by Priyanshu Tiwari

## Febuary #

### CodeChef Starters 24 #

Chef is playing badminton today. The service rules of this singles game of badminton are as follows:

1. The player who starts the game serves from the right side of their court.
2. Whenever a player wins a point, they serve next.
3. If the server has won an even number of points during a game, then they will serve from the right side of the service court for the subsequent point.

Given the number of points P obtained by Chef at the end of the game, please determine how many times Chef served from the right side of the court.

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

typedef long long int ll;
void solve()
{
ll p;
cin >> p;
cout << p/2 + 1 << endl;
}

int main()
{
ios_base::sync_with_stdio(false);
cin.tie(NULL);
cout.tie(NULL);
ll test;
for (cin >> test; test--;)
solve();
}


#### Avoid Contact #

A hostel has N rooms in a straight line. It has to accommodate X people. Unfortunately, out of these X people, Y of them are infected with chickenpox. Due to safety norms, the following precaution must be taken:

• No person should occupy a room directly adjacent to a room occupied by a chickenpox-infected person. In particular, two chickenpox-infected people cannot occupy adjacent rooms.

For example, if room 4 has a chickenpox-infected person, then nobody should occupy rooms 3 and 5. Similarly, if room 1 has a chickenpox-infected person then nobody should occupy room 2.

What’s the minimum value of N for which all the people can be accommodated in the hostel, following the above condition?

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

typedef long long int ll;
void solve()
{
ll x,y,ans = 0;
cin >> x >> y;
ans = x == y ? x+y-1 : x+y;
cout << ans << endl;
}

int main()
{
ios_base::sync_with_stdio(false);
cin.tie(NULL);
cout.tie(NULL);
ll test;
for (cin >> test; test--;)
solve();
}


#### EVM Hacking #

There are three cities and thus three EVMs. An insider told Chef that his party got A,B,C votes respectively in these three cities according to the EVMs. Also, the total number of votes cast are P,Q,R respectively for the three cities.

Chef, being the party leader, can hack at most one EVM so that his party wins. On hacking a particular EVM all the votes cast in that EVM are counted in favor of Chef’s party.

A party must secure strictly more than half of the total number of votes cast in order to be considered the winner. Can Chef achieve his objective of winning by hacking at most one EVM?

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

typedef long long int ll;
void solve()
{
ll a,b,c,p,q,r;
cin >> a >> b >> c >> p >> q >> r;
ll diff = max({p-a, q-b, r-c});
if(diff + a + b + c > (p + q + r)/2)
cout<<"YES\n";
else
cout << "NO\n";
}

int main()
{
ios_base::sync_with_stdio(false);
cin.tie(NULL);
cout.tie(NULL);
ll test;
for (cin >> test; test--;)
solve();
}


#### Yet Another Constructive Problem #

You are given a positive integer X which is at most 108.

Find three distinct non-negative integers A,B,C that do not exceed 109 and satisfy the following equation:

(A∣B)&(B∣C)&(C∣A)=X


Here, ∣ denotes the bitwise OR operator and & denotes the bitwise AND operator.

It can be shown that a solution always exists for inputs satisfying the given constraints.

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

typedef long long int ll;
void solve()
{
ll x;
cin >> x;
ll a = 0, b = x, c = b +1;
while(c < INT_MAX){
if(( (a|b) & (b|c) & (c|a)) == x)
break;
c++;
}
cout << a <<" "<< b <<" "<< c <<"\n";
}

int main()
{
ios_base::sync_with_stdio(false);
cin.tie(NULL);
cout.tie(NULL);
ll test;
for (cin >> test; test--;)
solve();
}


#### Anti Palindrome #

A (1-indexed) string S of length N is said to be anti-palindrome if, for each 1≤i≤N, Si≠S(N+1−i).

You are given a string S of length N (consisting of lowercase Latin letters only). Rearrange the string to convert it into an anti-palindrome or determine that there is no rearrangement which is an anti-palindrome.

If there are multiple rearrangements of the string which are anti-palindromic, print any of them.

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

typedef long long ll;

bool cmp(pair<char, ll>& a,
pair<char, ll>& b)
{
return a.second < b.second;
}

void solve()
{
ll n;
bool to_front = true;
string str, front="", rear="", ans = "";
vector<pair<char, ll> > vec;
map<char, ll> mp;
cin >> n >> str;
if(n%2){
cout << "NO\n";
return;
}

for (auto& ch : str) {
mp[ch]++;
}

for (auto& e : mp) {
vec.push_back(e);
}

sort(vec.begin(), vec.end(), cmp);

ll len = vec.size();

if(vec[len - 1].second > n/2){
cout << "NO\n";
return;
}

for(ll i = 0; i <len; i++ ){
string tmp ="";
ll times = vec[i].second;
char ch = vec[i].first;
while(times--)
tmp += ch;
ans += tmp;
}
len = ans.length();

for (ll start = 0, end = len/2 -1; start < end; start++, end--)
swap(ans[start], ans[end]);

cout << "YES\n" <<  ans << endl;

}

int main()
{
ios_base::sync_with_stdio(false);
cin.tie(NULL);
cout.tie(NULL);
ll test;
for (cin >> test; test--;)
solve();
}


## March #

### Lunchtime #

#### Parallel Processing #

There are N tasks waiting in line to be executed. The execution time for the ith task is Ai seconds.

Chef has two processors to execute these N tasks. Both these processors work simultaneously. Each processor executes the assigned tasks one by one.

Chef assigns a prefix of these tasks to the first processor and the remaining tasks to the second processor.

For example, if there are 3 tasks, Chef can do one of the following:

• Assign no task to the first processor. This means, the second processor will execute tasks 1,2 and 3.
• Assign task 1 to the first processor. This means, the second processor will execute tasks 2 and 3.
• Assign tasks 1 and 2 to the first processor. This means, the second processor will execute task 3.
• Assign tasks 1,2 and 3 to the first processor. Thus, second processor would execute no tasks.

Find the minimum time in which all the tasks can be executed.

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

typedef long long int ll;

ll solve()
{
ll n, e, ans(0);
cin >> n;
vector<ll> vec;

for(ll i=0; i<n; i++)
{
cin >> e;
vec.push_back(e);
}
if(n == 1) return vec[0];

if(n == 2) return max(vec[0], vec[1]);

ll start = 1, end = n - 1;

ll p1 = vec[0], p2 = vec[end];
end--;

while(start <= end){

if(p1 < p2){
p1 += vec[start];
start++;
}else{
p2 += vec[end];
end--;
}

}

return max(p1, p2);

}

int main()
{
ios_base::sync_with_stdio(false);
cin.tie(NULL);
cout.tie(NULL);
ll test;
for (cin >> test; test--;)
cout << solve() << endl;
}


#### Four Equidistant Points on a Grid #

 The manhattan distance between two points P1(x1,y1) and P2(x2,y2) is given by d(P1,P2)= x2−x1 + y2−y1 .

In other words, manhattan distance is the minimum number of moves required to reach P2 from P1 if, in each move, you are allowed to travel one unit along the X-axis or one unit along the Y-axis.

You are given an integer D. Find four points (P1,P2,P3,P4) with integer coordinates, such that:

• The absolute value of both X and Y coordinates of all points is at most 109.
• The manhattan distance between any pair of points is D . More formally, d(Pi,Pj)=D for all 1 ≤ i < j ≤ 4. If such set of points do not exist, print -1. If there are multiple solutions, you may print any.

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

typedef long long int ll;

void solve()
{
ll d;
cin >> d;

if(d%2){
cout << -1 << endl;
return;
}

cout << 0 << " " <<  d/2 << endl;
cout << d/2 << " " <<  0 << endl;
cout << d << " " <<  d/2 << endl;
cout << d/2  <<  " " << d << endl;

}

int main()
{
ios_base::sync_with_stdio(false);
cin.tie(NULL);
cout.tie(NULL);
solve();
}


## April #

### Cookoff #

#### A. Digit Sum Parities #

For a positive integer M, MoEngage defines digitSum(M) as the sum of digits of the number M (when written in decimal).

For example, digitSum(1023)=1+0+2+3=6.

Given a positive integer N, find the smallest integer X strictly greater than N such that:

• digitSum(N) and digitSum(X) have different parity, i.e. one of them is odd and the other is even.

• DIGSMPAR

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

typedef long long int ll;

ll getSum(ll n)
{
ll sum = 0;
while (n != 0)
{
sum = sum + n % 10;
n = n / 10;
}
return sum;
};

ll solve()
{
ll n, x, old_sum, new_sum;
cin >> n;

old_sum = getSum(n);
n++;
new_sum = getSum(n);

if(old_sum%2 and new_sum%2)
n++;

if(old_sum%2 == 0 and new_sum%2 == 0)
n++;

return n;
}

int main()
{
ios_base::sync_with_stdio(false);
cin.tie(NULL);
cout.tie(NULL);
ll test;
for (cin >> test; test--;)
cout << solve() << endl;
}


#### B. Sticks and Rectangles #

MoEngage has a bundle of N sticks. The ith stick has a length Li meters.

Find the minimum number of sticks (of any length) you need to add to the bundle such that you can construct some rectangles where each stick of the bundle belongs to exactly one rectangle and each side of a rectangle should be formed with exactly one stick.

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

typedef long long int ll;

ll solve()
{
ll n, e, ans = 0;
unordered_map<ll, ll> ump;
cin >> n;

for (ll i = 0; i < n; i++)
{
cin >> e;
ump[e]++;
}

for (auto e : ump)
if (e.second % 2)
{
ans++;
n++;
}
return n % 4 ? ans + 2 : ans;
}

int main()
{
ios_base::sync_with_stdio(false);
cin.tie(NULL);
cout.tie(NULL);
ll test;
for (cin >> test; test--;)
cout << solve() << endl;
}