project euler problem 12

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Highly divisible triangular number

Problem 12

The sequence of triangle numbers is generated by adding the natural numbers. So the 7^th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. The first ten terms would be:

1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...

Let us list the factors of the first seven triangle numbers:

1: 1
3: 1,3
6: 1,2,3,6
10: 1,2,5,10
15: 1,3,5,15
21: 1,3,7,21
28: 1,2,4,7,14,28

We can see that 28 is the first triangle number to have over five divisors.

What is the value of the first triangle number to have over five hundred divisors?

此题刚开始不敢尝试，因为做过了，超时了，等了好久，还没出来结果。所以做到了第16题，又做了POJ的一些题目，然后对记忆化递归了解了才写了这道题。

#include <iostream>#include <map>#include <string>#include <cstring>#include <cstdio>#include <cmath>#include <algorithm>using namespace std;int cmp(int n){    if(n==1) return 1;    int sum=cmp(n-1)+n;  //直接记住结果，就不会超时了。    return sum;}int abc(int n){    int i,sum=0;    for(i=1;i<=sqrt(n*1.0);i++)        if(n%i==0) sum++;   //虽然用了sqrt，但是还是超过了1秒，这个用不了记忆化，所以时间还是有点多。    return sum;}int main(){    int i;    for(i=1000;;i++)        if(abc(cmp(i))>=250) {cout<<cmp(i)<<endl;break;}  //因为sqrt之前的就知道了总共的因子了，乘以2就是其因子数。    return 0;}