Balanced Smileys - At any index, the number of closing brackets should be less than or equal to the number of opening brackets, if it is less, then the difference of closing brackets and opening brackets should be equal to the number of happy smileys. And a similar logic should be applied from the end considering the number of sad smileys.

BalancedSmileys.cpp

#include <vector>
#include <map>
#include <set>
#include <algorithm>
#include <iostream>
#include <cstdio>

#define FOR(i,a,b)                  for(int i=a;i<b;i++)
#define REP(i,a)                    FOR(i, 0, a)
#define all(a)                      a.begin(), a.end()
#define SORT(a)                     sort(all(a))

#define VI                          vector<int>

using namespace std;

bool is_valid(string &s){
    int n = s.length();
    VI opening(n), closing(n), happy(n), sad(n);
    FOR(i, 0, n){
        if(i){
            opening[i] = opening[i-1]; closing[i] = closing[i-1]; 
            happy[i] = happy[i-1]; sad[i] = sad[i-1];
        }
        if(s[i]== '('){
            opening[i]++;
            if(i - 1 >= 0 && s[i-1] == ':')
                sad[i]++;
        }
        else if(s[i] == ')'){
            closing[i]++;
            if(i - 1 >= 0 && s[i-1] == ':')
                happy[i]++;
        }
    }

    FOR(i, 0, n){
        if(opening[i] < closing[i]) {
            if(happy[i] < (closing[i] - opening[i]))
                return false;
        }
    }
    opening = VI(n);
    closing = VI(n);
    happy = VI(n);
    sad = VI(n);

    for(int i = n-1; i>0; i--){
        if(i != n-1){
            opening[i] = opening[i+1]; closing[i] = closing[i+1]; 
            happy[i] = happy[i+1]; sad[i] = sad[i+1];
        }
        if(s[i]== '('){
            opening[i]++;
            if(i - 1 >= 0 && s[i-1] == ':')
                sad[i]++;
        }
        else if(s[i] == ')'){
            closing[i]++;
            if(i - 1 >= 0 && s[i-1] == ':')
                happy[i]++;
        }
    }
    for(int i = n-1; i>=0; i--){
        if(opening[i] > closing[i]) {
            if(sad[i] < (opening[i] - closing[i]))
                return false;
        }
    }

    return true;
}

int main(){
    int T;
    cin >> T;
    cin.ignore();
    REP(tc, T){
        string s;
        getline(cin, s);
        if(is_valid(s))
            cout << "Case #" << tc + 1 << ": YES" << endl;
        else 
            cout << "Case #" << tc + 1 << ": NO" << endl;
    }
    return 0;
}

Please check your solution with an easy test case: "(", your solution returns YES, which is definitely wrong