# ORIGINAL #
def break_down_to_pow10(num):
nums = []
num_len = len(str(num)) - 1
for pw in reversed(range(num_len)):
nums.append(pow(10, pw))
return nums
# RESULT:
#For num = 67108864:
#Correct output: [60000000, 7000000, 100000, 8000, 800, 60, 4]
#Current output: [1000000, 100000, 10000, 1000, 100, 10, 1]
# NEW APPROACH 1: Base-10 Digit Decomposition
def break_down_to_pow10(num):
nums = []
num_str = str(num)
num_len = len(num_str)
for i, digit in enumerate(num_str):
power = num_len - i - 1
if digit != '0':
nums.append(int(digit) * pow(10, power))
return nums
# RESULT:
# For 67,108,864:
# [60000000, 7000000, 100000, 8000, 800, 60, 4]
# NEW APPROACH 2: Binary decomposition
def break_down_to_pow2(num):
nums = []
while num > 0:
highest_power = 1 << (num.bit_length() - 1)
nums.append(highest_power)
num -= highest_power
return nums
# RESULT:
# For 67,108,864:
# [33554432, 16777216, 8388608, 4194304, 2097152, 1048576, 524288, 262144, 131072, 65536, 32768, 16384, 8192, 4096, 2048, 1024, 512, 256, 128, 64, 32, 16, 8, 4, 2, 1]
