CareerCup 2^i * 3^j * 5^k * 7^l

最新推荐文章于 2017-09-08 16:16:50 发布

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本文介绍了一种使用优先队列生成形如2^i*3^j*5^k*7^l的有序数列的高效算法。通过不断将当前最小值乘以2、3、5、7并重新加入队列的方式，可以确保生成的数列始终有序。此方法适用于生成N个数的情况，其时间复杂度为O(NlogN)。

Given an equation in the form 2^i * 3^j * 5^k * 7^l where i,j,k,l >=0 are integers.write a program to generate numbers from that equation in sorted order efficiently.

for example numbers from that equation will be in the order 2,3,5,6,7,8,9.....and so on..

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The key here is to use a heap (aka priority queue). Start with number 1 and add it to the heap. Then, do a loop
a) Pop the minimum value from the heap
b) Print this minimum
c) Add minimum*2, *3, *5 and *7 to the heap

If we want N numbers, the complexity will be O(N log N).
Note that since i,j,k,l >=0, the first number should be 1, not 2.