경우의 수 계산이 어려워서, 프로그래밍으로 했다.
100개 slots에 무작위로 아무 숫자에나 사람들이 슈팅을 한다고 했을 때,
빨간 색은 사람이 0명인 slot 개수
파란 색은 사람이 1명인 slot 개수
사람이 10배 이상으로 모이면, 그 slot은 포기해야 할 듯.
import matplotlib.pyplot as plot
import random
n_slots = 100
n_people_range = range(0, 3000)
def random_histogram(n_slots, n_people):
slots = range(0, n_slots)
slot_histogram = [0 for i in slots]
#print slot_histogram
for i in range(0, n_people):
slot = random.randint(0, n_slots - 1)
slot_histogram[slot] = slot_histogram[slot] + 1
return slots, slot_histogram
people_x_range = range(n_people_range[-1] + 1)
n_0_hist = [0 for i in people_x_range]
n_1_hist = [0 for i in people_x_range]
for i_n_people in n_people_range:
#print i_n_people
slots, slot_histogram = random_histogram(n_slots, i_n_people)
n_0_slots = 0
n_1_slots = 0
for n_people_each_slot in slot_histogram:
if (n_people_each_slot == 0):
n_0_slots = n_0_slots + 1
if (n_people_each_slot == 1):
n_1_slots = n_1_slots + 1
n_0_hist[i_n_people] = n_0_slots if n_0_slots > 0 else -5
n_1_hist[i_n_people] = n_1_slots if n_1_slots > 0 else -5
print i_n_people, n_0_slots, n_1_slots
plot.scatter(people_x_range, n_0_hist, c='red', lw=0, alpha=0.5)
plot.scatter(people_x_range, n_1_hist, c='blue', lw=0, alpha=0.5)
plot.show()
한 번 더 계산해봐도 거의 비슷한 그래프
n_slots = 1000
#50000 people --> 1000 < 7000 < 10000
n_people_range = range(0, 10000)
으로 많이 계산하고,
def blur_histogram(histogram):
result = [0 for i in range(len(histogram))]
for i in range(len(histogram)):
blur_wing = 30
if (i - blur_wing > 0 and i + blur_wing < len(histogram)):
for j in range(i - blur_wing, i + blur_wing):
around_i = histogram[i - blur_wing : i + blur_wing]
result[i] = reduce(lambda x, y: x + y, around_i) / len(around_i)
으로 blur했더니, 예쁜 그래프가 됐다.
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언제나19
기본에 충실하는 19식 재테크. 교과서 중심으로 공부했어요.