Dsa
Union Find
Medium
Galaxy Collapse
There are N stars, each with a specific mass. Stars cluster into galaxies. When two galaxies merge, their total mass is the sum of the masses of all stars in both. If a galaxy's total mass exceeds a safety Limit L, it 'collapses' into a black hole cluster. Once a galaxy collapses, it remains collapsed even if it merges with other galaxies. Calculate how many stars are in collapsed galaxies after M merges.
Input Format:
Line 1: N (stars), M (merges), L (mass limit).
Line 2: N integers representing the mass of each star (0 to N-1).
Next M lines: Two integers u and v (a merge between the galaxy containing u and the galaxy containing v).
Output Format:
A single integer: total number of stars in collapsed galaxies.
Example:
Input:
4 2 10
5 6 3 2
0 1
2 3
Output:
2
Explanation:
Masses: [5, 6, 3, 2]. Limit: 10.
Merge (0,1): Total mass 5+6=11. 11 > 10, so galaxy {0,1} collapses. (2 stars)
Merge (2,3): Total mass 3+2=5. 5 <= 10, not collapsed.
Total stars in collapsed: 2.
Key concepts
union_findweight_summing
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