Q2 — Alpha-Beta Mid-Flight: The Cutoff Value of N

Even evals only — N = 2 slips under α = 4 at the MIN parent and cuts off its siblings: an α-cutoff.

The Question

Alpha-Beta is mid-flight on a MAX-root tree. Evals along the current path (root → N): 2, 14, 4, 10, N — all even, 0<n<150 < n < 15.

#QuestionOfficial answer
2.1Eval of N that induces a cutoff (pruning N's siblings)2
2.2Type of cutoffA — Alpha cutoff

The Topic in 60 Seconds

Levels alternate from the MAX root: MAX(2) → MIN(14) → MAX(4) → MIN(10) → N.

The window slides down the path:

  • α(MAX1)=2\alpha(\text{MAX}_1) = 2
  • β(MIN2)=14\beta(\text{MIN}_2) = 14
  • α(MAX3)=max⁡(2,4)=4\alpha(\text{MAX}_3) = \max(2, 4) = 4
  • β(MIN4)=min⁡(14,10)=10\beta(\text{MIN}_4) = \min(14, 10) = 10

N is a child of MIN₄, whose window is (α,β)=(4,10)(\alpha, \beta) = (4, 10).

Deep-dive: Alpha-Beta Pruning.

2.1 — The cutoff value → 2

A cutoff at MIN₄ fires the moment a child's value drops to α=4\alpha = 4 or below. N must satisfy:

N≤α=4,N even,0<N<15N \le \alpha = 4, \qquad N \text{ even}, \quad 0 < N < 15

The smallest (and keyed) value that forces the prune: N = 2 ✓ — MIN₄'s value collapses to 2, which MAX₃ (already holding 4) will never take, so N's siblings are pruned.

2.2 — Cutoff type → A (Alpha cutoff)

The cutoff happens at MIN₄ — a MIN node crashing through α\alpha. Per the course convention:

value reachednode typecutoff name
≥β\ge \betaMAXβ-cutoff
≤α\le \alphaMINα-cutoff ✓

→ Alpha cutoff ✓

Tricks & Tips

Answers: 2.1 2 · 2.2 A (Alpha cutoff)