Problem:


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Single Source Shortest Path

For a given weighted graph $G = (V, E)$, find the shortest path from a source to each vertex. For each vertex $u$, print the total weight of edges on the shortest path from vertex $0$ to $u$.

Input

  In the first line, an integer $n$ denoting the number of vertices in $G$ is given. In the following $n$ lines, adjacency lists for each vertex $u$ are respectively given in the following format:

$u$ $k$ $v_1$ $c_1$ $v_2$ $c_2$ ... $v_k$ $c_k$

  Vertices in $G$ are named with IDs $0, 1, ..., n-1$. $u$ is ID of the target vertex and $k$ denotes its degree. $v_i (i = 1, 2, ... k)$ denote IDs of vertices adjacent to $u$ and $c_i$ denotes the weight of a directed edge connecting $u$ and $v_i$ (from $u$ to $v_i$).

Output

  For each vertex, print its ID and the distance separated by a space character in a line respectively. Print in order of vertex IDs.

Constraints

$1 \leq n \leq 100$

$0 \leq c_i \leq 100,000$

$|E| \leq 10,000$

All vertices are reachable from vertex $0$

Sample Input 1

5
0 3 2 3 3 1 1 2
1 2 0 2 3 4
2 3 0 3 3 1 4 1
3 4 2 1 0 1 1 4 4 3
4 2 2 1 3 3

Sample Output 1

0 0
1 2
2 2
3 1
4 3

Reference

Introduction to Algorithms, Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. The MIT Press.



Sample input:
5
0 3 2 3 3 1 1 2
1 2 0 2 3 4
2 3 0 3 3 1 4 1
3 4 2 1 0 1 1 4 4 3
4 2 2 1 3 3


Sample output:
0 0
1 2
2 2
3 1
4 3

Submission status: Runtime Error

Solution code:
INFTY = 1 << 21
WHITE = 0
GRAY = 1
BLACK = 2
 
n = int(input())
M = [list(map(int, input().split())) for i in range(n)]
 
d = [INFTY for i in range(n)]
color = [WHITE for i in range(n)]
 
for i in range(n):
    u = int(input())
    k = int(input())
    for j in range(k):
        v = int(input())
        c = int(input())
        M[u][v] = c
        
def dijkstra():
    global M, d, color
    d[0] = 0
    color[0] = GRAY
    while(1):
        minv = INFTY
        u = -1
        for i in range(n):
            if (minv > d[i] and color[i] != BLACK):
                u = i
                minv = d[i]
        if (u == -1):
            break
        color[u] = BLACK
        for v in range(n):
            if (color[v] != BLACK and M[u][v] != INFTY):
                if (d[v] > d[u] + M[u][v]):
                    d[v] = d[u] + M[u][v]
                    color[v] = GRAY
    for i in range(n):
        print(i, (-1 if d[i] == INFTY else d[i]))
dijkstra()

Submission status: Runtime Error

Solution code:
INFTY = 1 << 21
WHITE = 0
GRAY = 1
BLACK = 2
 
n = int(input())
M = [list(map(int, input().split())) for i in range(n)]
 
d = [INFTY for i in range(n)]
color = [WHITE for i in range(n)]
 
for i in range(n):
    u = int(input())
    k = int(input())
    for j in range(k):
        v = int(input())
        c = int(input())
        M[u][v] = c
        
def dijkstra():
    global M, d, color
    d[0] = 0
    color[0] = GRAY
    while(1):
        minv = INFTY
        u = -1
        for i in range(n):
            if (minv > d[i] and color[i] != BLACK):
                u = i
                minv = d[i]
        if (u == -1):
            break
        color[u] = BLACK
        for v in range(n):
            if (color[v] != BLACK and M[u][v] != INFTY):
                if (d[v] > d[u] + M[u][v]):
                    d[v] = d[u] + M[u][v]
                    color[v] = GRAY
    for i in range(n):
        print(str(i), (-1 if d[i] == INFTY else str(d[i])))
dijkstra()

Submission status: Runtime Error

Solution code:
INFTY = 1 << 21
WHITE = 0
GRAY = 1
BLACK = 2
 
n = int(input())
M = [list(map(int, input().split())) for i in range(n)]
for u in range(0, n):
    U = list(map(int, input().split()[2:]))
    for j in range(0, len(U), 2):
        M[u][U[j]] = U[j + 1]
d = [INFTY for i in range(n)]
color = [WHITE for i in range(n)]

def dijkstra():
    global M, d, color, n
    d[0] = 0
    color[0] = GRAY
    while(1):
        minv = INFTY
        u = -1
        for i in range(n):
            if (minv > d[i] and color[i] != BLACK):
                u = i
                minv = d[i]
        if (u == -1):
            break
        color[u] = BLACK
        for v in range(n):
            if (color[v] != BLACK and M[u][v] != INFTY):
                if (d[v] > d[u] + M[u][v]):
                    d[v] = d[u] + M[u][v]
                    color[v] = GRAY
    for i in range(n):
        print(str(i), (-1 if d[i] == INFTY else str(d[i])))
dijkstra()

Submission status: Runtime Error

Solution code:
INFTY = 1 << 21
WHITE = 0
GRAY = 1
BLACK = 2
 
n = int(input())
M = [list(map(int, input().split())) for i in range(n)]
 
d = [INFTY for i in range(n)]
color = [WHITE for i in range(n)]
 
for u in range(n):
    U = list(map(int, input().split()[2:]))
    for j in range(0, len(U), 2):
        M[u][U[j]] = U[j + 1]
        
def dijkstra():
    global M, d, color
    d[0] = 0
    color[0] = GRAY
    while(1):
        minv = INFTY
        u = -1
        for i in range(n):
            if (minv > d[i] and color[i] != BLACK):
                u = i
                minv = d[i]
        if (u == -1):
            break
        color[u] = BLACK
        for v in range(n):
            if (color[v] != BLACK and M[u][v] != INFTY):
                if (d[v] > d[u] + M[u][v]):
                    d[v] = d[u] + M[u][v]
                    color[v] = GRAY
    for i in range(n):
        print(str(i), (-1 if d[i] == INFTY else str(d[i])))
dijkstra()

Submission status: Runtime Error

Solution code:
rootList = [-1 for i in range(n)]
parent = [0 for i in range(n)]
lenList = [0 for i in range(n)]

def getRoot(x):
    r = rootList[x]
    if r < 0:
        rootList[x] = x
    elif r != x:
        rootList[x] = getRoot(r)
    return rootList[x]


edgeList.sort(key=lambda x: x[0])
flag = True
while flag:
    flag = False
    for e in edgeList:    # weight:e[0], e[1]->e[2]
        if e[2] == 0:
            continue
        x = getRoot(e[1])
        y = getRoot(e[2])
        if x == 0 != y:
            parent[e[2]] = e[1]
            lenList[e[2]] += lenList[e[1]] + e[0]
            rootList[y] = 0
            flag = True
            break

for i, j in zip(range(n), lenList):
    print(i, j)

Submission status: Runtime Error

Solution code:
rootList = [-1 for i in range(n)]
parent = [0 for i in range(n)]
lenList = [0 for i in range(n)]

def getRoot(x):
    r = rootList[x]
    if r < 0:
        rootList[x] = x
    elif r != x:
        rootList[x] = getRoot(r)
    return rootList[x]


edgeList.sort(key=lambda x: x[0])
flag = True
while flag:
    flag = False
    for e in edgeList:
        if e[2] == 0:
            continue
        x = getRoot(e[1])
        y = getRoot(e[2])
        if x == 0 != y:
            parent[e[2]] = e[1]
            lenList[e[2]] += lenList[e[1]] + e[0]
            rootList[y] = 0
            flag = True
            break

for i, j in zip(range(n), lenList):
    print(i, j)

Submission status: Runtime Error

Solution code:
rootList = [-1 for i in range(n)]
parent = [0 for i in range(n)]
lenList = [float("inf") for i in range(n)]
lenList[0] = 0
def getRoot(x):
    r = rootList[x]
    if r < 0:
        rootList[x] = x
    elif r != x:
        rootList[x] = getRoot(r)
    return rootList[x]

flag = True
while flag:
    flag = False
    edgeList.sort(key=lambda x: (x[0] + lenList[x[1]]))
    for e in edgeList:    # weight:e[0], e[1]->e[2]
        if e[2] == 0:
            continue
        x = getRoot(e[1])
        y = getRoot(e[2])
        if x == 0 != y:
            parent[e[2]] = e[1]
            lenList[e[2]] = lenList[e[1]] + e[0]
            rootList[y] = 0
            flag = True
            break

for i, j in zip(range(n), lenList):
    print(i, j)

Submission status: Runtime Error

Solution code:
from sys import stdin

INFTY = 1 << 21
WHITE = 0
GRAY = 1
BLACK = 2

n = int(stdin.readline())
M = [[INFTY for i in range(n)] for j in range(n)]

for u in range(n):
    U = list(map(int, stdin.readline().split()[2:]))
    for j in range(0, len(U), 2):
        M[u][U[j]] = U[j+1]

d = [INFTY for i in range(n)]
color = [WHITE for i in range(n)]

def dijkstra():
    global n
    d[0] = 0
    color[0] = GRAY
    while(1):
        minv = INFTY
        u = -1
        for i in range(n):
            if (minv > d[i] and color[i] != BLACK):
                u = i
                minv = d[i]
        if (u == -1):
            break
        color[u] = BLACK
        for v in range(n):
            if (color[v] != BLACK and M[u][v] != INFTY):
                if(d[v] > d[u] + M[u][v]:)
                    d[v] = d[u] + M[u][v]
                    color[v] = GRAY
    for i in range(n):
        print(i, (-1 if d[i] == INFTY else d[i]))
dijkstra()

Submission status: Runtime Error

Solution code:
from sys import stdin

INFTY = 1 << 21
WHITE = 0
GRAY = 1
BLACK = 2

n = int(stdin.readline())
M = [[INFTY] * n for i in range(n)]

for u in range(n):
    U = list(map(int, stdin.readline().split()[2:]))
    for j in range(0, len(U), 2):
        M[u][U[j]] = U[j+1]

d = [INFTY for i in range(n)]
color = [WHITE for i in range(n)]

def dijkstra():
    global n
    d[0] = 0
    color[0] = GRAY
    while(1):
        minv = INFTY
        u = -1
        for i in range(n):
            if (minv > d[i] and color[i] != BLACK):
                u = i
                minv = d[i]
        if (u == -1):
            break
        color[u] = BLACK
        for v in range(n):
            if (color[v] != BLACK and M[u][v] != INFTY):
                if(d[v] > d[u] + M[u][v]:)
                    d[v] = d[u] + M[u][v]
                    color[v] = GRAY
    for i in range(n):
        print(i, (-1 if d[i] == INFTY else d[i]))
dijkstra()

Submission status: Runtime Error

Solution code:
from sys import stdin

INFTY = 1 << 21
WHITE = 0
GRAY = 1
BLACK = 2

n = int(stdin.readline())
M = [[INFTY for i in range(n)] for j in range(n)]

for u in range(0, n):
    U = list(map(int, stdin.readline().split()[2:]))
    for j in range(0, len(U), 2):
        M[u][U[j]] = U[j+1]

d = [INFTY for i in range(n)]
color = [WHITE for i in range(n)]

def dijkstra():
    global n
    d[0] = 0
    color[0] = GRAY
    while(1):
        minv = INFTY
        u = -1
        for i in range(0, n):
            if (minv > d[i] and color[i] != BLACK):
                u = i
                minv = d[i]
        if (u == -1):
            break
        color[u] = BLACK
        for v in range(0, n):
            if (color[v] != BLACK and M[u][v] != INFTY):
                if(d[v] > d[u] + M[u][v]:)
                    d[v] = d[u] + M[u][v]
                    color[v] = GRAY
    for i in range(0, n):
        print(i, (-1 if d[i] == INFTY else d[i]))
dijkstra()

Submission status: WA: Presentation Error

Solution code:
n = int(raw_input())

matrix = [[100001 for i in range(n)] for j in range(n)]

for i in range(n):
    line = raw_input()
    splited = line.split()
    splited = map(lambda x: int(x), splited)
    u = splited[0]
    k = splited[1]
    for j in range(k):
        matrix[u][splited[2 + j * 2]] = splited[2 + j * 2 + 1]

cost = [10000000000 for i in range(n)]
selected = []
now_node = 0
cost[now_node] = 0
while len(selected) != n + 1:
    selected.append(now_node)

    for (i, item) in enumerate(matrix[now_node]):
        if item < 100001 and cost[i] > item + cost[now_node] and cost[i] != -1:
            cost[i] = item + cost[now_node]
    now_node = -1
    for (i, item) in enumerate(cost):
        if i not in selected and now_node == -1:
            now_node = i
        elif i not in selected and item < cost[now_node]:
            now_node = i

for (i, item) in enumerate(cost):
    print i, " ", item