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"""
BOJ #1753. ์ตœ๋‹จ๊ฒฝ๋กœ (๊ณจ๋“œ4)
https://www.acmicpc.net/problem/1753
์œ ํ˜•: Dijkstra , Graph
"""
import sys
import heapq
input = sys.stdin.readline
INF = 1e12
V , E = map(int, input().split())
start = int(input())

graph = [[] for _ in range(V+1)]
for _ in range(E) :
a,b , c =map(int, input().split())
graph[a].append((b,c))

distance = [INF]*(V+1)
# ๋‹ค์ต์ŠคํŠธ๋ผ ํ•จ์ˆ˜
def dijkstra(start) :
q = []
distance[start]=0
heapq.heappush(q,(0,start))
while q :
# 2.๊ฒฝ์œ ์ง€ ๋ฝ‘๊ธฐ
dist , now = heapq.heappop(q)
# 3-1. ์ด๋ฏธ ์ฒ˜๋ฆฌํ•œ ๊ฒฝ์œ ์ง€์ธ ๊ฒฝ์šฐ -> ๋ฌด์‹œ
if distance[now] < dist :
continue
#3-2. ํ˜„์žฌ ๊ฒฝ์œ ์ง€์—์„œ ๋ฐ”๋กœ ๊ฐˆ ์ˆ˜ ์žˆ๋Š” ๋…ธ๋“œ ์ฒ˜๋ฆฌ
for t in graph[now]:
cost = dist + t[1] # ๊ฒฝ์œ ์ง€๋ฅผ ๊ฑฐ์นœ start - t[0] ์˜ ๊ฑฐ๋ฆฌ
if cost < distance[t[0]] : # ๊ฒฝ์œ ์ง€ cost ๊ฐ€ ๋” ์ž‘์œผ๋ฉด ์—…๋ฐ์ดํŠธ
distance[t[0]] = cost
heapq.heappush(q, (cost , t[0]))
#4. ์ถœ๋ ฅ
dijkstra(start)
for node in range(1 , V+1) :
print("INF"if distance[node] >= INF else distance[node] )

16 changes: 16 additions & 0 deletions _WeeklyChallenges/W28-[Graph-Dijkstra]/README.md
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## ๐Ÿš€6์›” 4์ฃผ์ฐจ (6/23) ์Šคํ„ฐ๋”” ๋ฐœ์ œ ์ฃผ์ œ: Dijkstra
> ๋ฐœ์ œ์ž: ๊น€ํ™์ฃผ (zaqquum)

> [!NOTE]
> ์ฃผ์ œ: Dijkstra

### ๐Ÿ—‚๏ธ ์Šคํ„ฐ๋”” ์ž๋ฃŒ
- PDF: [๋ฐ”๋กœ๊ฐ€๊ธฐ
](Study_BOJ_1504.pdf)

### ๐Ÿ“– ๋ฌธ์ œ
- [๋ฐฑ์ค€ #1504. ํŠน์ •ํ•œ ์ตœ๋‹จ๊ฒฝ๋กœ](https://www.acmicpc.net/problem/1504): Dijkstra / ๊ณจ๋“œ 4
- ์ •๋‹ต ์ฝ”๋“œ: [Study_BOJ_1504_ํŠน์ •ํ•œ์ตœ๋‹จ๊ฒฝ๋กœ.py](Study_BOJ_1504_ํŠน์ •ํ•œ์ตœ๋‹จ๊ฒฝ๋กœ.py)
### ๐Ÿ’ป ๊ณผ์ œ
- [๋ฐฑ์ค€ #1753. ์ตœ๋‹จ๊ฒฝ๋กœ](https://www.acmicpc.net/problem/1753): Dijkstra / ๊ณจ๋“œ4
- ์ •๋‹ต ์ฝ”๋“œ: [Assignment_BOJ_1753_์ตœ๋‹จ๊ฒฝ๋กœ.py](Assignment_BOJ_1753_์ตœ๋‹จ๊ฒฝ๋กœ.py)
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"""
BOJ #1504. ํŠน์ •ํ•œ ์ตœ๋‹จ๊ฒฝ๋กœ (๊ณจ๋“œ4)
https://www.acmicpc.net/problem/1504
์œ ํ˜•: Dijkstra , Graph
"""
import sys
import heapq
from collections import deque

INF = 1e9
input = sys.stdin.readline
answer = -1
# 0. ์ž…๋ ฅ ๋ณ€์ˆ˜
N ,E = map(int, input().split())
graph =[[] for _ in range(N+1)] #์ธ์ ‘๋ฆฌ์ŠคํŠธ ์ดˆ๊ธฐํ™”
for i in range(E) :
a, b , cost = map(int, input().split())
graph[a].append([b , cost ]) ; graph[b].append([a, cost])
v1 ,v2 = map(int, input().split())

#1. ๋‹ค์ต์ŠคํŠธ๋ผ ์ดˆ๊ธฐ ์„ค์ • - ์‹œ์ž‘์ 
start =1 ; target = N

#2. ๋‹ค์ต์ŠคํŠธ๋ผ ํ•จ์ˆ˜ ์ •์˜
def dikstra(start) :
# ์ตœ๋‹จ ๊ฑฐ๋ฆฌ ํ…Œ์ด๋ธ” ์ดˆ๊ธฐํ™”
distance =[INF]*(N+1)
q = []
heapq.heappush(q, (0,start))
distance[start] = 0
#[2] ๊ฒฝ์œ ์ง€ ์„ ํƒ
while q :
dist , now = heapq.heappop(q)
#3-1 ํ˜„์žฌ ๋…ธ๋“œ๊ฐ€ ์ด๋ฏธ ์—…๋ฐ์ดํŠธ ์™„๋ฃŒ๋˜๋ฉด ๋ฌด์‹œ
if distance[now] <dist :
continue
#3-2. ํ˜„์žฌ ๋…ธ๋“œ์™€ ์ธ์ ‘ํ•œ ๋…ธ๋“œ ํ™•์ธ , ๋ฐฉ๋ฌธ
for i in graph[now] :
cost = dist + i[1]
# 4. ํ˜„์žฌ ๋…ธ๋“œ now์„ ๊ฒฝ์œ ํ•ด์„œ , ๋‹ค๋ฅธ ๋…ธ๋“œ(i)๋กœ ์ด๋™ํ•˜๋Š” ๊ฑฐ๋ฆฌ๊ฐ€ ๋” ์งง์€ ๊ฒฝ์šฐ
if cost <distance[i[0]] :
distance[i[0]] = cost # ์—…๋ฐ์ดํŠธ
heapq.heappush(q , (cost ,i[0]))
return distance

# 3. v1,v2 ์ง€๋‚˜๋Š” 1- > N ์˜ ์ตœ๋‹จ ๊ฑฐ๋ฆฌ ๊ณ ๋ฅด๊ธฐ
s_distance = dikstra(start)
e_distance = dikstra(target) # ์–‘๋ฐฉํ–ฅ
s_v1 = s_distance[v1]
s_v2 = s_distance[v2]
v1_e = e_distance[v1]
v2_e = e_distance[v2]
v1_v2 = dikstra(v1)[v2] # v1 - v2 ๊ฑฐ๋ฆฌ(๊ณตํ†ต)

answer =min(s_v1 + v2_e , s_v2+v1_e ) + v1_v2
if answer >= INF :
print(-1)
else :
print(answer)


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