Problem4-Project Euler

Largest palindrome product

 

A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 × 99.

Find the largest palindrome made from the product of two 3-digit numbers.

寻找能够分解为两个三位数乘积的回文数：

先分析，回文数范围在：100^2=10000到999^2=998001之间，暴力也可行……但适当剪枝会快一些

考虑100000及以上时，回文数能被11整除，在循环中就可以抛去其它部分数，解答会快一些。

还想用用时间换空间可以先打个质数表……之类的

 #include"stdio.h"
 #include"stdlib.h"
 #include"string.h"

 int palindrome(int a,int b)        /*palindrome function:to test if a product is palindrome*/
 {
     int sum,i,j;
     char num[];
     sum=a*b;
     itoa(sum,num,);
     for(i=,j=strlen(num)-;i<j;i++,j--)
         if(num[i]!=num[j])
             return();
     return();
 }

 int main()            /*problem4-Largest palindrome product*/
 {
     int i,j,max=,m1=,m2=;
     for(i=;i>=;i--)
         for(j=i;j>=;j--)
         {
             if(i%!=&&j%!=)            //剪枝，i,j之中必有一个为11倍数
                 continue;
             if(palindrome(i,j)==&&i*j>max)
             {
                 max=i*j;
                 m1=i;
                 m2=j;
             }
         }
     printf("max palindrome is %d=%d*%d\n",max,m1,m2);
     return();
 }