哈密頓循環(huán)是哈密頓路徑，因此從哈密頓路徑的最后一個頂點到第一個頂點有一條邊(在圖中)。它在無向圖中是一條路徑，該路徑恰好訪問該圖的每個頂點一次。

功能和目的：Begin

1.function?isSafe()?is?used?to?check?for?whether?it?is?adjacent?to?the?previously?added?vertex?and?already?not?added.

2.?function?hamiltonianCycle()?solves?the?hamiltonian?problem.

3.?function?hamCycle()?uses?hamiltonianCycle()?to?solve?the?hamiltonian?problem.

It?returns?false?if?there?is?no?Hamiltonian?Cycle?possible,?otherwise?return?true?and?prints?the?path.

End

示例#include?

#include?

#include?

#define?N?5

using?namespace?std;

void?displaytheSolution(int?path[]);

bool?isSafe(int?n,?bool?g[N][N],?int?path[],?int?pos)?{

if?(g?[path[pos-1]][n]?==?0)

return?false;

for?(int?i?=?0;?i?

if?(path[i]?==?n)

return?false;

return?true;

}

bool?hamiltonianCycle(bool?g[N][N],?int?path[],?int?pos)?{

//如果所有頂點都包含在哈密頓循環(huán)中

if?(pos?==?N)?{

if?(g[?path[pos-1]?][?path[0]?]?==?1)

return?true;

else

return?false;

}

for?(int?n?=?1;?n?

if?(isSafe(n,?g,?path,?pos))?//Check?if?this?vertex?can?be?added?to?Hamiltonian?Cycle

{

path[pos]?=?n;

//重復構建其余路徑

if?(hamiltonianCycle?(g,?path,?pos+1)?==?true)

return?true;

path[pos]?=?-1;?//remove?vertex?if?it?doesn’t?lead?to?the?solution

}

}

return?false;

}

bool?hamCycle(bool?g[N][N])?{

int?*path?=?new?int[N];

for?(int?i?=?0;?i?

path[i]?=?-1;

//將頂點0作為路徑中的第一個頂點。

If?there?is?a?Hamiltonian?Cycle,?then?the?path?can?be?started?from?any?point

//圖是無向的循環(huán)周期

path[0]?=?0;

if?(hamiltonianCycle(g,?path,?1)?==?false)?{

cout<

return?false;

}

displaytheSolution(path);

return?true;

}

void?displaytheSolution(int?p[])?{

cout<

cout<

for?(int?i?=?0;?i?

cout<

cout<

}

int?main()?{

bool?g[N][N]?=?{

{0,?1,?0,?1,?1},

{0,?0,?1,?1,?0},

{0,?1,?0,?1,?1},

{1,?1,?1,?0,?1},

{0,?1,?1,?0,?0},

};

hamCycle(g);

return?0;

}

輸出結果存在周期：?Following?is?one?Hamiltonian?Cycle

0?4?1?2?3?0

總結

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