今天呢在OIwiki上面看到了一个奇怪的生成随机数函数：mt19937年，看到后直接看起来很傻。这是什么？
一开始，我以为这是一个名字M.T.19937937/1937年发明了函数，但回顾过去，他们发现了这一点mt好像是梅森缠绕器(好像有人说是梅森旋转算法)，19937是质数，19937是2^19937-1，随后我只是在网上复制了一段代码，粘到DEV里面，然后我震惊地发现代码CE了
然后我抱着尝试的想法复制到最新版本VS2022年，然后我震惊地发现这个东西真的被编译了，生成了一个数字。看完之后，我决定测试这个随机性，所以我有以下代码
#include <cstdio> #include <ctime> #include <iostream> #include <random> using namespace std; int cnt[30050]; struct val { int x;//下标 int y;//数量 }all; int main() { srand(time(0)); std :: mt19937 rng(time(0)); //1-5000,5001-10000,10001-15000,15001-20000,20001-25000,25001-30000; for (int i = 0; i < 1000000; i ) { unsigned int x = rng() % 30000 1; //unsigned int x = rand() % 30000 1; if (1 <= x && x <= 5000) cnt[1] ; else if (5001 <= x && x <= 10000) cnt[2] ; else if (10001 <= x && x <= 15000) cnt[3] ; else if (15001 <= x && x <= 20000) cnt[4] ; else if (20001 <= x && x <= 25000) cnt[5] ; else cnt[6] ; } cout << "第一个数：1-5000 第二个数：5001-10000 第三个数：10001-15000 第四个数：15001-20000 第五个数：20001-25000 第六个数：25001-30000" << endl; cout << cnt[1] << " " << cnt[2] << " " << cnt[3] << " " << cnt[4] << " " << cnt[5] << " " << cnt[6] << endl; memset(cnt, 0, sizeof(cnt)); for (int i = 0; i < 1000000; i ) { unsigned int x = rng() % 30000 1; //unsigned int x = rand() % 30000 1; cnt[x] ; } int maxn = -1, minn = 1000050; for (int i = 1; i <= 30000; i ) { if (cnt[i] > maxn) maxn = cnt[i]; if (cnt[i] < minn) minn = cnt[i]; } cout << "maxn：最多出现在1-30000中，minn：最少出现在1-30000中" << endl; cout << "maxn - minn = " << maxn - minn << endl; long long sum1 = 0, middle, sum2 = 0; for (int i = 1; i <= 30000; i ) { sum1 = i * cnt[i]; if (sum2 < 500000 && sum2 cnt[i] >= 500000) middle = i 1; sum2 = cnt[i]; } double average = (double)sum1 / 1000000.0; cout << "平均数：" << average << endl; cout << "中位数：" << middle << endl; maxn = -1; for (int i = 1; i <= 30000; i ) if (cnt[i] > maxn) maxn = cnt[i]; for (int i = 1; i <= 30000; i ) if (cnt[i] == maxn) all.x = i, all.y = maxn; cout << "众数：" << all.x; return 0; }经过n次测试，以下是差距最大的组：
可以看到，mt19937的随机性还是很好的，分布均匀，众数随机，平均，中位数接近，maxn-minn相对较小，测试后的随机性，我决定再次测试速度，添加几行代码
#include <cstdio> #include <ctime> #include <iostream> #include <random> using namespace std; int cnt[30050]; struct val { int x;//下标 int y;//数量 }all; int main() { srand(time(0)); std :: mt19937 rng(time(0)); //1-5000,5001-10000,10001-15000,15001-20000,20001-25000,25001-30000; for (int i = 0; i < 1000000; i ) { unsigned int x = rng() % 30000 1; //unsigned int x = rand() % 30000 1; if (1 <= x && x <= 5000) cnt[1] ; else if (5001 <= x && x <= 10000) cnt[2] ; else if (10001 <= x && x <= 15000) cnt[3] ; else if (15001 <= x && x <= 20000) cnt[4] ; else if (20001 <= x && x <= 25000) cnt[5] ; else cnt[6] ; } cout << "第一个数：1-5000 第二个数：5001-10000 第三个数：10001-15000 第四个数：15001-20000 第五个数：20001-25000 第六个数：25001-30000" << endl; cout << cnt[1] << " " << cnt[2] << " " << cnt[3] << " " << cnt[4] << " " << cnt[5] << " " << cnt[6] << endl; memset(cnt, 0, sizeof(cnt)); for (int i = 0; i < 1000000; i ) { unsigned int x = rng() % 30000 1; //unsigned int x = rand() % 30000 1; cnt[x] ; } int maxn = -1, minn = 1000050; for (int i = 1; i <= 30000; i ) { if (cnt[i] > maxn) maxn = cnt[i]; if (cnt[i] < minn) minn = cnt[i]; } cout << "maxn：最多出现在1-30000中，minn：最少出现在1-30000中" << endl; cout << "maxn - minn = " << maxn - minn << endl; long long sum1 = 0, middle, sum2 = 0; for (int i = 1; i <= 30000; i ) { sum1 = i * cnt[i]; if (sum2 < 500000 && sum2 cnt[i] >= 500000) middle = i 1; sum2 = cnt[i]; } double average = (double)sum1 / 1000000.0; cout << "平均数：" << average << endl; cout << "中位数：" << middle << endl; maxn = -1; for (int i = 1; i <= 30000; i ) if (cnt[i] > maxn) maxn = cnt[i]; for (int i = 1; i <= 30000; i ) if (cnt[i] == maxn) all.x = i, all.y = maxn; cout << "众数：" << all.x; clock_t start clock();
for (int i = 0; i < 10000000; i++) {
unsigned int x = rng() % 30000 + 1;
//unsigned int x = rand() % 30000 + 1;
}
cout << endl << "生成10000000个随机数的速度（ms）：" << clock() - start;
return 0;
}这个时候我发现这个mt19937几乎是个O(1)的算法，我准备再测一下rand函数的性能
首先是随机性
代码：
#include <cstdio>
#include <ctime>
#include <iostream>
#include <random>
using namespace std;
int cnt[30050];
struct val {
int x;//下标
int y;//数量
}all;
int main() {
srand(time(0));
std :: mt19937 rng(time(0));
//1-5000,5001-10000,10001-15000,15001-20000,20001-25000,25001-30000;
for (int i = 0; i < 1000000; i++) {
unsigned int x = rng() % 30000 + 1;
//unsigned int x = rand() % 30000 + 1;
if (1 <= x && x <= 5000) cnt[1]++;
else if (5001 <= x && x <= 10000) cnt[2]++;
else if (10001 <= x && x <= 15000) cnt[3]++;
else if (15001 <= x && x <= 20000) cnt[4]++;
else if (20001 <= x && x <= 25000) cnt[5]++;
else cnt[6]++;
}
cout << "第一个数：1-5000 第二个数：5001-10000 第三个数：10001-15000 第四个数：15001-20000 第五个数：20001-25000 第六个数：25001-30000" << endl;
cout << cnt[1] << " " << cnt[2] << " " << cnt[3] << " " << cnt[4] << " " << cnt[5] << " " << cnt[6] << endl;
memset(cnt, 0, sizeof(cnt));
for (int i = 0; i < 1000000; i++) {
unsigned int x = rng() % 30000 + 1;
//unsigned int x = rand() % 30000 + 1;
cnt[x]++;
}
int maxn = -1, minn = 1000050;
for (int i = 1; i <= 30000; i++) {
if (cnt[i] > maxn) maxn = cnt[i];
if (cnt[i] < minn) minn = cnt[i];
}
cout << "maxn：在1-30000中出现最多的数，minn：在1-30000中出现最少的数" << endl;
cout << "maxn - minn = " << maxn - minn << endl;
long long sum1 = 0, middle, sum2 = 0;
for (int i = 1; i <= 30000; i++) {
sum1 += i * cnt[i];
if (sum2 < 500000 && sum2 + cnt[i] >= 500000) middle = i + 1;
sum2 += cnt[i];
}
double average = (double)sum1 / 1000000.0;
cout << "平均数：" << average << endl;
cout << "中位数：" << middle << endl;
maxn = -1;
for (int i = 1; i <= 30000; i++) if (cnt[i] > maxn) maxn = cnt[i];
for (int i = 1; i <= 30000; i++) if (cnt[i] == maxn) all.x = i, all.y = maxn;
cout << "众数：" << all.x;
//clock_t start = clock();
//for (int i = 0; i < 10000000; i++) {
//unsigned int x = rng() % 30000 + 1;
//unsigned int x = rand() % 30000 + 1;
//}
//cout << endl << "生成10000000个随机数的速度（ms）：" << clock() - start;
return 0;
}
对比一下和mt19937函数，发现不论是均匀分布还是最大值-最小值，rand都要比mt19937差一大截
最后是rand的时间
代码：
#include <cstdio>
#include <ctime>
#include <iostream>
#include <random>
using namespace std;
int cnt[30050];
struct val {
int x;//下标
int y;//数量
}all;
int main() {
srand(time(0));
std :: mt19937 rng(time(0));
//1-5000,5001-10000,10001-15000,15001-20000,20001-25000,25001-30000;
for (int i = 0; i < 1000000; i++) {
//unsigned int x = rng() % 30000 + 1;
unsigned int x = rand() % 30000 + 1;
if (1 <= x && x <= 5000) cnt[1]++;
else if (5001 <= x && x <= 10000) cnt[2]++;
else if (10001 <= x && x <= 15000) cnt[3]++;
else if (15001 <= x && x <= 20000) cnt[4]++;
else if (20001 <= x && x <= 25000) cnt[5]++;
else cnt[6]++;
}
cout << "第一个数：1-5000 第二个数：5001-10000 第三个数：10001-15000 第四个数：15001-20000 第五个数：20001-25000 第六个数：25001-30000" << endl;
cout << cnt[1] << " " << cnt[2] << " " << cnt[3] << " " << cnt[4] << " " << cnt[5] << " " << cnt[6] << endl;
memset(cnt, 0, sizeof(cnt));
for (int i = 0; i < 1000000; i++) {
//unsigned int x = rng() % 30000 + 1;
unsigned int x = rand() % 30000 + 1;
cnt[x]++;
}
int maxn = -1, minn = 1000050;
for (int i = 1; i <= 30000; i++) {
if (cnt[i] > maxn) maxn = cnt[i];
if (cnt[i] < minn) minn = cnt[i];
}
cout << "maxn：在1-30000中出现最多的数，minn：在1-30000中出现最少的数" << endl;
cout << "maxn - minn = " << maxn - minn << endl;
long long sum1 = 0, middle, sum2 = 0;
for (int i = 1; i <= 30000; i++) {
sum1 += i * cnt[i];
if (sum2 < 500000 && sum2 + cnt[i] >= 500000) middle = i + 1;
sum2 += cnt[i];
}
double average = (double)sum1 / 1000000.0;
cout << "平均数：" << average << endl;
cout << "中位数：" << middle << endl;
maxn = -1;
for (int i = 1; i <= 30000; i++) if (cnt[i] > maxn) maxn = cnt[i];
for (int i = 1; i <= 30000; i++) if (cnt[i] == maxn) all.x = i, all.y = maxn;
cout << "众数：" << all.x;
clock_t start = clock();
for (int i = 0; i < 10000000; i++) {
//unsigned int x = rng() % 30000 + 1;
unsigned int x = rand() % 30000 + 1;
}
cout << endl << "生成10000000个随机数的速度（ms）：" << clock() - start;
return 0;
}然后后我们可以得出1个结论，rand比mt19937除了适用性外都差很多
最后介绍一下用法，就是再代码前面加上这样一行代码初始化
std :: mt19937 rng(time(0));然后再调用rng()就行了，生成的是unsigned int的范围的随机数，如果用int会有负数
具体的就看OIWIKI吧
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