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实例003:完全平方数 一个整数,它加上100后是一个完全平方数,再加上168又是一个完全平方数,请问该数是多少?
2022-07-05 08:16:00 【懒笑翻】
实例003:完全平方数
题目:一个整数,它加上100后是一个完全平方数,再加上168又是一个完全平方数,请问该数是多少?
程序分析:因为168对于指数爆炸来说实在太小了,所以可以直接省略数学分析,用最朴素的方法来获取上限,
n = 0
while (n + 1) ** 2 - n * n <= 168:
n += 1
print('----n=', n) # 可以得出范围是在(n+1)**2内
思路是:
最坏的结果是n的平方与(n+1)的平方刚好差168,由于是平方的关系,不可能存在比这更大的间隙。
设这个数是i (i+100)**0.5 (i+100+168)**0.5 则结果都是整数。
至于判断是否是完全平方数,最简单的方法是:平方根的值小数为0即可。
for i in range((n + 1) ** 2):
if i ** 0.5 == int(i ** 0.5) and (i + 168) ** 0.5 == int((i + 168) ** 0.5):
print(i - 100)
结合起来就是:
# 最坏的结果就是n的平方与(n+1)的平方刚好差168,不可能存在比这更大的间隙,我们据此先得出n
n = 0
while (n + 1) ** 2 - n * n <= 168:
n += 1
print('----n=', n) # 可以得出范围是在(n+1)**2内
for i in range((n + 1) ** 2):
if i ** 0.5 == int(i ** 0.5) and (i + 168) ** 0.5 == int((i + 168) ** 0.5):
print(i - 100)
------n= 84
-99
21
261
1581
因此该数可以是:-99 21 61 1581
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