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Lets apply alg T to lines 166-174 of test, listed here

msprime.CoalescenceRecord(left=0.0,  right=0.2,  node=4,  children=(2,  3),  time=0.4,  population=0),  # 1
msprime.CoalescenceRecord(left=0.2,  right=0.8,  node=4,  children=(0,  2),  time=0.4,  population=0),  # 2
msprime.CoalescenceRecord(left=0.8,  right=1.0,  node=4,  children=(2,  3),  time=0.4,  population=0),  # 3
msprime.CoalescenceRecord(left=0.0,  right=1.0,  node=5,  children=(1,  4),  time=0.5,  population=0),  # 4
msprime.CoalescenceRecord(left=0.8,  right=1.0,  node=6,  children=(0,  5),  time=0.7,  population=0),  # 5
msprime.CoalescenceRecord(left=0.0,  right=0.2,  node=7,  children=(0,  5),  time=1.0,  population=0),  # 6

The ordered index vectors would be (indexing starting at 1)

I = [1, 4, 6, 2, 3, 5] and O = [6, 1, 2, 5, 4, 3].

  1. initialize by setting pi_j = 0 for j in 1 to 7 + 1. So pi = 00000000 and j = 1, k = 1, x= 0.0. Also the number of records is M = 6

  2. Insert for x = 0.0?

    • j = 1; h=1, yes. pi = 00440000
    • j = 2; h=4, yes. pi = 05445000
    • j = 3; h=6, yes. pi = 75445700
    • j = 4; h=2, no. x=0.0 =/= l_2 =0.2

  3. Visit pi= 75445700, which matches A below although it's unclear 7 is the root. j = 4 < M = 6 so set x = 0.2

  4. Remove for x = 0.2?

    • k = 1; h=6, yes. pi = 05445000
    • k = 2; h=1, yes. pi = 05005000
    • k = 3; h=2, no. x=0.2 =/= r_2 = 0.8

  5. Insert for x = 0.2?

    • j = 4; h=2, yes. pi = 45405000
    • j = 5; h=3, no. x=0.2 =/= l_3 = 0.8

  6. Visit pi= 4540500 which matches B although it's unclear that 5 is the root. j= 5 < M=6 so set x = 0.8

  7. Remove for x = 0.8?

    • k = 3; h=2, yes. pi = 05005000
    • k = 4; h=5, no. x=0.8 =/= r_5 = 1.0

  8. Insert for x = 0.8?

    • j = 5; h=3, yes. pi = 05445000
    • j = 6; h=5, yes. pi = 65445600
    • j = 7; j > M = 6 so goto visit

  9. Visit pi= 65445600 which matches C although it's unclear that 6 is the root. j= 7 > M so terminate.

    Same, but renumbered:

    1.0 7

    0.7 / \ 6

    / \ / \

    0.5 / 5 5 / 5

    / / \ / \ / / \

    0.4 / / 4 / 4 / / 4

    / / / \ / / \ / / / \

    / / 3 \ / / \ / / 3 \

    / / \ / / \ / / \

    0.0 0 1 2 1 0 2 0 1 2

    A(0.0, 0.2), B(0.2, 0.8), C(0.8, 1.0)

output from trees.py

Lists the records in and out and prints each tree visited (in two ways):

in: CoalescenceRecord(left=0.0, right=0.2, node=4, children=(2, 3), time=0.4, population=0)
in: CoalescenceRecord(left=0.0, right=1.0, node=5, children=(1, 4), time=0.5, population=0)
in: CoalescenceRecord(left=0.0, right=0.2, node=7, children=(0, 5), time=1.0, population=0)
([7, 5, 4, 4, 5, 7, -1, -1], [[], [], [], [], (2, 3), (1, 4), [], (0, 5)])
out: CoalescenceRecord(left=0.0, right=0.2, node=7, children=(0, 5), time=1.0, population=0)
out: CoalescenceRecord(left=0.0, right=0.2, node=4, children=(2, 3), time=0.4, population=0)
in: CoalescenceRecord(left=0.2, right=0.8, node=4, children=(0, 2), time=0.4, population=0)
([4, 5, 4, -1, 5, -1, -1, -1], [[], [], [], [], (0, 2), (1, 4), [], []])
out: CoalescenceRecord(left=0.2, right=0.8, node=4, children=(0, 2), time=0.4, population=0)
in: CoalescenceRecord(left=0.8, right=1.0, node=4, children=(2, 3), time=0.4, population=0)
in: CoalescenceRecord(left=0.8, right=1.0, node=6, children=(0, 5), time=0.7, population=0)
------------- works in python ----------