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[8];
    sum=a*b;
    itoa(sum,num,10);
    for(i=0,j=strlen(num)-1;i<j;i++,j--)
        if(num[i]!=num[j])
            return(0);
    return(1);
}

int main()            /*problem4-Largest palindrome product*/
{
    int i,j,max=0,m1=0,m2=0;
    for(i=999;i>=100;i--)
        for(j=i;j>=100;j--)
        {
            if(i%11!=0&&j%11!=0)            //剪枝，i,j之中必有一个为11倍数
                continue;
            if(palindrome(i,j)==1&&i*j>max)
            {
                max=i*j;
                m1=i;
                m2=j;
            }
        }
    printf("max palindrome is %d=%d*%d
",max,m1,m2);
    return(0);
}