Quiz: Monotonicity Implication

If a cost function satisfies quadrangle inequality, what can we conclude about optimal split points opt[i][j]?

1. A.opt[i][j] = (i + j) / 2 always
2. B.opt[i][j] depends only on length j - i
3. C.opt[i][j-1] <= opt[i][j] <= opt[i+1][j]
4. D.opt[i][j] is always the leftmost valid split