蓝桥杯基础练习VIP-分解质因数 （C++代码）

解题思路:

打表打表，我去年打了个大表

递归一下

没优化...随便写的...不过还是过了，200多ms

注意事项:
还可以再优化，可以用时间换空间，把factors数组的索引改成素数的值，把查找复杂度降到O(1)，然后先判断是否是素数再分解，避免不必要的遍历！

打表打到4999就可以了，再大打不了。如果大于4999的数分解不出说明肯定是素数

参考代码:

#define _CRT_SECURE_NO_WARNINGS
#include <iostream>
#include <vector>
#include <algorithm>
#include <stdio.h>
#define M 200
#define N 200

using namespace std;

int factors[] = {2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509,521,523,541,547,557,563,569,571,577,587,593,599,601,607,613,617,619,631,641,643,647,653,659,661,673,677,683,691,701,709,719,727,733,739,743,751,757,761,769,773,787,797,809,811,821,823,827,829,839,853,857,859,863,877,881,883,887,907,911,919,929,937,941,947,953,967,971,977,983,991,997,1009,1013,1019,1021,1031,1033,1039,1049,1051,1061,1063,1069,1087,1091,1093,1097,1103,1109,1117,1123,1129,1151,1153,1163,1171,1181,1187,1193,1201,1213,1217,1223,1229,1231,1237,1249,1259,1277,1279,1283,1289,1291,1297,1301,1303,1307,1319,1321,1327,1361,1367,1373,1381,1399,1409,1423,1427,1429,1433,1439,1447,1451,1453,1459,1471,1481,1483,1487,1489,1493,1499,1511,1523,1531,1543,1549,1553,1559,1567,1571,1579,1583,1597,1601,1607,1609,1613,1619,1621,1627,1637,1657,1663,1667,1669,1693,1697,1699,1709,1721,1723,1733,1741,1747,1753,1759,1777,1783,1787,1789,1801,1811,1823,1831,1847,1861,1867,1871,1873,1877,1879,1889,1901,1907,1913,1931,1933,1949,1951,1973,1979,1987,1993,1997,1999,2003,2011,2017,2027,2029,2039,2053,2063,2069,2081,2083,2087,2089,2099,2111,2113,2129,2131,2137,2141,2143,2153,2161,2179,2203,2207,2213,2221,2237,2239,2243,2251,2267,2269,2273,2281,2287,2293,2297,2309,2311,2333,2339,2341,2347,2351,2357,2371,2377,2381,2383,2389,2393,2399,2411,2417,2423,2437,2441,2447,2459,2467,2473,2477,2503,2521,2531,2539,2543,2549,2551,2557,2579,2591,2593,2609,2617,2621,2633,2647,2657,2659,2663,2671,2677,2683,2687,2689,2693,2699,2707,2711,2713,2719,2729,2731,2741,2749,2753,2767,2777,2789,2791,2797,2801,2803,2819,2833,2837,2843,2851,2857,2861,2879,2887,2897,2903,2909,2917,2927,2939,2953,2957,2963,2969,2971,2999,3001,3011,3019,3023,3037,3041,3049,3061,3067,3079,3083,3089,3109,3119,3121,3137,3163,3167,3169,3181,3187,3191,3203,3209,3217,3221,3229,3251,3253,3257,3259,3271,3299,3301,3307,3313,3319,3323,3329,3331,3343,3347,3359,3361,3371,3373,3389,3391,3407,3413,3433,3449,3457,3461,3463,3467,3469,3491,3499,3511,3517,3527,3529,3533,3539,3541,3547,3557,3559,3571,3581,3583,3593,3607,3613,3617,3623,3631,3637,3643,3659,3671,3673,3677,3691,3697,3701,3709,3719,3727,3733,3739,3761,3767,3769,3779,3793,3797,3803,3821,3823,3833,3847,3851,3853,3863,3877,3881,3889,3907,3911,3917,3919,3923,3929,3931,3943,3947,3967,3989,4001,4003,4007,4013,4019,4021,4027,4049,4051,4057,4073,4079,4091,4093,4099,4111,4127,4129,4133,4139,4153,4157,4159,4177,4201,4211,4217,4219,4229,4231,4241,4243,4253,4259,4261,4271,4273,4283,4289,4297,4327,4337,4339,4349,4357,4363,4373,4391,4397,4409,4421,4423,4441,4447,4451,4457,4463,4481,4483,4493,4507,4513,4517,4519,4523,4547,4549,4561,4567,4583,4591,4597,4603,4621,4637,4639,4643,4649,4651,4657,4663,4673,4679,4691,4703,4721,4723,4729,4733,4751,4759,4783,4787,4789,4793,4799,4801,4813,4817,4831,4861,4871,4877,4889,4903,4909,4919,4931,4933,4937,4943,4951,4957,4967,4969,4973,4987,4993,4999};

void getFactors(int& n, vector<int>& facs)
{
    for(int i = 0;i < sizeof(factors)/sizeof(int);i++)
    {
        if(factors[i] > n)
            return;
        else if(n % factors[i] == 0)
        {
            facs.push_back(factors[i]);
            n /= factors[i];
            getFactors(n, facs);
        }
    }
}

void showFactors(int n, vector<int>& facs)
{
    cout << n << "=";

    if(facs.size() == 0)
    {
        cout << n << endl;
        return;
    }

    for(vector<int>::iterator it = facs.begin();it < facs.end();it++)
    {
        if(it == --facs.end())
            cout << *it;
        else
            cout << *it << "*";

    }
    cout << endl;
}

int main()
{
    int a,b;
    cin >> a >> b;

    for(int i = a;i <= b;i++)
    {
        vector<int> v;
        int iBak = i;
        getFactors(i, v);
        i = iBak;
        showFactors(i, v);
    }
    return 0;
}

#include <cstdio>
#include <string>
#include <algorithm>
#include <cmath>
#include <vector>
#include <iostream>
using namespace std;
const int maxn = 10010;

int primeCheck[maxn];
vector<int> primeList;

int getPrime(int n){
	for(int i = 2; i <= n; i++){
		if(primeCheck[i] == 0) primeList.push_back(i);
		for(int j = 0; j < primeList.size() && i*primeList[j] <= n; j++){
			primeCheck[i*primeList[j]] = 1;
			if(i % primeList[j] == 0) break;
		}
	}
}

int main(void){
	int a,b;
	cin >> a >> b;
	getPrime(b);
	for(int i = a; i <= b; i++){
		vector<int> vec;
		int tmp_i = i;
		for(int j = 0; j < primeList.size() && primeList[j] <= sqrt(1.0*tmp_i); j++){
			if(tmp_i % primeList[j] == 0){
				do{
					vec.push_back(primeList[j]);
					tmp_i /= primeList[j];
				}while(tmp_i % primeList[j] == 0);
			}
		}
		if(tmp_i != 1){
			vec.push_back(tmp_i);
		}
		printf("%d=",i);
		for(vector<int>::iterator it = vec.begin(); it != vec.end(); it++){
			if(it > vec.begin()) cout << '*';
			cout << *it;
		}
		cout << endl;
	} 
	return 0;
}