USACO 1.5 Prime Palindromes (pprime)
2014-02-21 13:34
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/* ID: haolink1 PROG: pprime LANG: C++ */ // For this problem, the usaco give two hint: // 1 Generate the palindromes and see if they are prime. // 2 Generate palindromes by combining digits properly. You might need more than one of the loops like below. ///* generate five digit palindrome: */ //for (d1 = 1; d1 <= 9; d1+=2) { /* only odd; evens aren't so prime */ // for (d2 = 0; d2 <= 9; d2++) { // for (d3 = 0; d3 <= 9; d3++) { // palindrome = 10000*d1 + 1000*d2 +100*d3 + 10*d2 + d1; // ... deal with palindrome ... // } // } //} //Use this two hint, we can found //If a number can be divided exactly by 11, after the sum of its odd digts minus the sum of its even //digits, the difference can be divided exactly by 11.Eg: 1234567, sum of odd digits 1+3+5+7=16 //sum of even digits : 2+4+6=12, 16 -12 = 4, which can't be devided by 11, that is 1234567 can't be //devided by 11. //Considering even palindromes,from above conclusion, it should be devided by 11 exactly,which means they //can't be prime,like 135531, except 11. //Considering odd palindromes, we can construct them by the form like: a*10001+b*1010+c*100 //during enumerating a,b,c..., we find "a" should not be a even value, otherwise, the whole number isn't prime. //#include <iostream> #include <fstream> #include <math.h> using namespace std; ofstream fout("pprime.out"); bool IsPrime(int num){ int temp = sqrt(num); for (int i = 2; i <= temp; i++){ if(num%i==0) return false; } return true; } void CheckValid(int begin,int end,int target_num){ if(target_num >= begin && target_num <= end && IsPrime(target_num)) fout << target_num <<endl; } int main(){ ifstream fin("pprime.in"); int begin = 0; int end = 0; fin >> begin; fin >> end; //Handle special case if(begin == 5) fout << 5 <<endl; if(begin <= 7 && end >= 7) fout << 7 <<endl; if(begin <= 11 && end >= 11) fout << 11 <<endl; //Handle regular case; if(begin <= 999 && end >= 101){ for(short a = 1; a <= 9; a+=2){ for(short b = 0; b <= 9; b++){ CheckValid(begin,end,a*101+b*10); } } } if(begin <= 99999 && end >= 10001){ for(short a = 1; a <= 9; a+= 2){ for(short b = 0; b <= 9; b++){ for(short c = 0; c <= 9; c++){ CheckValid(begin,end,a*10001+b*1010+c*100); } } } } if(begin <= 9999999 && end >= 1000001){ for(short a = 1; a <= 9; a+= 2){ for(short b = 0; b <= 9; b++){ for(short c = 0; c <= 9; c++){ for(short d = 0; d <=9; d++ ){ CheckValid(begin,end,a*1000001+b*100010+c*10100+d*1000); } } } } } return 0; }
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