Searching for Graph (Codeforces 402C)
Tags: Others, graphs

Let's call an undirected graph of n vertices p-interesting, if the following conditions fulfill:   the graph contains exactly 2n + p edges;  the graph doesn't contain self-loops and multiple edges;  for any integer k (1 ≤ k ≤ n), any subgraph consisting of k vertices contains at most 2k + p edges. A subgraph of a graph is some set of the graph vertices and some set of the graph edges. At that, the set of edges must meet the condition: both ends of each edge from the set must belong to the chosen set of vertices. Your task is to find a p-interesting graph consisting of n vertices.

Input: The first line contains a single integer t (1 ≤ t ≤ 5) — the number of tests in the input. Next t lines each contains two space-separated integers: n, p (5 ≤ n ≤ 24; p ≥ 0; ) — the number of vertices in the graph and the interest value for the appropriate test. It is guaranteed that the required graph exists.

Output: For each of the t tests print 2n + p lines containing the description of the edges of a p-interesting graph: the i-th line must contain two space-separated integers ai, bi (1 ≤ ai, bi ≤ n; ai ≠ bi) — two vertices, connected by an edge in the resulting graph. Consider the graph vertices numbered with integers from 1 to n. Print the answers to the tests in the order the tests occur in the input. If there are multiple solutions, you can print any of them.


Sample Inputs:
1
6 0

Sample Outputs:
1 2
1 3
1 4
1 5
1 6
2 3
2 4
2 5
2 6
3 4
3 5
3 6

Solution (Python):
for _ in range(int(input())):
    (n, p) = map(int, input().split())
    r = 2 * n + p
    for i in range(1, n + 1):
        for j in range(i + 1, n + 1):
            if not r:
                break
            print(i, j)
            r -= 1

Solution (Python):
def solve(k):
    for i in range(1, n + 1):
        for j in range(i + 1, n + 1):
            print(i, j)
            k -= 1
            if k == 0:
                return
T = int(input())
for _ in range(0, T):
    (n, p) = map(int, input().split())
    k = 2 * n + p
    solve(k)

Solution (Python):
from sys import stdin, stdout
input = stdin.readline

def print(*args, end='\n', sep=' ') -> None:
    stdout.write(sep.join(map(str, args)) + end)
for _ in range(int(input())):
    (n, p) = map(int, input().split())
    cond = False
    ans = 2 * n + p
    summ = 0
    for i in range(1, n + 1):
        for j in range(i + 1, n + 1):
            if summ == ans:
                cond = True
                break
            print(i, j)
            summ += 1
        if cond:
            break