[英]Why is the runtime of this algorithm O(m+n)?
我不明白以下算法的運行時間如何是 O(m+n)。 關於算法,它用於尋找兩個列表的公共節點(兩個列表的長度可以不同)。
if (len1 < len2)
{
head1 = list2;
head2 = list1;
diff = len2 - len1;
}
這應該是 O(1)。
for(int i = 0; i < diff; i++)
head1 = head1->next;
O(n)。
while(head1 != NULL && head2 != NULL)
{
if(head1 == head2)
return head1->data;
head1= head1->next;
head2= head2->next;
}
O(n)。
總的來說,我得到了 O(n^2)...
這里完整的算法:
struct node* findMergeNode(struct node* list1, struct node* list2)
{
int len1, len2, diff;
struct node* head1 = list1;
struct node* head2 = list2;
len1 = getlength(head1);
len2 = getlength(head2);
diff = len1 - len2;
if (len1 < len2)
{
head1 = list2;
head2 = list1;
diff = len2 - len1;
}
for(int i = 0; i < diff; i++)
head1 = head1->next;
while(head1 != NULL && head2 != NULL)
{
if(head1 == head2)
return head1->data;
head1= head1->next;
head2= head2->next;
}
return NULL;
}
您所做的只是相互獨立地迭代給定的列表。 這里耗時最長的是確定列表的大小。 (僅此,如果O(n+m)
)
struct node* findMergeNode(struct node* list1, struct node* list2)
{
// Assuming list1 is of size m
// Assuming list2 is of size n
int len1, len2, diff;
struct node* head1 = list1;
struct node* head2 = list2;
len1 = getlength(head1); // O(m) - as you need to iterate though it
len2 = getlength(head2); // O(n) - same here
diff = len1 - len2;
// Right now you already reached O(m+n)
if (len1 < len2) // O(1)
{
// this entire block is of constant length, as there are no loops or anything
head1 = list2;
head2 = list1;
diff = len2 - len1;
}
// So we are still at O(m+n)
for(int i = 0; i < diff; i++) // O(abs(m-n)) = O(diff)
head1 = head1->next;
// As diff = abs(m-n) which is smaller than m and n, we can 'ignore' this as well
// So we are - again - still at O(m+n)
while(head1 != NULL && head2 != NULL) // O(n-diff) or O(m-diff) - depending on the previous if-statement
{
// all the operations in here are of constant time as well
// however, as we loop thorugh them, the time is as stated above
if(head1 == head2)
return head1->data;
head1= head1->next;
head2= head2->next;
}
// But here again: n-diff < n+m and m-diff < n+m
// So we sill keep O(m+n)
return NULL;
}
希望這會有所幫助。
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