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_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_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_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_ex_Q1_398112(): # Lecture: Quick-Union Improvements 1:22
"""seed = 398112 """
# estimate b: 7:58
# N seconds
# -------------------
strData = """
128 0.000
256 0.001
512 0.006
1024 0.029
2048 0.158
4096 0.852
8192 4.561
16384 24.586
32768 129.467
65536 697.828
131072 3730.438
"""
data = getData(strData)
est_b(data)
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_ex_Q1_398112(): # Lecture: Quick-Union Improvements 1:22
"""seed = 398112 """
# estimate b: 7:58
# N seconds
# -------------------
strData = """
128 0.000
256 0.001
512 0.006
1024 0.029
2048 0.158
4096 0.852
8192 4.561
16384 24.586
32768 129.467
65536 697.828
131072 3730.438
"""
data = getData(strData)
est_b(data)
def test_week1_ex_Q1_130450(): # Lecture: Quick-Union Improvements 1:22
"""seed = 130450 """
# estimate b: 7:58
# N seconds
# -------------------
strData = """
1024 0.000
2048 0.001
4096 0.003
8192 0.013
16384 0.053
32768 0.227
65536 0.953
131072 3.998
262144 16.756
524288 70.385
1048576 295.766
2097152 1243.879
"""
data = getData(strData)
est_b(data)
def test_week1_ex_Q1_990354(): # Lecture: Quick-Union Improvements 1:22
"""seed = 990354 """
# estimate b: 7:58
# N seconds
# -------------------
strData = """
256 0.000
512 0.001
1024 0.005
2048 0.022
4096 0.099
8192 0.467
16384 2.133
32768 9.998
65536 46.309
131072 214.246
262144 998.222
524288 4622.897
"""
data = getData(strData)
est_b(data)
def test_week1_ex_Q1_130450(): # Lecture: Quick-Union Improvements 1:22
"""seed = 130450 """
# estimate b: 7:58
# N seconds
# -------------------
strData = """
1024 0.000
2048 0.001
4096 0.003
8192 0.013
16384 0.053
32768 0.227
65536 0.953
131072 3.998
262144 16.756
524288 70.385
1048576 295.766
2097152 1243.879
"""
data = getData(strData)
est_b(data)
def test_week1_ex_Q1_990354(): # Lecture: Quick-Union Improvements 1:22
"""seed = 990354 """
# estimate b: 7:58
# N seconds
# -------------------
strData = """
256 0.000
512 0.001
1024 0.005
2048 0.022
4096 0.099
8192 0.467
16384 2.133
32768 9.998
65536 46.309
131072 214.246
262144 998.222
524288 4622.897
"""
data = getData(strData)
est_b(data)
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)
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)
