### amnchouhn's blog

By amnchouhn, history, 5 weeks ago,

I have found a very short solution of 1997C - Even Positions compared to what's available everywhere. Please upvote if found helpful.

Shayan, adedalic, BledDest, Neon, awoo Is there any edge case for this solution?

#include <bits/stdc++.h>
using namespace std;
#define nl '\n'
#define FAST_IO ios::sync_with_stdio(false); cin.tie(nullptr);

void solve() {
int n; cin >> n;
string s; cin >> s;
int ans = 0;
for (int i = 0; i < n; i += 2) {
if (s[i + 1] == ')') {
ans += 1;
}
else {
ans += 3;
}
}
cout << ans << nl;
}

int main() {
FAST_IO
int tc; cin >> tc;
while (tc--) {solve();}
}

• +8

 » 5 weeks ago, # |   0 Auto comment: topic has been updated by amnchouhn (previous revision, new revision, compare).
 » 5 weeks ago, # |   0 Auto comment: topic has been updated by amnchouhn (previous revision, new revision, compare).
 » 5 weeks ago, # | ← Rev. 3 →   0 This is pretty clever! Starting from the end of the string helped me understand this approach -- the last character must be a ')', and from there you can have either -)-) or -(-). In the first case, you can do -)(), and ignore the last block () of size 2, adding 1 to the answer. Otherwise, for -(-) the next best thing to do is (()), adding 3 to the answer and ignoring the this last block of size 4. I think this solution works great!
 » 5 weeks ago, # |   0 shorter one i still don't get how it works lol
•  » » 5 weeks ago, # ^ |   0 Realized a flaw in my previous reasoning that aligns with the solution you mentioned -- starting from the back, we can only block off when you hit another ')'. Until then, we have something like )-(-(...-(-). Now, a ')' can be greedily put in every space except the first one from the left. That needs to be a '(' to block it off. So we can think of each '(' as adding 3 to the answer: 1 for the '()' that's formed, and 2 for the cost of the last ')', which is paired with the first '(' in the block. The fixed ')' at the end also adds 1 to its cost.The solution you mentioned works similarly -- it adds 1 for each '()' at the start with pairs/2. Then it counts the extra +2s for each '('. Hope that helps =D
•  » » » 5 weeks ago, # ^ |   0 Thanks for explaining, it really helped.