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# Prime Pattern CodeChef Solution

## Prime Pattern CodeChef Solution in C++14

``````#include <bits/stdc++.h>

#pragma optimization_level 3
#pragma GCC optimize("Ofast,no-stack-protector,unroll-loops,fast-math,O3")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx")
#pragma GCC optimize("Ofast")//Comment optimisations for interactive problems (use endl)
#pragma GCC target("avx,avx2,fma")
#pragma GCC optimization ("unroll-loops")

using namespace std;

struct PairHash {inline std::size_t operator()(const std::pair<int, int> &v) const { return v.first * 31 + v.second; }};

// speed
#define Code ios_base::sync_with_stdio(false);
#define By ios::sync_with_stdio(0);
#define Sumfi cout.tie(NULL);

// alias
using ll = long long;
using ld = long double;
using ull = unsigned long long;

// constants
const ld PI = 3.14159265358979323846;  /* pi */
const ll INF = 1e18;
const ld EPS = 1e-9;
const ll MAX_N = 202020;
const ll mod = 1e9 + 7;

// typedef
typedef pair<ll, ll> pll;
typedef vector<pll> vpll;
typedef array<ll,3> all3;
typedef array<ll,5> all5;
typedef vector<all3> vall3;
typedef vector<all5> vall5;
typedef vector<ld> vld;
typedef vector<ll> vll;
typedef vector<vll> vvll;
typedef vector<int> vi;
typedef deque<ll> dqll;
typedef deque<pll> dqpll;
typedef pair<string, string> pss;
typedef vector<pss> vpss;
typedef vector<string> vs;
typedef vector<vs> vvs;
typedef unordered_set<ll> usll;
typedef unordered_set<pll, PairHash> uspll;
typedef unordered_map<ll, ll> umll;
typedef unordered_map<pll, ll, PairHash> umpll;

// macros
#define rep(i,m,n) for(ll i=m;i<n;i++)
#define rrep(i,m,n) for(ll i=n;i>=m;i--)
#define all(a) begin(a), end(a)
#define rall(a) rbegin(a), rend(a)
#define ZERO(a) memset(a,0,sizeof(a))
#define MINUS(a) memset(a,0xff,sizeof(a))
#define INF(a) memset(a,0x3f3f3f3f3f3f3f3fLL,sizeof(a))
#define ASCEND(a) iota(all(a),0)
#define sz(x) ll((x).size())
#define BIT(a,i) (a & (1ll<<i))
#define BITSHIFT(a,i,n) (((a<<i) & ((1ll<<n) - 1)) | (a>>(n-i)))
#define pyes cout<<"YES\n";
#define pno cout<<"NO\n";
#define endl "\n"
#define pneg1 cout<<"-1\n";
#define ppossible cout<<"Possible\n";
#define pimpossible cout<<"Impossible\n";
#define TC(x) cout<<"Case #"<<x<<": ";
#define X first
#define Y second

// utility functions
template <typename T>
void print(T &&t)  { cout << t << "\n"; }
template<typename T>
void printv(vector<T>v){ll n=v.size();rep(i,0,n){cout<<v[i];if(i+1!=n)cout<<' ';}cout<<endl;}
template<typename T>
void printvln(vector<T>v){ll n=v.size();rep(i,0,n)cout<<v[i]<<endl;}
void fileIO(string in = "input.txt", string out = "output.txt") {freopen(in.c_str(),"r",stdin); freopen(out.c_str(),"w",stdout);}
template<typename T>
template<typename T, typename U>
template<typename T, typename U>

struct Combination {
vll fac, inv;
ll n, MOD;

ll modpow(ll n, ll x, ll MOD = mod) { if(!x) return 1; ll res = modpow(n,x>>1,MOD); res = (res * res) % MOD; if(x&1) res = (res * n) % MOD; return res; }

Combination(ll _n, ll MOD = mod): n(_n + 1), MOD(MOD) {
inv = fac = vll(n,1);
rep(i,1,n) fac[i] = fac[i-1] * i % MOD;
inv[n - 1] = modpow(fac[n - 1], MOD - 2, MOD);
rrep(i,1,n - 2) inv[i] = inv[i + 1] * (i + 1) % MOD;
}

ll fact(ll n) {return fac[n];}
ll nCr(ll n, ll r) {
if(n < r or n < 0 or r < 0) return 0;
return fac[n] * inv[r] % MOD * inv[n-r] % MOD;
}
};

struct Matrix {
ll r,c;
vvll matrix;
Matrix(ll r, ll c, ll v = 0): r(r), c(c), matrix(vvll(r,vll(c,v))) {}

Matrix operator*(const Matrix& B) const {
Matrix res(r, B.c);
rep(i,0,r) rep(j,0,B.c) rep(k,0,B.r) {
res.matrix[i][j] = (res.matrix[i][j] + matrix[i][k] * B.matrix[k][j] % mod) % mod;
}
return res;
}

Matrix copy() {
Matrix copy(r,c);
copy.matrix = matrix;
return copy;
}

Matrix pow(ll n) {
assert(r == c);
Matrix res(r,r);
Matrix now = copy();
rep(i,0,r) res.matrix[i][i] = 1;
while(n) {
if(n & 1) res = res * now;
now = now * now;
n /= 2;
}
return res;
}
};

// geometry data structures
template <typename T>
struct Point {
T y,x;
Point(T y, T x) : y(y), x(x) {}
Point(pair<T,T> p) : y(p.first), x(p.second) {}
Point() {}
void input() {cin>>y>>x;}
friend ostream& operator<<(ostream& os, const Point<T>& p) { os<<p.y<<' '<<p.x<<'\n'; return os;}
Point<T> operator+(Point<T>& p) {return Point<T>(y + p.y, x + p.x);}
Point<T> operator-(Point<T>& p) {return Point<T>(y - p.y, x - p.x);}
Point<T> operator*(ll n) {return Point<T>(y*n,x*n); }
Point<T> operator/(ll n) {return Point<T>(y/n,x/n); }
bool operator<(const Point &other) const {if (x == other.x) return y < other.y;return x < other.x;}
Point<T> rotate(Point<T> center, ld angle) {
ld si = sin(angle * PI / 180.), co = cos(angle * PI / 180.);
ld y = this->y - center.y;
ld x = this->x - center.x;

return Point<T>(y * co - x * si + center.y, y * si + x * co + center.x);
}
ld distance(Point<T> other) {
T dy = abs(this->y - other.y);
T dx = abs(this->x - other.x);
return sqrt(dy * dy + dx * dx);
}

T norm() { return x * x + y * y; }
};

template<typename T>
struct Line {
Point<T> A, B;
Line(Point<T> A, Point<T> B) : A(A), B(B) {}
Line() {}

void input() {
A = Point<T>();
B = Point<T>();
A.input();
B.input();
}

T ccw(Point<T> &a, Point<T> &b, Point<T> &c) {
T res = a.x * b.y + b.x * c.y + c.x * a.y;
res -= (a.x * c.y + b.x * a.y + c.x * b.y);
return res;
}

bool isIntersect(Line<T> o) {
T p1p2 = ccw(A,B,o.A) * ccw(A,B,o.B);
T p3p4 = ccw(o.A,o.B,A) * ccw(o.A,o.B,B);
if (p1p2 == 0 && p3p4 == 0) {
pair<T,T> p1(A.y, A.x), p2(B.y,B.x), p3(o.A.y, o.A.x), p4(o.B.y, o.B.x);
if (p1 > p2) swap(p2, p1);
if (p3 > p4) swap(p3, p4);
return p3 <= p2 && p1 <= p4;
}
return p1p2 <= 0 && p3p4 <= 0;
}

pair<bool,Point<ld>> intersection(Line<T> o) {
if(!this->intersection(o)) return {false, {}};
ld det = 1. * (o.B.y-o.A.y)*(B.x-A.x) - 1.*(o.B.x-o.A.x)*(B.y-A.y);
ld t = ((o.B.x-o.A.x)*(A.y-o.A.y) - (o.B.y-o.A.y)*(A.x-o.A.x)) / det;
return {true, {A.y + 1. * t * (B.y - A.y), B.x + 1. * t * (B.x - A.x)}};
}

//@formula for : y = ax + b
//@return {a,b};
pair<ld, ld> formula() {
T y1 = A.y, y2 = B.y;
T x1 = A.x, x2 = B.x;
if(y1 == y2) return {1e9, 0};
if(x1 == x2) return {0, 1e9};
ld a = 1. * (y2 - y1) / (x2 - x1);
ld b = -x1 * a + y1;
return {a, b};
}
};

template<typename T>
struct Circle {
Point<T> center;
Circle() {}

void input() {
center = Point<T>();
center.input();
}

bool circumference(Point<T> p) {
return (center.x - p.x) * (center.x - p.x) + (center.y - p.y) * (center.y - p.y) == radius * radius;
}

bool intersect(Circle<T> c) {
T d = (center.x - c.center.x) * (center.x - c.center.x) + (center.y - c.center.y) * (center.y - c.center.y);
}

bool include(Circle<T> c) {
T d = (center.x - c.center.x) * (center.x - c.center.x) + (center.y - c.center.y) * (center.y - c.center.y);
}
};

ll __gcd(ll x, ll y) { return !y ? x : __gcd(y, x % y); }
all3 __exgcd(ll x, ll y) { if(!y) return {x,1,0}; auto [g,x1,y1] = __exgcd(y, x % y); return {g, y1, x1 - (x/y) * y1}; }
ll __lcm(ll x, ll y) { return x / __gcd(x,y) * y; }
ll modpow(ll n, ll x, ll MOD = mod) { n%=MOD; if(!x) return 1; ll res = modpow(n,x>>1,MOD); res = (res * res) % MOD; if(x&1) res = (res * n) % MOD; return res; }

const static int bits = 19, mask = (1<<19) - 1;
unsigned long long mul(unsigned long long x, unsigned long long y, unsigned long long M)
{
if (x <= UINT_MAX && y <= UINT_MAX) return x * y % M;
unsigned long long rslt = y * (x & mask) % M;
while (x >>= bits) rslt = (rslt + (y = (y << bits) % M) * (x & mask)) % M;
return rslt;
}
static int test(unsigned long long n, unsigned long long a) {
unsigned long long s, t, nmin1 = n - 1;
int r;
for (s = nmin1, r = 0; !(s & 1); s >>= 1, r++) ;
for(t = a; s >>= 1; )
{
a = mul(a, a, n);
if (s & 1) t = mul(t, a, n);
}
if (t == 1 || t == nmin1) return 1;
while (--r) if ((t = mul(t, t, n)) == nmin1) return 1;
return 0;
}

static int millerRabin(unsigned long long n) {
if(n<29) return n==2 || n==3 || n==5 || n==7 || n==11 || n==13 || n==17 || n==19 || n==23;
if(!(n&1 && n%3 && n%5 && n%7 && n%11 && n%13 && n%17 && n%19 && n%23)) return 0;
return test(n, 2) && test(n, 1215) &&(n==17431 || test(n, 34862) && (n==3281359 || test(n, 574237825)));
}

ll work(ll x, ll y) {
ll ma = max(abs(x), abs(y));
if(x == ma) return 4 * ma * ma - 4 * ma + 1 + y - (1 - ma);
if(y == ma) return 4 * ma * ma - 2 * ma + abs(x - ma);
if(x == -ma) return 4 * ma * ma + abs(y - ma);
if(y == -ma) return 4 * ma * ma + 2 * ma + abs(x + ma);
return -1;
}
ll solve(ll a, ll b) {
if(millerRabin(work(a,b))) return 0;
rep(res,1,INF) {
rep(x,1,res + 1) if(millerRabin(work(a + x, b + res - x))) return res;
rep(x,1-res,1) if(millerRabin(work(a + x, b + res + x))) return res;
rep(x,-res,0)  if(millerRabin(work(a + x, b - res - x))) return res;
rep(x,0,res) if(millerRabin(work(a + x, b - res + x))) return res;
}
return -1;
}
int main() {
Code By Sumfi
cout.precision(12);
ll tc = 1;
cin>>tc;
rep(i,1,tc+1) {
ll a,b;
cin>>a>>b;
print(solve(a,b));
}
return 0;
}``````

## Prime Pattern CodeChef Solution in C

``````#include <stdio.h>
#include <math.h>

const static int bits = 19, mask = (1<<19) - 1;
#define UINT_MAX 32767

#define NN 4000001
#define RR 2000000

long long cor2ind(long long x,long long y)
{
long long sum=0;

if(x-y>0 && x+y<=1) // south
{
sum=(y-1)*(4*y+2)+2;
sum+=x-y;
}
else if(x+y>1 && x-y>=0) // east
{
sum=(4*x-6)*x+2;
sum+=2*x-1;
sum+=x+y-1;
}
else if(x-y<0 && x+y>=0) // north
{
sum=(4*y-6)*y+2;
sum+=(y-1)*4+2;
sum+=y-x;
}
else if(x+y<0 &&x-y<=0) // west
{
sum=(8*x+12)*x/2+2;
sum+=(-x-1)*6+4;
sum+=-x-y;
}
return sum;
}

unsigned long long mul(unsigned long long x, unsigned long long y, unsigned long long M)
{
if (x <= UINT_MAX && y <= UINT_MAX) return x * y % M;
unsigned long long rslt = y * (x & mask) % M;
while (x >>= bits) rslt = (rslt + (y = (y << bits) % M) * (x & mask)) % M;
return rslt;
}

static int test(unsigned long long n, unsigned long long a) {
unsigned long long s, t, nmin1 = n - 1;
int r;
for (s = nmin1, r = 0; !(s & 1); s >>= 1, r++) ;
for(t = a; s >>= 1; )
{
a = mul(a, a, n);
if (s & 1) t = mul(t, a, n);
}
if (t == 1 || t == nmin1) return 1;
while (--r) if ((t = mul(t, t, n)) == nmin1) return 1;
return 0;
}

static int isprime(unsigned long long n) {
if(n<29) return n==2 || n==3 || n==5 || n==7 || n==11 || n==13 || n==17 || n==19 || n==23;
if(!(n&1 && n%3 && n%5 && n%7 && n%11 && n%13 && n%17 && n%19 && n%23)) return 0;
return test(n, 2) && test(n, 1215) &&(n==17431 || test(n, 34862) && (n==3281359 || test(n, 574237825)));
}

int main()
{
long long T, x0, y0, dist;
long long found, x, y;

scanf("%lld",&T);
while(T--)
{
scanf("%lld%lld",&x0,&y0);
found=0;
if(isprime(cor2ind(x0,y0)))
dist=0;
else
for(dist=1;;dist++)
{
// here x and y are relative coordinates
{
y=dist-x;
if(isprime(cor2ind(x+x0,y+y0)))
{
found=1;
break;
}
}
if(found) break;
{
y=dist+x;
if(isprime(cor2ind(x+x0,y+y0)))
{
found=1;
break;
}
}
if(found) break;
{
y=-dist-x;
if(isprime(cor2ind(x+x0,y+y0)))
{
found=1;
break;
}
}
if(found) break;
{
y=-dist+x;
if(isprime(cor2ind(x+x0,y+y0)))
{
found=1;
break;
}
}
if(found) break;
}
printf("%lld\n",dist);
}

return 0;
}  ``````

## Prime Pattern CodeChef Solution in JAVA

``````
import java.math.BigInteger;
import java.util.Scanner;

class PrimeNo {

public static int mod(int x){
return Math.abs(x);
}

public static boolean isPrime(long n){
BigInteger b = new BigInteger(Long.toString(n));
return b.isProbablePrime(10);
}
public static long index(int x1,int y1) {
//	System.out.print(x1+" "+y1+" ");

int c = Math.max(mod(x1), mod(y1));
long y=(long)y1;
long x= (long)x1;
long indexSquare=0;
if (c == Math.abs(y1)) {
if (y1 > 0) {
indexSquare = 4 *y*y-y - x;
} else {
indexSquare = 4*y*y-3*y + x;
}
}else{
if (x1 >0) {
indexSquare = 4*x*x-3*x+y;
} else {
indexSquare = 4*x*x-(x)-y;
}
}
//	System.out.println(indexSquare);
return indexSquare;
}

public static int distance(int x,int y) {
for (int k = 0; ; k++) {
int i = k;
//	System.out.println(i);
for (int j = 0;j<=k; j++,i--) {
//	System.out.println(j);
if(isPrime(index(x+i, y+j))||isPrime(index(x-i, y-j))||isPrime(index(x-j,y+i))||isPrime(index(x+j, y-i))){
return k;
}
}

}

}

public static void main(String[] args) {

Scanner scanner = new Scanner(System.in);
int T = scanner.nextInt();
for (int t = 0; t < T; t++) {
int x = scanner.nextInt();
int y = scanner.nextInt();
System.out.println(distance(x,y));
}

}
}
``````

## Prime Pattern CodeChef Solution in PYTH

``````def millerRabin(n):
# Returns true if probable prime, false if composite
bases     = [2,3,5,7,11,13,17,19,23]
nm1       = n-1
m         = nm1
d         = 0

if n in bases:
return True
if n < 2:
return False

while not m&1:
d    += 1
m   >>= 1

for a in bases:
done_for_base = False

b   = pow(a,m,n)
if b == 1 or b == nm1 :
#done_for_base = True
continue
for k in range(d-1):
b = pow(b,2,n)
if b == 1:
return False
elif b == nm1:
done_for_base = True
break
if not done_for_base:
return False
return True

def valAt(x,y):
if x>y:
if x+y > 0:
n  = 4*x*x - 3*x + y
else :
n  = 4*y*y - 3*y + x
else:
if x+y > 0:
n  = 4*y*y -  x - y
else :
n  = 4*x*x -  y - x
return n

def solveCase(x,y):
r    = 0
n    = valAt(x,y)
if millerRabin(n):
return r
while True:
r  += 1
for k in range(r):
n1  = valAt(x + r-k, y + 0-k)
n2  = valAt(x + 0-k, y - r+k)
n3  = valAt(x - r+k, y + 0+k)
n4  = valAt(x + 0+k, y + r-k)
for n in [n1,n2,n3,n4]:
if millerRabin(n):
return r

def main():
T  = int(raw_input(''))
for t in range(T):
x,y = [ int(i) for i in raw_input().split() ]
ans = solveCase(x,y)
print ans

main()``````
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