洛谷P3366 【模板】最小生成树.Prim算法

题目：https://www.luogu.com.cn/problem/P3366

普利姆算法：

每次选(与已选的点相连的)最小边,循环n-1次

C语言：

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

const int MaxValue = 0x7fffffff;
int n, m;
int a[5005][5005], dis[5005], vis[5005];

int min(int a, int b)
{
    if (a > b)
        return b;
    else
        return a;
}

void Prim()
{
    int i, tot = 1, min1, j, sum = 0;

    while (tot < n)
    {
        min1 = MaxValue;
        j = 0;
        for (i = 1; i <= n; i++)    //找到最小边
        {
            if (vis[i] == 0 && dis[i] < min1)
            {
                j = i;
                min1 = dis[i];
            }
        }

        if (j == 0) //不连通
        {
            printf("orz");
            return ;
        }
        tot += 1;
        vis[j] = 1;
        sum += dis[j];
        for (i = 1; i <= n; i++)
        {
            if (vis[i] == 0 && dis[i] > a[j][i])
                dis[i] = a[j][i];
        }
    }

    printf("%d", sum);
}


int main()
{
    int i, x, y, z, j;

    scanf("%d%d", &n, &m);
    memset(vis, 0, sizeof(vis));
    for (i = 1; i <= n; i++)
    {
        dis[i] = MaxValue;
        for (j = 1; j <= n; j++)
            a[i][j] = MaxValue;
    }
    for (i = 0; i < m; i++)
    {
        scanf("%d%d%d", &x, &y, &z);
        a[x][y] = min(a[x][y], z);
        a[y][x] = min(a[x][y], z);
        if (x == 1) //先选定1点
            dis[y] = min(dis[y], z);
        else if (y == 1)
            dis[x] = min(dis[x], z);
    }
    vis[1] = 1;
    Prim();

    return 0;
}

Python：

用字典类型 + 结构体数组 存储边：

定义：

class Edge():
    def __init__(self, _y, _data):
        self.y = _y
        self.data = _data

造边：

for i in range(m):
    s = input()
    x, y, z = s.split(' ')    #从x到y，长度z
    x = int(x)
    y = int(y)
    z = int(z)
    if x in edg.keys():    #x中是否已有数
        a = edg[x]    #有
    else:
        a = []    #无则创造列表
    a.append(Edge(y, z))    
    edg[x] = a    

代码：

class Edge():
    def __init__(self, _y, _data):
        self.y = _y
        self.data = _data


s = input()
n, m = s.split(' ')
n = int(n)
m = int(m)
edg = {}
dis = [0x7fffffff for i in range(n + 5)]
vis = [0 for i in range(n + 5)]
for i in range(m):
    s = input()
    x, y, z = s.split(' ')
    x = int(x)
    y = int(y)
    z = int(z)
    if x in edg.keys():
        a = edg[x]
    else:
        a = []
    a.append(Edge(y, z))
    edg[x] = a
    if y in edg.keys():
        a = edg[y]
    else:
        a = []
    a.append(Edge(x, z))
    edg[y] = a
    if x == 1:
        dis[y] = min(dis[y], z)
    elif y == 1:
        dis[x] = min(dis[x], z)

tot = 1
vis[1] = 1
ans = 0
while tot < n:
    min1 = 0x7fffffff
    j = 0
    for i in range(1, n + 1):
        if dis[i] < min1 and vis[i] == 0:
            j = i
            min1 = dis[i]
    if j == 0:
        print("orz")
        exit(0)
    vis[j] = 1
    tot += 1
    ans += dis[j]
    for i in edg[j]:
        if i.data < dis[i.y] and vis[i.y] == 0:
            dis[i.y] = i.data
print(ans)