我尝试了解Codility问题的解决方案。该问题要求计算不是每个元素的除数的数组的元素数。完整描述如下:
You are given a non-empty zero-indexed array A consisting of N integers.
For each number A[i] such that 0 ≤ i < N, we want to count the number of elements of the array that are not the divisors of A[i]. We say that these elements are non-divisors.
For example, consider integer N = 5 and array A such that:
A[0] = 3
A[1] = 1
A[2] = 2
A[3] = 3
A[4] = 6
For the following elements:
A[0] = 3, the non-divisors are: 2, 6,
A[1] = 1, the non-divisors are: 3, 2, 3, 6,
A[2] = 2, the non-divisors are: 3, 3, 6,
A[3] = 3, the non-divisors are: 2, 6,
A[6] = 6, there aren't any non-divisors.
Write a function:
class Solution { public int[] solution(int[] A); }
that, given a non-empty zero-indexed array A consisting of N integers, returns a sequence of integers representing the amount of non-divisors.
The sequence should be returned as:
a structure Results (in C), or
a vector of integers (in C++), or
a record Results (in Pascal), or
an array of integers (in any other programming language).
For example, given:
A[0] = 3
A[1] = 1
A[2] = 2
A[3] = 3
A[4] = 6
the function should return [2, 4, 3, 2, 0], as explained above.
Assume that:
N is an integer within the range [1..50,000];
each element of array A is an integer within the range [1..2 * N].
Complexity:
expected worst-case time complexity is O(N*log(N));
expected worst-case space complexity is O(N), beyond input storage (not counting the storage required for input arguments).
Elements of input arrays can be modified.
我也有解决方案。
// int[] A = {3, 1, 2, 3, 6};
public static int[] solution(int[] A) {
int[][] D = new int[2 * A.length + 1][2];
int[] res = new int[A.length];
//-----
// 0 1
// 0 0
// 1 -1
// 1 -1
// 2 -1
// 0 0
// 0 0
// 1 -1
// 0 0
// 0 0
// 0 0
// 0 0
//-----
for (int i = 0; i < A.length; i++) {
// D[A[i]][0]++;
D[A[i]][0] = D[A[i]][0] + 1;
D[A[i]][1] = -1;
}
for (int i = 0; i < A.length; i++){
if(D[A[i]][1]==-1){
D[A[i]][1]=0;
for (int j = 1; j*j <= A[i]; j++) {
if(A[i] % j == 0) {
// D[A[i]][1] = D[A[i]][1] + D[j][0];
D[A[i]][1] += D[j][0];
if (A[i]/j != j){
D[A[i]][1]+= D[A[i]/j][0];
}
}
}
}
}
for (int i = 0; i < A.length; i++) {
res[i] = A.length - D[A[i]][1];
}
return res;
}
当我试图密切关注时,我有点失去了for循环中发生的事情的轨迹,
for (int j = 1; j*j <= A[i]; j++) {
if(A[i] % j == 0) {
// D[A[i]][1] = D[A[i]][1] + D[j][0];
D[A[i]][1] += D[j][0];
if (A[i]/j != j){
D[A[i]][1]+= D[A[i]/j][0];
}
}
}
例如,为什么我们需要检查j*j <= A[i]
等条件以及if(A[i] % j == 0)
的内容。我需要解释他们为解决问题而部署的算法。
我没有懒惰,因为我已经得到了解决方案而没有尝试。实际上,我现在需要花时间和帮助。问题硬度在网站中列为RESPECTABLE
。
答案 0 :(得分:1)
D
数据结构/矩阵使得0th
列和jth
行计算j
在数组A
中出现的次数。换句话说,D[A[j]][0]
是A[j]
的值在数组中的次数。
在循环之后,1st
列和kth
行计算数组中除A[k]
之间的元素数。换句话说,D[A[k]][1]
是数组中A[k]
的除数。
最后,结果r[j]
只是r[j] = (A.length) - D[A[j]][1]
。因为我们想要的元素数量不是除数。
为什么循环有效?
如果A[i] % j == 0
那么我们想要做的是计算j
中A
出现的次数,然后将其添加到D[A[i]][1]
。这就是你有D[A[i]][1] += D[j][0];
行的原因。此外,A[i]/j
也是一个不同的因素(A[i] = j
除外)。
数学部分来证明集合{A,B | A * B = N&amp; A&lt; sqrt(N)} = {N的除数组}。换句话说,你必须证明所有的除数都被覆盖了(这应该很容易,但我现在太累了,不能想到证明,这就是Stack溢出)。