TAOCP 6.2.4: Multiway Trees

Section 6.2.4 exercises: 10/10 solved.

10 items

Section 6.2.4. Multiway Trees

Exercises from TAOCP Volume 3 Section 6.2.4: 10/10 solved.

# Rating Category Status Time
1 [10] simple solved 1m
2 [15] simple verified 2m30s
3 ▶ [23] medium solved 5m02s
4 [21] medium solved 4m05s
5 ▶ [21] medium solved 5m26s
6 [23] medium solved 4m44s
7 [28] hard solved 1m27s
8 ▶ [HM47] hm-research solved 4m26s
9 [22] medium verified 1m14s
10 ▶ [35] hard solved 2m04s
Practice › Mathematics › TAOCP › TAOCP Vol 3: Sorting and Searching › TAOCP 6.2.4: Multiway Trees ›

TAOCP 6.2.4 Exercise 1

The search for $613$ proceeds from the root by repeated comparison with the keys in each visited node, following the rightmost pointer at each step since $613$ exceeds every key encountered in Fig.
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Practice › Mathematics › TAOCP › TAOCP Vol 3: Sorting and Searching › TAOCP 6.2.4: Multiway Trees ›

TAOCP 6.2.4 Exercise 2

Let $m=7$.
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Practice › Mathematics › TAOCP › TAOCP Vol 3: Sorting and Searching › TAOCP 6.2.4: Multiway Trees ›

TAOCP 6.2.4 Exercise 3

Let $m=101$.
taocp mathematics algorithms volume-3 Medium Jun 29, 2026
Practice › Mathematics › TAOCP › TAOCP Vol 3: Sorting and Searching › TAOCP 6.2.4: Multiway Trees ›

TAOCP 6.2.4 Exercise 4

We restart from the standard Bayer–McCreight B-tree model and make explicit the structural object being modified.
taocp mathematics algorithms volume-3 Medium Jun 29, 2026
Practice › Mathematics › TAOCP › TAOCP Vol 3: Sorting and Searching › TAOCP 6.2.4: Multiway Trees ›

TAOCP 6.2.4 Exercise 5

We correct the analysis by rebuilding the argument from the actual insertion model and then performing a genuine worst-case optimization over all valid full nodes and all valid splits.
taocp mathematics algorithms volume-3 Medium Jun 29, 2026
Practice › Mathematics › TAOCP › TAOCP Vol 3: Sorting and Searching › TAOCP 6.2.4: Multiway Trees ›

TAOCP 6.2.4 Exercise 6

We restart the construction in a fully TAOCP-consistent form by defining a single recursive deletion procedure in which every descent step is preceded by an invariant-preserving repair.
taocp mathematics algorithms volume-3 Medium Jun 29, 2026
Practice › Mathematics › TAOCP › TAOCP Vol 3: Sorting and Searching › TAOCP 6.2.4: Multiway Trees ›

TAOCP 6.2.4 Exercise 7

Let $T$ and $T'$ be B-trees of order $m > 3$ such that every key in $T$ is strictly less than every key in $T'$.
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Practice › Mathematics › TAOCP › TAOCP Vol 3: Sorting and Searching › TAOCP 6.2.4: Multiway Trees ›

TAOCP 6.2.4 Exercise 8

Working
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Practice › Mathematics › TAOCP › TAOCP Vol 3: Sorting and Searching › TAOCP 6.2.4: Multiway Trees ›

TAOCP 6.2.4 Exercise 9

A B-tree can be adapted to support retrieval by position in a linear list by augmenting each node with information about subtree sizes, so that navigation is driven by rank rather than key comparison.
taocp mathematics algorithms volume-3 Medium Jun 29, 2026
Practice › Mathematics › TAOCP › TAOCP Vol 3: Sorting and Searching › TAOCP 6.2.4: Multiway Trees ›

TAOCP 6.2.4 Exercise 10

We consider a large file organized as a $B$-tree of order $m\ge 3$ as defined in Section 6.
taocp mathematics algorithms volume-3 Hard Jul 29, 2026