κ·Έλž˜ν”„ μ•Œκ³ λ¦¬μ¦˜Intermediate

ν”„λ¦Ό μ΅œμ†Œ μ‹ μž₯ 트리

MSTλ₯Ό MSTκ°€ μ•„λ‹Œ 정점에 μ—°κ²°ν•˜λŠ” μ΅œμ†Œ κ°€μ€‘μΉ˜ 간선을 μΆ”κ°€ν•˜μ—¬ ν•œ λ²ˆμ— ν•œ 정점씩 MSTλ₯Ό μ„±μž₯μ‹œν‚€λŠ” νƒμš• μ•Œκ³ λ¦¬μ¦˜μž…λ‹ˆλ‹€. O(E log V) λ³΅μž‘λ„λ₯Ό μœ„ν•΄ μš°μ„ μˆœμœ„ 큐λ₯Ό μ‚¬μš©ν•˜λ©° λ°€μ§‘ κ·Έλž˜ν”„μ— μ΅œμ μž…λ‹ˆλ‹€. 인접 행렬에 λŒ€ν•΄ ν¬λ£¨μŠ€μΉΌλ³΄λ‹€ κ΅¬ν˜„μ΄ 더 κ°„λ‹¨ν•©λ‹ˆλ‹€. λ„€νŠΈμ›Œν¬ 섀계, 근사 μ•Œκ³ λ¦¬μ¦˜, νƒμš•μ  선택 μ΄ν•΄μ˜ μ‘μš©μ΄ μžˆμŠ΅λ‹ˆλ‹€.

#graph#minimum-spanning-tree#greedy#priority-queue

Complexity Analysis

Time (Average)

O(E log V)

Expected case performance

Space

O(V)

Memory requirements

Time (Best)

O(E log V)

Best case performance

Time (Worst)

O(E log V)

Worst case performance

πŸ“š CLRS Reference

Introduction to Algorithmsβ€’Chapter 23β€’Section 23.2

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Implementation

Prim's Minimum Spanning Tree - Algorithm Vision