版本 fda0dc8b42cd57f2d394539a419754537efec382

acm/course/MST

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#MST(Minimum Spanning Tree, 最小生成樹)
##Spanning Tree(生成樹)
1.一棵<b>包含圖上所有點</b>的樹，稱作該圖的生成樹

2.一張圖的生成樹可能會有很多種

3.完全連通圖才有生成樹(不連通時，則稱為生成森林)

4.生成樹的權重為樹上每條邊的權重總和

##Minimum Spanning Tree
擁有最小權重的生成樹，稱為最小生成樹

###Kruskal’s algorithm(greedy based)
1.依照權重排序

2.選擇較小的邊，並邊檢查是否有迴圈

![](/acm/MST_Kruskal.gif)

* Psuedocode

        totalcost← 0 

        for each v ∈ V

            do MAKE-SET (v)

        sort the edges into non-decreasing order by weight

        for each edge (u, v) ∈ E, taken in non-decreasing order

            do if FIND-SET (u) ≠ FIND-SET (v)

                then UNION (u, v) 

                    totalcost← totalcost+ w(u, v)

        return totalcost

###Prim’s algorithm(relaxation based)

```c++
#include <cstdio>
using namespace std;
int main()
{
}
```