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_exerciseA_Q2():
"""seed = 331534 """
# N seconds
# -------------------
strData = """
2 7.000
4 31.000
8 127.000
16 511.000
32 2047.000
64 8191.000
128 32767.000
"""
data = getData(strData)
b = est_b(data)
solve_a(data, b)
def test_week1_exerciseA_Q2():
"""seed = 331534 """
# N seconds
# -------------------
strData = """
2 7.000
4 31.000
8 127.000
16 511.000
32 2047.000
64 8191.000
128 32767.000
"""
data = getData(strData)
b = est_b(data)
solve_a(data, 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_week1_exerciseA_Q1():
"""seed = 331534 """
# N seconds
# -------------------
strData = """
64 0.001
128 0.008
256 0.062
512 0.564
1024 5.092
2048 48.765
4096 439.291
8192 3998.962
"""
data = getData(strData)
b = est_b(data)
solve_a(data, b)
def test_week1_exercise_Q1b(): # Lecture: Quick-Union Improvements 1:22
"""seed = 686658 """
# N seconds
# -------------------
strData = """
64 0.001
128 0.006
256 0.072
512 0.713
1024 6.837
2048 68.530
4096 666.576
8192 6594.977
"""
data = getData(strData)
b = est_b(data)
solve_a(data, b)
def test_week1_exerciseA_Q1():
"""seed = 331534 """
# N seconds
# -------------------
strData = """
64 0.001
128 0.008
256 0.062
512 0.564
1024 5.092
2048 48.765
4096 439.291
8192 3998.962
"""
data = getData(strData)
b = est_b(data)
solve_a(data, b)
def test_week1_exercise_Q1b(): # Lecture: Quick-Union Improvements 1:22
"""seed = 686658 """
# N seconds
# -------------------
strData = """
64 0.001
128 0.006
256 0.072
512 0.713
1024 6.837
2048 68.530
4096 666.576
8192 6594.977
"""
data = getData(strData)
b = est_b(data)
solve_a(data, b)
def test_week1_exercise_Q1d(): # Lecture: Quick-Union Improvements 1:22
"""seed = 262435 """
# N seconds
# -------------------
strData = """
256 0.000
512 0.001
1024 0.005
2048 0.028
4096 0.146
8192 0.812
16384 4.448
32768 24.280
65536 134.049
131072 728.101
262144 3978.674
"""
data = getData(strData)
b = est_b(data)
solve_a(data, b)
def test_week1_exercise_Q1d(): # Lecture: Quick-Union Improvements 1:22
"""seed = 262435 """
# N seconds
# -------------------
strData = """
256 0.000
512 0.001
1024 0.005
2048 0.028
4096 0.146
8192 0.812
16384 4.448
32768 24.280
65536 134.049
131072 728.101
262144 3978.674
"""
data = getData(strData)
b = est_b(data)
solve_a(data, b)
def test_week1_exercise_Q1c(): # Lecture: Quick-Union Improvements 1:22
"""seed = 410426 """
# N seconds
# -------------------
strData = """
32768 0.000
65536 0.000
131072 0.001
262144 0.003
524288 0.008
1048576 0.022
2097152 0.057
4194304 0.148
8388608 0.386
16777216 1.008
33554432 2.632
67108864 6.872
134217728 17.944
268435456 46.850
536870912 122.325
"""
data = getData(strData)
b = est_b(data)
solve_a(data, b)
def test_week1_exercise_Q1c(): # Lecture: Quick-Union Improvements 1:22
"""seed = 410426 """
# N seconds
# -------------------
strData = """
32768 0.000
65536 0.000
131072 0.001
262144 0.003
524288 0.008
1048576 0.022
2097152 0.057
4194304 0.148
8388608 0.386
16777216 1.008
33554432 2.632
67108864 6.872
134217728 17.944
268435456 46.850
536870912 122.325
"""
data = getData(strData)
b = est_b(data)
solve_a(data, 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)
