PROBLEM LINK
CONTEST PANEL
Author:admin2
DIFFICULTY
EASY
PROBLEM
Given N sets whose elements range from 1 to k, find the number of pairs among those N sets which contain all elements ranging from 1 to k.
EXPLANATION
This solution only runs due to the constraints: 1≤len1+len2+..+lenN≤10000
This problem can be solved by making pairs among only the ones whose sum of set length is greater than k in a boolean 2D vector.
For each input set mark the values as true from 1 to k which are appearing in the set, refer below pseudo code.2D vector sets
vector length
for(i from 1 to k){
input length of set and push this length in length vector
bool vector temp
for(j from 0 to len){
input individual set element
set the corresponding index as true in temp vector
}
push the temp vector in sets
}
We will now have a 2D vector representing all the sets.
Input part in complete!
Now all that remains in the problem is to make pairs among different sets of only those whose sum of length of sets exceeds or equals k since only then there is possibility of having the union equal k elements. (basic logic :P)
Pairs are made!
Now for each pair we need to check whether their union will contain all the elements ranging from 1 to k.
With each pair what we do is iterate from 1 to k and check whether at least one of those set has a set bit in each iteration, if not we strictly break as that element is not present in both the set and thus the pair we chose can never have all k elements.
If there is no such condition where both chosen pairs have false bit then all elements are present from 1 to k in the union of the chosen pairs and thus we increment our answer count!
Refer pseudo code below on how to check for each pair
bool check = true
for(i from 0 to n-1)
for(j from i+1 to n)
if k<= length[i] + length[j]
for(y from 1 to k)
if !(sets[i]||sets[j])
check = false
if check
ans++
Feel free to share your approach below !
If you forget to take into account the set length vector, it will result in exceeded time
SOLUTION
My AC
Execution Time: 0.21 s
Memory:3.3M