全排列的不同写法(茴字的不同写法)及对应的时间开销

资源课件：

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;
}

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～