int i=2;i*i<=x;i++) if(x%i==0) return 0 ;return (x==1? 0 : 1);}
                                        
int solve(int n, int k, int x, vector<int>& a) {
    sortv(a);  
    int ans = 0;               
    vi gaps;
    for (int i = 1; i < n; i++) {
        if (a[i] - a[i-1] > x) {
            int gap = a[i] - a[i-1];
            gaps.push_back(gap);
        }
    }
    sortv(gaps);
    ans = gaps.size()+1;
    for(int i = 0;i<gaps.size();i++){
      int element = (ceil((double)gaps[i] / x)) - 1;  
            if (element <= k) {
                k -= element; 
                ans--;
            }else{
                break;
            }
    }
    return ans; 
}

signed main() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    cout.tie(NULL);
        int n, k, x;
        in n;
        in k;
        in x;
        
        vi a(n);
        for (int i = 0; i < n; i++) {
            in a[i];
        }
        
        out solve(n, k, x, a) nl;
}