[英]Print all n-digit numbers whose product of digits equals to given product python
[英]Explain the logic of 'Count of N-digit numbers with absolute difference of adjacent digits not exceeding K' in Detail
有人可以帮我理解以下动态编程问题的逻辑在 geeksforgeeks.com 找到这个问题。 即使经过提供的答案,我也无法理解。
问题:
相邻位数绝对差不超过K的N位数个数| 设置 2
给定两个整数 N 和 K,任务是找到 N 位数字的计数,使得该数字中相邻数字的绝对差不大于 K。
例子:
输入:N = 2,K = 1
Output:26
解释: 数字是 10, 11, 12, 21, 22, 23, 32, 33, 34, 43, 44, 45, 54, 55, 56, 65, 66, 67, 76, 77, 78, 87, 88 , 89, 98, 99
输入:N = 3,K = 2
Output:188
Python3解决方案:
# Function to return the count of such numbers
def getCount(n, K):
# For 1-digit numbers, the count is 10 irrespective of K
if(n == 1):
return 10
# dp[j] stores the number of such i-digit numbers ending with j
dp = [0] * 11
# Stores the results of length i
next = [0] * 11
# Initialize count for 1-digit numbers
for i in range(1, 9 + 1):
dp[i] = 1
# Compute values for count of digits greater than 1
for i in range(2, n + 1):
for j in range(9 + 1):
# Find the range of allowed numbers if last digit is j
l = max(0, j - k)
r = min(9, j + k)
# Perform Range update
next[l] += dp[j]
next[r + 1] -= dp[j]
# Prefix sum to find actual count of i-digit numbers ending with j
for j in range(1, 9 + 1):
next[j] += next[j - 1]
# Update dp[]
for j in range(10):
dp[j] = next[j]
next[j] = 0
# Stores the final answer
count = 0
for i in range(9 + 1):
count += dp[i]
return count
if __name__ == '__main__':
n = 2
k = 1
print(getCount(n, k))
此代码由 Shivam Singh 提供
我无法理解以下几行的逻辑
# Compute values for count of
# digits greater than 1
for i in range(2, n + 1):
for j in range(9 + 1):
# Find the range of allowed
# numbers if last digit is j
l = max(0, j - k)
r = min(9, j + k)
# Perform Range update
next[l] += dp[j]
next[r + 1] -= dp[j]
# Prefix sum to find actual count
# of i-digit numbers ending with j
for j in range(1, 9 + 1):
next[j] += next[j - 1]
# Update dp[]
for j in range(10):
dp[j] = next[j]
next[j] = 0
N=2
所以我们正在处理严格的 2 位数字
K=1
,因此当前数字中的每个数字应比其相邻数字大或小不超过 1 个数字
虽然答案是26
(这些数字的计数),但让我们看看为什么答案包括10
、 11
和12
而不是13
10
是好的,因为1
- 0
( 10
的数字)的绝对值小于或等于1
( K
的值)
13
不好,因为1
- 3
的绝对值为2
且2
大于K
请注意,随着N
的增加,所需的成对数字比较的数量也会增加。
我将跳过用无意义的变量名解析别人的代码。 以下是我可能尝试解决的方法:
def is_valid_number(number_to_test, allowed_digit_spread):
if number_to_test < 10:
# apparently all 1 digit numbers pass
return True
# get the individual digits as a list
digits = [int(digit) for digit in str(number_to_test)]
for i in range(1, len(digits)):
current_digit = digits[i]
prior_digit = digits[i-1]
if abs(current_digit - prior_digit) > allowed_digit_spread:
# bad pairwise compare so reject
return False
return True
def get_numbers_to_test(allowed_digits):
start = pow(10, allowed_digits -1)
end = pow(10, allowed_digits)
return range(start, end)
def getCount(allowed_digits, allowed_digit_spread):
count = 0
for n in get_numbers_to_test(allowed_digits):
if is_valid_number(n, allowed_digit_spread):
count += 1
return count
if __name__ == '__main__':
n = 2
k = 1
print(getCount(n, k))
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