#include <iostream> #include <string> #include <vector> #include <stdio.h> #include <string.h> using namespace std; #define MODDER 1000000000 #define DIGITSIZE 9 #define INT32 int #define INT64 long long class BigInteger { vector<int> digit; short signum; static bool CHECK; int setSignum(INT64&); BigInteger add(const BigInteger &) const; BigInteger subtract(const BigInteger &) const; char* trim(char *); public: BigInteger() { signum = 0; } BigInteger(INT64); BigInteger(char*); BigInteger(string&); BigInteger(const BigInteger&); BigInteger operator = (INT64); BigInteger operator = (char *); BigInteger operator = (string &); BigInteger operator = (BigInteger); BigInteger operator + (const BigInteger&) const; BigInteger operator - (const BigInteger&) const; bool operator == (const BigInteger&) const; bool operator < (const BigInteger&) const; bool operator <= (const BigInteger&) const; void setCheck(bool check); string toString(); void printDigit(); }; bool BigInteger::CHECK; inline int BigInteger::setSignum(INT64 &n) { if (n == 0) signum = 0; else if (n > 0) signum = 1; else { signum = -1; n = -n; } return signum; } BigInteger BigInteger::add(const BigInteger &b) const { BigInteger temp; int i; int len1 = digit.size(); int len2 = b.digit.size(); int minLen = len1 < len2 ? len1 : len2; int digitSum = 0, carry = 0; for (i = 0; i < minLen; i++) { digitSum = carry + digit[i] + b.digit[i]; temp.digit.push_back(digitSum % MODDER); carry = digitSum / MODDER; } if (len1 == len2 && carry) temp.digit.push_back(carry); else if (len1 > len2) { while (i < len1) { digitSum = carry + digit[i++]; temp.digit.push_back(digitSum % MODDER); carry = digitSum / MODDER; } if (carry) temp.digit.push_back(carry); } else { while (i < len2) { digitSum = carry + b.digit[i++]; temp.digit.push_back(digitSum % MODDER); carry = digitSum / MODDER; } if (carry) temp.digit.push_back(carry); } temp.signum = 1; return temp; } BigInteger BigInteger::subtract(const BigInteger &b) const { BigInteger temp; int size = b.digit.size(); int borrow = 0, prevBorrow = 0, i; for (i = 0; i < size; i++) { borrow = (digit[i] - prevBorrow) < b.digit[i] ? 1 : 0; temp.digit.push_back((digit[i] - prevBorrow) + borrow*MODDER - b.digit[i]); prevBorrow = borrow ? 1 : 0; } int biggerSize = digit.size(); while (i < biggerSize) { temp.digit.push_back(digit[i] - prevBorrow); i++; prevBorrow = 0; } i--; while (temp.digit[i] == 0) { temp.digit.pop_back(); i--; } temp.signum = 1; return temp; } char* BigInteger::trim(char *n) { int len = strlen(n); int index = 0, i; char *nnew = new char[len]; if (n[0] == '-' || n[0] == '+') { nnew[0] = n[0]; index++; } for (i = index; n[i] == '0'; i++); if (i == len) { strcpy(nnew, "0"); return nnew; } if (i != index) { while (i != len) nnew[index++] = n[i++]; } nnew[index] = 0; return nnew; } BigInteger::BigInteger(INT64 n) { setSignum(n); while (n) { digit.push_back(n % MODDER); n /= MODDER; } } BigInteger::BigInteger(char *n) { if (((n[0] == '+' || n[0] == '-') && n[1] == '0') || n[0] == '0') n = trim(n); int length, msb; char tempDigit[DIGITSIZE + 1]; for (length = msb = 0; n[length] != 0; length++) { if (n[length] == '0') msb++; } if (msb == length) { signum = 0; return; } if (n[0] == '-') { signum = -1; length--; msb = 1; } else if (n[0] == '+') { signum = 1; length--; msb = 1; } else { signum = 1; msb = 0; } if (length <= DIGITSIZE) { memcpy(tempDigit, n + msb, length); tempDigit[length] = '\0'; digit.push_back(stoi(tempDigit)); } else { int k = length, chunkLen; while (k != 0) { k -= DIGITSIZE; chunkLen = k >= 0 ? DIGITSIZE : k + DIGITSIZE; k = k < 0 ? 0 : k; memcpy(tempDigit, n + msb + k, chunkLen); tempDigit[chunkLen] = '\0'; digit.push_back(stoi(tempDigit)); } } } BigInteger::BigInteger(string &n) { int l = n.length(); char *num = new char[l + 1]; for (int i = 0; i < l; i++) num[i] = n[i]; num[l] = 0; (*this) = num; } BigInteger::BigInteger(const BigInteger &n) { digit = n.digit; signum = n.signum; } BigInteger BigInteger::operator=(INT64 n) { digit.clear(); if (setSignum(n) == 0) { char ret[] = "0"; return ret; } while (n) { digit.push_back(n % MODDER); n /= MODDER; } return *this; } BigInteger BigInteger::operator=(char *n) { BigInteger temp(n); (*this) = temp; return *this; } BigInteger BigInteger::operator=(string &n) { BigInteger temp(n); (*this) = temp; return *this; } BigInteger BigInteger::operator=(BigInteger b) { digit = b.digit; signum = b.signum; return *this; } BigInteger BigInteger::operator+(const BigInteger &b) const { if (b.signum == 0) return *this; if (signum == 0) return b; if (signum == 1 && b.signum == 1) return (*this).add(b); if (signum == 1 && b.signum == -1) return (*this).subtract(b); if (signum == -1 && b.signum == 1) return b.subtract(*this); BigInteger temp = (*this).add(b); if (temp.signum == 1) temp.signum = -1; return temp; } BigInteger BigInteger::operator-(const BigInteger &b) const { if ((*this) == b) { char ret[] = "0"; return ret; } if (signum == 1 && b.signum == 1) { if (*this < b) { BigInteger temp = b.subtract((*this)); temp.signum = -1; return temp; } else return (*this).subtract(b); } if (signum == 1 && b.signum == -1) return (*this).add(b); if (signum == -1 && b.signum == 1) { BigInteger temp = (*this).add(b); temp.signum = -1; return temp; } if (*this < b) { BigInteger temp = (*this).subtract(b); temp.signum = -1; return temp; } return b.subtract((*this)); } bool BigInteger::operator==(const BigInteger &b) const { if (signum != b.signum) return false; if (signum == 0) return true; int size1 = digit.size(); int size2 = b.digit.size(); if (size1 == size2) { int i = 0; while (i < size1) { if (digit[i] == b.digit[i]) i++; else return false; } if (i == size1) return true; } return false; } bool BigInteger::operator<(const BigInteger &b) const { if (signum != b.signum) return signum < b.signum; int size1 = digit.size(); int size2 = b.digit.size(); switch (signum) { case 1: if (size1 == size2) { int i = size1 - 1; while (i >= 0) { if (digit[i] == b.digit[i]) i--; else return digit[i] < b.digit[i]; } if (i == size1) return false; } return size1 < size2; case -1: if (size1 == size2) { int i = size1 - 1; while (i >= 0) { if (digit[i] == b.digit[i]) i--; else return digit[i] > b.digit[i]; } if (i == size1) return false; } return size1 > size2; } } bool BigInteger::operator<=(const BigInteger &b) const { if (*this < b || *this == b) return true; return false; } inline void BigInteger::setCheck(bool check) { CHECK = check; } string BigInteger::toString() { if (signum == 0) return "0"; int length = digit.size(); string number, temp; int len; number = to_string(digit[length - 1]); for (int i = length - 2; i >= 0; i--) { temp = to_string(digit[i]); len = temp.length(); if (len != DIGITSIZE) temp.insert(0, DIGITSIZE - len, '0'); number += temp; } if (signum == -1) return "-" + number; return number; } //void BigInteger::printDigit() //{ // for (int i = 0; i < digit.size(); i++) // printf("digit %d: %d\n", i, digit[i]); //} BigInteger fib[120]; string toFibinary(BigInteger &b) { vector<int> chosenFibs; int i = 1, length; while (fib[i] <= b) { i++; } length = i - 1; i -= 2; chosenFibs.push_back(length); b = b - fib[length]; BigInteger zero; while (!(b == zero)) { while (b < fib[i]) i--; b = b - fib[i]; chosenFibs.push_back(i); } char *fibinary = new char[length]; memset(fibinary, '0', length); int size = chosenFibs.size(); for (int i = 0; i < size; i++) fibinary[length - chosenFibs[i]] = '1'; fibinary[length] = 0; return fibinary; } int main() { fib[1] = 1; fib[2] = 2; for (int i = 3; i < 120; i++) fib[i] = fib[i - 1] + fib[i - 2]; string n1, n2; BigInteger sum; int len, i; bool firsttime = true; while (cin >> n1 >> n2) { if(!firsttime) printf("\n"); if (n1 == "0" && n2 == "0") { printf("0\n"); continue; } len = n1.length(); for (i = 0; i < len; i++) { if (n1[i] == '1') sum = sum + fib[len - i]; } len = n2.length(); for (i = 0; i < len; i++) { if (n2[i] == '1') sum = sum + fib[len - i]; } cout << toFibinary(sum) << endl; sum = "0"; firsttime = false; } return 0; }
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