permutation

在标准库算法中,prev_permutation和next_permutation应用在数列操作上比较广泛.

这个函数可以计算一组数据的全排列.包含在algorithm头文件中.

调用next_permutation使数列逐次增大，这个过程按照字典序增，同理prev_permutation按字典序递减.

如数组a[3]= {0, 1, 2} 有6种排序

0 1 2
0 2 1
1 0 2
1 2 0
2 0 1
2 1 0
令初始排列为 0 1 2 
next_permutation(a, a+ 3);
->0 2 1

prev_permutation(a,
a+ 3);

->0
1 2

现在用操作符重载来实现：

#include<iostream>
#include<algorithm>
using namespace std;
class permu {
public:
permu(int n = 1, int state = 0) : n(n), state(state) {
maxn = 1;
for (int i = 0; i < n; i++) {
a[i] = i;
maxn *= i+1;
}
int tmp = state;
while (tmp--) {
++(*this);
}
}
permu & operator ++() {
state++;
if (state == maxn) {
state = 0;
for (int i = 0; i < n; i++) a[i] = i;
return *this;
}
next_permutation(a, a+n);
return *this;
}
permu operator ++(int x) {
permu tmp(*this);
++(*this);
return tmp;
}
permu & operator --() {
state--;
if (state == -1) {
state = maxn-1;
for (int i = 0; i < n; i++) a[i] = n-i-1;
return *this;
}
prev_permutation(a, a+n);
return *this;
}
permu operator --(int x) {
permu tmp(*this);
--(*this);
return tmp;
}
friend ostream& operator << (ostream& os, const permu& x) {
os << x.a[0];
for (int i = 1; i < x.n; i++) os << " " << x.a[i];
return os;
}
private:
int n;
int a[11];
int state;
int maxn;
};

main函数：
#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
using namespace std;
int main() {
int n, m;
cin >> n >> m;
permu a(n); // n是排列的长度。初始排列为0,1,2,...,n-1
permu b = a;
b = ++a;
cout << b << endl;
b = a++;
cout << b << endl;
for (int i = 0; i < m; i++) {
--a;
}
b = a--;
cout << a << endl;
cout << b << endl;
}