564. Find the Closest Palindrome

Given a string n representing an integer, return the closest integer (not including itself), which is a palindrome. If there is a tie, return the smaller one.

The closest is defined as the absolute difference minimized between two integers.

class BigInt{
public:
    string digits;

    //Constructors:
    BigInt(unsigned long long n = 0);
    BigInt(string &);
    BigInt(const char *);
    BigInt(BigInt &);

    //Helper Functions:
    friend void divide_by_2(BigInt &a);
    friend bool Null(const BigInt &);
    friend int Length(const BigInt &);
    int operator[](const int)const;

    /* * * * Operator Overloading * * * */

    //Direct assignment
    BigInt &operator=(const BigInt &);

    //Post/Pre - Incrementation
    BigInt &operator++();
    BigInt operator++(int temp);
    BigInt &operator--();
    BigInt operator--(int temp);

    //Addition and Subtraction
    friend BigInt &operator+=(BigInt &, const BigInt &);
    friend BigInt operator+(const BigInt &, const BigInt &);
    friend BigInt operator-(const BigInt &, const BigInt &);
    friend BigInt &operator-=(BigInt &, const BigInt &);

    //Comparison operators
    friend bool operator==(const BigInt &, const BigInt &);
    friend bool operator!=(const BigInt &, const BigInt &);

    friend bool operator>(const BigInt &, const BigInt &);
    friend bool operator>=(const BigInt &, const BigInt &);
    friend bool operator<(const BigInt &, const BigInt &);
    friend bool operator<=(const BigInt &, const BigInt &);

    //Multiplication and Division
    friend BigInt &operator*=(BigInt &, const BigInt &);
    friend BigInt operator*(const BigInt &, const BigInt &);
    friend BigInt &operator/=(BigInt &, const BigInt &);
    friend BigInt operator/(const BigInt &, const BigInt &);

    //Modulo
    friend BigInt operator%(const BigInt &, const BigInt &);
    friend BigInt &operator%=(BigInt &, const BigInt &);

    //Power Function
    friend BigInt &operator^=(BigInt &,const BigInt &);
    friend BigInt operator^(BigInt &, const BigInt &);

    //Square Root Function
    friend BigInt sqrt(BigInt &a);

    //Read and Write
    friend ostream &operator<<(ostream &,const BigInt &);
    friend istream &operator>>(istream &, BigInt &);

    //Others
    friend BigInt NthCatalan(int n);
    friend BigInt NthFibonacci(int n);
    friend BigInt Factorial(int n);
    string toString() {
        string res = "";
        for (int i = digits.size() - 1; i >= 0;i--)
            res += to_string((short)digits[i]);
        return res;
    }
};

BigInt::BigInt(string & s){
    digits = "";
    int n = s.size();
    for (int i = n - 1; i >= 0;i--){
        if(!isdigit(s[i]))
            throw("ERROR");
        digits.push_back(s[i] - '0');
    }
}
BigInt::BigInt(unsigned long long nr){
    do{
        digits.push_back(nr % 10);
        nr /= 10;
    } while (nr);
}
BigInt::BigInt(const char *s){
    digits = "";
    for (int i = strlen(s) - 1; i >= 0;i--)
    {
        if(!isdigit(s[i]))
            throw("ERROR");
        digits.push_back(s[i] - '0');
    }
}
BigInt::BigInt(BigInt & a){
    digits = a.digits;
}

bool Null(const BigInt& a){
    if(a.digits.size() == 1 && a.digits[0] == 0)
        return true;
    return false;
}
int Length(const BigInt & a){
    return a.digits.size();
}
int BigInt::operator[](const int index)const{
    if(digits.size() <= index || index < 0)
        throw("ERROR");
    return digits[index];
}
bool operator==(const BigInt &a, const BigInt &b){
    return a.digits == b.digits;
}
bool operator!=(const BigInt & a,const BigInt &b){
    return !(a == b);
}
bool operator<(const BigInt&a,const BigInt&b){
    int n = Length(a), m = Length(b);
    if(n != m)
        return n < m;
    while(n--)
        if(a.digits[n] != b.digits[n])
            return a.digits[n] < b.digits[n];
    return false;
}
bool operator>(const BigInt&a,const BigInt&b){
    return b < a;
}
bool operator>=(const BigInt&a,const BigInt&b){
    return !(a < b);
}
bool operator<=(const BigInt&a,const BigInt&b){
    return !(a > b);
}

BigInt &BigInt::operator=(const BigInt &a){
    digits = a.digits;
    return *this;
}

BigInt &BigInt::operator++(){
    int i, n = digits.size();
    for (i = 0; i < n && digits[i] == 9;i++)
        digits[i] = 0;
    if(i == n)
        digits.push_back(1);
    else
        digits[i]++;
    return *this;
}
BigInt BigInt::operator++(int temp){
    BigInt aux;
    aux = *this;
    ++(*this);
    return aux;
}

BigInt &BigInt::operator--(){
    if(digits[0] == 0 && digits.size() == 1)
        throw("UNDERFLOW");
    int i, n = digits.size();
    for (i = 0; digits[i] == 0 && i < n;i++)
        digits[i] = 9;
    digits[i]--;
    if(n > 1 && digits[n - 1] == 0)
        digits.pop_back();
    return *this;
}
BigInt BigInt::operator--(int temp){
    BigInt aux;
    aux = *this;
    --(*this);
    return aux;
}

BigInt &operator+=(BigInt &a,const BigInt& b){
    int t = 0, s, i;
    int n = Length(a), m = Length(b);
    if(m > n)
        a.digits.append(m - n, 0);
    n = Length(a);
    for (i = 0; i < n;i++){
        if(i < m)
            s = (a.digits[i] + b.digits[i]) + t;
        else
            s = a.digits[i] + t;
        t = s / 10;
        a.digits[i] = (s % 10);
    }
    if(t)
        a.digits.push_back(t);
    return a;
}
BigInt operator+(const BigInt &a, const BigInt &b){
    BigInt temp;
    temp = a;
    temp += b;
    return temp;
}

BigInt &operator-=(BigInt&a,const BigInt &b){
    if(a < b)
        throw("UNDERFLOW");
    int n = Length(a), m = Length(b);
    int i, t = 0, s;
    for (i = 0; i < n;i++){
        if(i < m)
            s = a.digits[i] - b.digits[i]+ t;
        else
            s = a.digits[i]+ t;
        if(s < 0)
            s += 10,
                    t = -1;
        else
            t = 0;
        a.digits[i] = s;
    }
    while(n > 1 && a.digits[n - 1] == 0)
        a.digits.pop_back(),
                n--;
    return a;
}
BigInt operator-(const BigInt& a,const BigInt&b){
    BigInt temp;
    temp = a;
    temp -= b;
    return temp;
}

BigInt &operator*=(BigInt &a, const BigInt &b)
{
    if(Null(a) || Null(b)){
        a = BigInt();
        return a;
    }
    int n = a.digits.size(), m = b.digits.size();
    vector<int> v(n + m, 0);
    for (int i = 0; i < n;i++)
        for (int j = 0; j < m;j++){
            v[i + j] += (a.digits[i] ) * (b.digits[j]);
        }
    n += m;
    a.digits.resize(v.size());
    for (int s, i = 0, t = 0; i < n; i++)
    {
        s = t + v[i];
        v[i] = s % 10;
        t = s / 10;
        a.digits[i] = v[i] ;
    }
    for (int i = n - 1; i >= 1 && !v[i];i--)
        a.digits.pop_back();
    return a;
}
BigInt operator*(const BigInt&a,const BigInt&b){
    BigInt temp;
    temp = a;
    temp *= b;
    return temp;
}

BigInt &operator/=(BigInt& a,const BigInt &b){
    if(Null(b))
        throw("Arithmetic Error: Division By 0");
    if(a < b){
        a = BigInt();
        return a;
    }
    if(a == b){
        a = BigInt(1);
        return a;
    }
    int i, lgcat = 0, cc;
    int n = Length(a), m = Length(b);
    vector<int> cat(n, 0);
    BigInt t;
    for (i = n - 1; t * 10 + a.digits[i] < b;i--){
        t *= 10;
        t += a.digits[i] ;
    }
    for (; i >= 0; i--){
        t = t * 10 + a.digits[i];
        for (cc = 9; cc * b > t;cc--);
        t -= cc * b;
        cat[lgcat++] = cc;
    }
    a.digits.resize(cat.size());
    for (i = 0; i < lgcat;i++)
        a.digits[i] = cat[lgcat - i - 1];
    a.digits.resize(lgcat);
    return a;
}
BigInt operator/(const BigInt &a,const BigInt &b){
    BigInt temp;
    temp = a;
    temp /= b;
    return temp;
}

BigInt &operator%=(BigInt& a,const BigInt &b){
    if(Null(b))
        throw("Arithmetic Error: Division By 0");
    if(a < b){
        return a;
    }
    if(a == b){
        a = BigInt();
        return a;
    }
    int i, lgcat = 0, cc;
    int n = Length(a), m = Length(b);
    vector<int> cat(n, 0);
    BigInt t;
    for (i = n - 1; t * 10 + a.digits[i] < b;i--){
        t *= 10;
        t += a.digits[i];
    }
    for (; i >= 0; i--){
        t = t * 10 + a.digits[i];
        for (cc = 9; cc * b > t;cc--);
        t -= cc * b;
        cat[lgcat++] = cc;
    }
    a = t;
    return a;
}
BigInt operator%(const BigInt &a,const BigInt &b){
    BigInt temp;
    temp = a;
    temp %= b;
    return temp;
}

BigInt &operator^=(BigInt & a,const BigInt & b){
    BigInt Exponent, Base(a);
    Exponent = b;
    a = 1;
    while(!Null(Exponent)){
        if(Exponent[0] & 1)
            a *= Base;
        Base *= Base;
        divide_by_2(Exponent);
    }
    return a;
}
BigInt operator^(BigInt & a,BigInt & b){
    BigInt temp(a);
    temp ^= b;
    return temp;
}

void divide_by_2(BigInt & a){
    int add = 0;
    for (int i = a.digits.size() - 1; i >= 0;i--){
        int digit = (a.digits[i] >> 1) + add;
        add = ((a.digits[i] & 1) * 5);
        a.digits[i] = digit;
    }
    while(a.digits.size() > 1 && !a.digits.back())
        a.digits.pop_back();
}

BigInt sqrt(BigInt & a){
    BigInt left(1), right(a), v(1), mid, prod;
    divide_by_2(right);
    while(left <= right){
        mid += left;
        mid += right;
        divide_by_2(mid);
        prod = (mid * mid);
        if(prod <= a){
            v = mid;
            ++mid;
            left = mid;
        }
        else{
            --mid;
            right = mid;
        }
        mid = BigInt();
    }
    return v;
}

BigInt NthCatalan(int n){
    BigInt a(1),b;
    for (int i = 2; i <= n;i++)
        a *= i;
    b = a;
    for (int i = n + 1; i <= 2 * n;i++)
        b *= i;
    a *= a;
    a *= (n + 1);
    b /= a;
    return b;
}

BigInt NthFibonacci(int n){
    BigInt a(1), b(1), c;
    if(!n)
        return c;
    n--;
    while(n--){
        c = a + b;
        b = a;
        a = c;
    }
    return b;
}

BigInt Factorial(int n){
    BigInt f(1);
    for (int i = 2; i <= n;i++)
        f *= i;
    return f;
}

istream &operator>>(istream &in,BigInt&a){
    string s;
    in >> s;
    int n = s.size();
    for (int i = n - 1; i >= 0;i--){
        if(!isdigit(s[i]))
            throw("INVALID NUMBER");
        a.digits[n - i - 1] = s[i];
    }
    return in;
}

ostream &operator<<(ostream &out,const BigInt &a){
    for (int i = a.digits.size() - 1; i >= 0;i--)
        cout << (short)a.digits[i];
    return cout;
}

class Solution {
public:
    string nearestPalindromic(string n) {
        if(n.length() < 2) return to_string(stoll(n)-1);
        BigInt val = BigInt(n);
        long long half = stoll(n.substr(0,n.length()/2));
        BigInt res(1e18), diff(n);
        BigInt zero(0ull);
        auto check = [&](string x) {
            for(int i = 0, j = x.length() - 1; i < j; i++,j--) {
                if(x[i] != x[j]) return false;
            }
            BigInt X = BigInt(x);
            BigInt d = val > X ? val - X : X - val;
            if(d != zero) {
                if(d < diff or (d == diff and X < res)) {
                    res = X;
                    diff = d;
                    return true;
                }
            }
            return false;
        };
        auto udt = [&](string x) {
            if(check(x)) {
                BigInt now(x);
                BigInt nxt = 2 * val - now;
                check(nxt.toString());
            }
        };
        for(long long i = max(1ll,half - 1000); i <= half + 1000; i++) {
            string s = to_string(i);
            string rev = s;
            reverse(begin(rev), end(rev));
            if(i < 10) udt(s);
            udt(s + rev);
            for(int j = 0; j < 10; j++) {
                string now = s;
                now.push_back(j + '0');
                now += rev;
                udt(now);
            }
        }
        return res.toString();
    }
};