def test_week1_exercise_Q1(): # Lecture: Quick-Union Improvements 1:22
"""seed = 254585 """
# estimate b: 7:58
# N seconds
# -------------------
strData = """
16384 0.000
32768 0.001
65536 0.001
131072 0.004
262144 0.009
524288 0.023
1048576 0.059
2097152 0.152
4194304 0.389
8388608 0.996
16777216 2.553
33554432 6.540
67108864 16.756
134217728 42.927
268435456 109.962
536870912 281.688
"""
data = getData(strData)
b = est_b(data)
a = solve_a(data, b)
do_plot(data, a, b)
def test_week1_exercise_Q1(): # Lecture: Quick-Union Improvements 1:22
"""seed = 254585 """
# estimate b: 7:58
# N seconds
# -------------------
strData = """
16384 0.000
32768 0.001
65536 0.001
131072 0.004
262144 0.009
524288 0.023
1048576 0.059
2097152 0.152
4194304 0.389
8388608 0.996
16777216 2.553
33554432 6.540
67108864 16.756
134217728 42.927
268435456 109.962
536870912 281.688
"""
data = getData(strData)
b = est_b(data)
a = solve_a(data, b)
do_plot(data, a, b)
def test_Lecture_Observations_Question():
"""Question from the end of the Week 1 Lecture, Observations.
EXPLANATION: We assume T(N) = aN^b for some constants a and b.
As we double the size of the input N, the running time
approximately quadruples, indicating a algorithm or b=2.
Plugging in T(64,000) = 20.5 and solving for a, we obtain
a = 20.5/64,000^2 ~ 5.0 x 10-9
"""
strData = """
1000 0.0
2000 0.0
4000 0.1
8000 0.3
16000 1.3
32000 5.1
64000 20.5
"""
data = getData(strData)
b = est_b(data)
a = solve_a(data, b)
do_plot(data, a, b)
def test_Lecture_Observations_Question():
"""Question from the end of the Week 1 Lecture, Observations.
EXPLANATION: We assume T(N) = aN^b for some constants a and b.
As we double the size of the input N, the running time
approximately quadruples, indicating a algorithm or b=2.
Plugging in T(64,000) = 20.5 and solving for a, we obtain
a = 20.5/64,000^2 ~ 5.0 x 10-9
"""
strData = """
1000 0.0
2000 0.0
4000 0.1
8000 0.3
16000 1.3
32000 5.1
64000 20.5
"""
data = getData(strData)
b = est_b(data)
a = solve_a(data, b)
do_plot(data, a, b)