# Missing Coin Sum (CSES)

Source: https://thealphajas.github.io/fun/cses/missing-coin-sum/
Difficulty: Easy
Topics: Sorting and Searching
Language: C++
Code on GitHub: https://github.com/TheAlphaJas/cses-sols/blob/main/Sorting%20and%20Searching/Missing_Coin_Sum.cpp

Key idea: Sort the coins and greedily extend the reachable prefix sum, stopping at the first gap.

## Solution

```cpp
#include <bits/stdc++.h>
using namespace std;
//author: von_Braun
#define ll long long
#define lli long long int
#define pb push_back
#define rep(var, start, num) for(ulli var = start; var <start + num; var++)
#define all(x) x.begin(), x.end()
#define ulli unsigned long long int
#define ull unsigned long long
bool sortbysec(const pair<ll,ll> &a,const pair<ll,ll> &b) { return (a.second < b.second); }

void solve() {
    int n;
    cin>>n;
    int a[n];
    rep(i,0,n) {cin>>a[i];}
    sort(a,a+n);
    ll s=0;
    bool fl=0;
    rep(i,0,n) {
        if (a[i]>s+1) {
            cout<<s+1<<endl;
            fl=1;
            break;
        } else {
            s+=a[i];
        }
    }      
    if (!fl) {cout<<s+1<<endl;}
}

int main() {
    //add quotes incase input output file
    //freopen(input.txt,r,stdin);
    //freopen(output.txt,w,stdout);
    ios_base::sync_with_stdio(0);
    cin.tie(0); cout.tie(0);
    int tc = 1;
    // cin >> tc;
    for (int t = 1; t <= tc; t++) {
        solve();
    }
}
```