资源课件：
- CS106B-recursion-ppt
- stanford library-timer.h
- stanford library-set.h
不同的方法
1------
Set<string> permutations1Rec(string remaining) {
Set<string> res;
if(remaining.size() == 0) {
res += "";
}
else {
for(int i = 0; i < remaining.size(); ++i) {
char selectCharacter = remaining[i];
string newRemaining = remaining.substr(0, i) + remaining.substr(i+1);
Set<string> subres = permutations1Rec(newRemaining);
for(auto str : subres) {
res += selectCharacter + str;
}
}
}
return res;
}
void permutations1(const string &str) {
Set<string> res = permutations1Rec(str);
cout << res << endl;
}
2------
Set<string> permutations2Rec(string remaining) {
Set<string> res;
if(remaining.size() == 0) {
res += "";
}
else {
char firstCharacter = remaining[0];
string newRemaining = remaining.substr(1);
Set<string> subres = permutations2Rec(newRemaining);
for(string subpermutation : subres) {
for(int i = 0; i <= subpermutation.size(); ++i) {
string subpermutationCp = subpermutation;
subpermutationCp.insert(subpermutationCp.begin() + i, firstCharacter);
res += subpermutationCp;
}
}
}
return res;
}
void permutations2(const string &str) {
Set<string> res = permutations2Rec(str);
cout << res << endl;
}
3------
Set<string> permutations3Rec(string str, int pos) {
Set<string> res;
if(pos == str.size()) {
res += str;
}
else {
for(int i = pos; i < str.size(); ++i) {
if(i == pos || str[i] != str[pos]) {
swap(str[i], str[pos]);
res += permutations3Rec(str, pos+1);
swap(str[i], str[pos]);
}
}
}
return res;
}
void permutations3(const string &str) {
Set<string> res = permutations3Rec(str, 0);
cout << res << endl;
}
4------
Set<string> permutations4Rec(string remaining,
string alreadyMade) {
Set<string> res;
if(remaining.size() == 0) {
res += alreadyMade;
}
else {
for(int i = 0; i < remaining.size(); ++i) {
string newRemaining = remaining.substr(0, i) + remaining.substr(i+1);
res += permutations4Rec(newRemaining, alreadyMade+remaining[i]);
}
}
return res;
}
void permutations4(const string &str) {
Set<string> res = permutations4Rec(str, "");
cout << res << endl;
}
运行代码
其中X为不同写法，permutationsXRec为具体实现函数，permutationsX为wrapper 函数。
#include <iostream>
#include "set.h"
#include "timer.h"
using namespace std;
Set<string> permutations1Rec(string remaining) {
Set<string> res;
if(remaining.size() == 0) {
res += "";
}
else {
for(int i = 0; i < remaining.size(); ++i) {
char selectCharacter = remaining[i];
string newRemaining = remaining.substr(0, i) + remaining.substr(i+1);
Set<string> subres = permutations1Rec(newRemaining);
for(auto str : subres) {
res += selectCharacter + str;
}
}
}
return res;
}
void permutations1(const string &str) {
Set<string> res = permutations1Rec(str);
cout << res << endl;
}
Set<string> permutations2Rec(string remaining) {
Set<string> res;
if(remaining.size() == 0) {
res += "";
}
else {
char firstCharacter = remaining[0];
string newRemaining = remaining.substr(1);
Set<string> subres = permutations2Rec(newRemaining);
for(string subpermutation : subres) {
for(int i = 0; i <= subpermutation.size(); ++i) {
string subpermutationCp = subpermutation;
subpermutationCp.insert(subpermutationCp.begin() + i, firstCharacter);
res += subpermutationCp;
}
}
}
return res;
}
void permutations2(const string &str) {
Set<string> res = permutations2Rec(str);
cout << res << endl;
}
Set<string> permutations3Rec(string str, int pos) {
Set<string> res;
if(pos == str.size()) {
res += str;
}
else {
for(int i = pos; i < str.size(); ++i) {
if(i == pos || str[i] != str[pos]) {
swap(str[i], str[pos]);
res += permutations3Rec(str, pos+1);
swap(str[i], str[pos]);
}
}
}
return res;
}
void permutations3(const string &str) {
Set<string> res = permutations3Rec(str, 0);
cout << res << endl;
}
Set<string> permutations4Rec(string remaining,
string alreadyMade) {
Set<string> res;
if(remaining.size() == 0) {
res += alreadyMade;
}
else {
for(int i = 0; i < remaining.size(); ++i) {
string newRemaining = remaining.substr(0, i) + remaining.substr(i+1);
res += permutations4Rec(newRemaining, alreadyMade+remaining[i]);
}
}
return res;
}
void permutations4(const string &str) {
Set<string> res = permutations4Rec(str, "");
cout << res << endl;
}
int main() {
Timer tim;
tim.start();
cout << "....." << endl;
tim.stop();
cout << "The code took " << tim.elapsed() << "ms to finish." << endl;
tim.start();
permutations1("123");
tim.stop();
cout << "The code took " << tim.elapsed() << "ms to finish." << endl;
tim.start();
permutations2("123");
tim.stop();
cout << "The code took " << tim.elapsed() << "ms to finish." << endl;
tim.start();
permutations3("123");
tim.stop();
cout << "The code took " << tim.elapsed() << "ms to finish." << endl;
tim.start();
permutations4("123");
tim.stop();
cout << "The code took " << tim.elapsed() << "ms to finish." << endl;
return 0;
}
…
The code took 34ms to finish.
{“123”, “132”, “213”, “231”, “312”, “321”}
The code took 2ms to finish.
{“123”, “132”, “213”, “231”, “312”, “321”}
The code took 2ms to finish.
{“123”, “132”, “213”, “231”, “312”, “321”}
The code took 2ms to finish.
{“123”, “132”, “213”, “231”, “312”, “321”}
The code took 3ms to finish.
时间测试（非正式）
int main() {
Timer tim;
tim.start();
cout << "....." << endl;
tim.stop();
cout << "The code took " << tim.elapsed() << "ms to finish." << endl;
tim.start();
permutations1("12345678");
tim.stop();
cout << "The code-1 took " << tim.elapsed() << "ms to finish." << endl;
tim.start();
permutations2("12345678");
tim.stop();
cout << "The code-2 took " << tim.elapsed() << "ms to finish." << endl;
tim.start();
permutations3("12345678");
tim.stop();
cout << "The code-3 took " << tim.elapsed() << "ms to finish." << endl;
tim.start();
permutations4("12345678");
tim.stop();
cout << "The code-4 took " << tim.elapsed() << "ms to finish." << endl;
tim.start();
permutations1("12345678");
tim.stop();
cout << "The code-1 took " << tim.elapsed() << "ms to finish." << endl;
tim.start();
permutations2("12345678");
tim.stop();
cout << "The code-2 took " << tim.elapsed() << "ms to finish." << endl;
tim.start();
permutations3("12345678");
tim.stop();
cout << "The code-3 took " << tim.elapsed() << "ms to finish." << endl;
tim.start();
permutations4("12345678");
tim.stop();
cout << "The code-4 took " << tim.elapsed() << "ms to finish." << endl;
return 0;
}
The code took 38ms to finish.
The code-1 took 1150ms to finish.
The code-2 took 279ms to finish.
The code-3 took 1077ms to finish.
The code-4 took 1135ms to finish.
The code-1 took 1141ms to finish.
The code-2 took 279ms to finish.
The code-3 took 1071ms to finish.
The code-4 took 1129ms to finish.
感受
- 其实第一种方法和第四种方法它们思想是几乎一致的，从时间上它们也很接近。
- 第三种方法比1、4快些，但是函数调用依旧在
for循环里，开销较大。 - 第二种方法函数调用在
for循环外面，节省了很多时间。似乎也更好理解一些？ - 这里纯属娱乐，学的比较晕，记录一下～
