You are given two non-empty linked lists representing two non-negative integers. The digits are stored in reverse order and each of their nodes contain a single digit. Add the two numbers and return it as a linked list.
Example:
Input: (2 -> 4 -> 3) + (5 -> 6 -> 4)
Output: 7 -> 0 -> 8
Explanation: 342 + 465 = 807
class Solution {
public:
ListNode* addTwoNumbers(ListNode* l1, ListNode* l2) {
vector<int> a1;
vector<int> a2;
vector<int> result;
while(l1->next||l2->next)
{
a1.push_back(l1->val);
a2.push_back(l2->val);
l1=l1->next;
l2=l2->next;
}
int v1=0;
int v2=0;
for(auto d:a1)
{
v1=v1*10+d;
}
for(auto f:a2)
{
v2=v2*10+f;
}
int v3=v1+v2;
int r;
while(v3>0)
{
r=v3%10;
v3=v3/10;
result.push_back(r);
}
ListNode* p= new ListNode(result[0]);
ListNode* start=p;
ListNode* add=p;
int i;
for(i=1;i<result.size();i++)
{
ListNode* temp=new ListNode(result[i]);
add->next=temp;
add=add->next;
}
return p;
}
};
Output(1st element of the linked list is not printing)
Input: [2,4,3]
[5,6,4]
Your answer:[0,8]
Expected answer:[7,0,8]
I am not able to print the first element of the resultant linked list. I Tried with different test cases and its printing everything right except the first element.
while(l1->next||l2->next)
{
a1.push_back(l1->val);
a2.push_back(l2->val);
l1=l1->next;
l2=l2->next;
}
This will crash if l1 and l2 have different lengths. It will continue looping once a list is done. But, in the immediate the issue is that the last element has:
valid l1->val
null l1->next
So, for the last element, you will not push into a1 and/or a2.
If you are sure you have identical length, then you could simply:
while(l1 || l2)
{
a1.push_back(l1->val);
a2.push_back(l2->val);
l1=l1->next;
l2=l2->next;
}
I think you are not considering the carry. If the sum of last digits of two numbers > 9, additional node needs to be created.
When I see the implement of levelDB's cache, address. I can not understand why it use while loop in for loop(in function Resize), and I think it can replace by if statement. I hope someone can help me.
void Resize() {
uint32_t new_length = 4;
while (new_length < elems_) {
new_length *= 2;
}
LRUHandle** new_list = new LRUHandle*[new_length];
memset(new_list, 0, sizeof(new_list[0]) * new_length);
uint32_t count = 0;
for (uint32_t i = 0; i < length_; i++) {
LRUHandle* h = list_[i];
while (h != NULL) {
LRUHandle* next = h->next_hash;
uint32_t hash = h->hash;
LRUHandle** ptr = &new_list[hash & (new_length - 1)];
h->next_hash = *ptr;
*ptr = h;
h = next;
count++;
}
}
assert(elems_ == count);
delete[] list_;
list_ = new_list;
length_ = new_length;
}
};
list_ is apparently an array of linked lists. while (h != NULL), combined with h = next (where next is h->next_hash), means the while loop will operate on all the elements of every linked list, stopping only when the last element is reached (when h becomes NULL, either because the list was empty or because next_hash of an element was NULL).
If you replaced it with if (h != NULL), it would only work on the first element of the linked list.
It looks like list_ is a dynamic array of singly linked lists.
I assume the list_ looks something like the following
list_[0]-> node_1 -> node_2 -> null
list_[1]-> node_3 -> null
list_[2]-> null
....
list_[n]-> node_m-1 -> node_m -> null
To properly copy all of the elements into new_list you need to use the while loop. Otherwise any element that is not directly addressable from list_ will not be copied/hashed into the new_list. In the above diagram that would mean node_2 and node_m+1 would not be added to the new_list.
The new_list will keep the same shape but should have fewer collisions.
Using an if statement the new_list would look something like:
new_list[0]-> node_1 -> null
new_list[1]-> null
new_list[2]-> node_2 -> null
...
new_list[p-1]-> node_k -> null
new_list[p] -> null
That is each item in new_list would point to a list of 1 or zero elements.
Note node_1 in this diagram isn't necessarily the same as node 1 in the above diagram.
Using an If statement instead of a while loop will also lead to a memory leak since you can no longer access all of the elements.
Variable list_[i] has a sub list, while inside the for loop is looping over the sub list.
The if-statement doesn't work, if you have two elements list_[i] and list_[j] are both hashed to a same index new_list[m]. In such a case, you have to use while-statement to merge two buckets. Meanwhile, the length of every bucket in this implementation is less than 1 on average, so the while-statement here is actually as fast as the if-statement.
I have written a function to merge two singly linked lists. For example, if A = 1 2 3 and B = 3 4 5 and I merge them both, I get A = 1 2 3 3 4 5 and B = NULL. What I want to do now is to write a function which sorts a singly linked list using the mergesort algorithm (somehow using my merge function). For mergesort, if I'm not wrong, I would have to break the linked list in half in some way and then do the rest of the work. I have a small outline written down on how I want to do it. I'm not sure how I would go about doing the splitting at the moment. Any help is appreciated!
List mergeSort(List L) {
if(|L| > 1) {
split L into L1 and L2;
L1 = mergeSort(L1);
L2 = mergeSort(L1);
return(merge(L1,L2));
}
}
My merge function below:
void mylist::merge(mylist& b)
{
if (!this->isSorted() || !b.isSorted())
cout << "error" << endl;
Node* ptr1 = b.head;
Node* prev_a = NULL;
Node* curr_a = head;
Node* curr_b = ptr1;
while (curr_b) {
if (curr_a && head->key < ptr1->key) {
prev_a=curr_a;
curr_a = curr_a->next;
}
else {
Node* b_next = curr_b->next;
curr_b->next = curr_a;
if (prev_a) prev_a->next = curr_b;
else head = curr_b; // curr_b is first element in 'a'
prev_a = curr_b;
curr_b = b_next;
}
return;
}
To divide the list into two halves, two pointers can be used.
Both pointers start at the head of the list. One pointer move every two steps, while the other
move one step each time.
When the fast pointer reach null, the slower pointer will points to the middle of the list.
ListNode *fast(head->next), *slow(head);
while(fast && fast->next) {
fast = fast->next->next;
slow = slow->next;
}
void insert(int number){
Node* temp0 = NULL;
Node* temp1 = head;
Node* temp = new Node();
int sum = 0;
while(temp1!= NULL && sum<=number){
// loop condition edited, before it was temp1!= NULL && sum>=number
sum+=temp1->content;
temp0=temp1;
temp1=temp1->next;
}
if(temp0 == NULL){
temp->content = number;
temp->next = head;
if(head!=NULL){
head->content -= temp->content;
}
head = temp;
}
else{
temp0->next = temp;
temp->content = number - sum;
temp1->content -= temp->content;
temp->next = temp1;
}// end of else
}// end of void insert
I ran into a problem, which i described in one of my previous questions, but still, i'm looking to implement the solution on my own.
In short, i want to make a "relative" list:
for example, for elements 1 5 7 2 4 6 the list would look like 1 1 2 1 1 1
I would make a priority queue list 1 2 4 5 7 6, and then i would change elements relative to the previous one:first element would stay 1,second would be 2-1 = 1, third would be 4-2 = 2, fourth 5-4 = 1 and so on.
When i form a priority queue, i would replace the current element with the difference of it's value and the value of the previous element.
I'm having problems implementing the insert feature. The code is given at the top of the question.
The idea is, i go through the list, adding the "difference" (which is the content field of my Node* structure) to a counter variable. When the sum counter becomes greater or equal to the element i need to insert, i found the position where to insert it.
If temp0 is null, i insert the element on the first position. If it's not the only element, i update the content of the next element - head, which was the previous first element.
If the number needs to be inserted somewhere in the middle of the list (or at the end), i update the content as sum - number, which would be a number >= 0, which is okay. Also, i update the content of the new's next element (temp1) as temp->content - temp->content.
For some reason, this does not work.
When i insert 4 2 8, instead of 2 2 4, i'm getting 4 -2 6 as the result list.
Your loop is "wrong", sum starts out being 0, so as long as number is not zero or negative, it never enters "find the place" loop. So every number is inserted at the beginning, rather than in its rightful place.
while(temp1!= NULL && sum>=number){
sum+=temp1->content;
temp0=temp1;
temp1=temp1->next;
}
Change it to sum <= number, and I believe it will work. Not sure what you want to have happen if you insert the same number multiple times... May you want sum < number instead?
Edit: You will also have some method to detect that your "new" value is less than the existing one, and if so insert a new head, rather than after the existing number. I'm not sure what the exact code for this would be, but you do need to do something along the lines of:
if (number < sum)
{
temp->next = head;
head->content -= temp->content;
head = temp;
}
else
{
... existing insert code ...
}
I have to permute N first elements of a singly linked list of length n, randomly. Each element is defined as:
typedef struct E_s
{
struct E_s *next;
}E_t;
I have a root element and I can traverse the whole linked list of size n. What is the most efficient technique to permute only N first elements (starting from root) randomly?
So, given a->b->c->d->e->f->...x->y->z I need to make smth. like f->a->e->c->b->...x->y->z
My specific case:
n-N is about 20% relative to n
I have limited RAM resources, the best algorithm should make it in place
I have to do it in a loop, in many iterations, so the speed does matter
The ideal randomness (uniform distribution) is not required, it's Ok if it's "almost" random
Before making permutations, I traverse the N elements already (for other needs), so maybe I could use this for permutations as well
UPDATE: I found this paper. It states it presents an algorithm of O(log n) stack space and expected O(n log n) time.
I've not tried it, but you could use a "randomized merge-sort".
To be more precise, you randomize the merge-routine. You do not merge the two sub-lists systematically, but you do it based on a coin toss (i.e. with probability 0.5 you select the first element of the first sublist, with probability 0.5 you select the first element of the right sublist).
This should run in O(n log n) and use O(1) space (if properly implemented).
Below you find a sample implementation in C you might adapt to your needs. Note that this implementation uses randomisation at two places: In splitList and in merge. However, you might choose just one of these two places. I'm not sure if the distribution is random (I'm almost sure it is not), but some test cases yielded decent results.
#include <stdio.h>
#include <stdlib.h>
#define N 40
typedef struct _node{
int value;
struct _node *next;
} node;
void splitList(node *x, node **leftList, node **rightList){
int lr=0; // left-right-list-indicator
*leftList = 0;
*rightList = 0;
while (x){
node *xx = x->next;
lr=rand()%2;
if (lr==0){
x->next = *leftList;
*leftList = x;
}
else {
x->next = *rightList;
*rightList = x;
}
x=xx;
lr=(lr+1)%2;
}
}
void merge(node *left, node *right, node **result){
*result = 0;
while (left || right){
if (!left){
node *xx = right;
while (right->next){
right = right->next;
}
right->next = *result;
*result = xx;
return;
}
if (!right){
node *xx = left;
while (left->next){
left = left->next;
}
left->next = *result;
*result = xx;
return;
}
if (rand()%2==0){
node *xx = right->next;
right->next = *result;
*result = right;
right = xx;
}
else {
node *xx = left->next;
left->next = *result;
*result = left;
left = xx;
}
}
}
void mergeRandomize(node **x){
if ((!*x) || !(*x)->next){
return;
}
node *left;
node *right;
splitList(*x, &left, &right);
mergeRandomize(&left);
mergeRandomize(&right);
merge(left, right, &*x);
}
int main(int argc, char *argv[]) {
srand(time(NULL));
printf("Original Linked List\n");
int i;
node *x = (node*)malloc(sizeof(node));;
node *root=x;
x->value=0;
for(i=1; i<N; ++i){
node *xx;
xx = (node*)malloc(sizeof(node));
xx->value=i;
xx->next=0;
x->next = xx;
x = xx;
}
x=root;
do {
printf ("%d, ", x->value);
x=x->next;
} while (x);
x = root;
node *left, *right;
mergeRandomize(&x);
if (!x){
printf ("Error.\n");
return -1;
}
printf ("\nNow randomized:\n");
do {
printf ("%d, ", x->value);
x=x->next;
} while (x);
printf ("\n");
return 0;
}
Convert to an array, use a Fisher-Yates shuffle, and convert back to a list.
I don't believe there's any efficient way to randomly shuffle singly-linked lists without an intermediate data structure. I'd just read the first N elements into an array, perform a Fisher-Yates shuffle, then reconstruct those first N elements into the singly-linked list.
First, get the length of the list and the last element. You say you already do a traversal before randomization, that would be a good time.
Then, turn it into a circular list by linking the first element to the last element. Get four pointers into the list by dividing the size by four and iterating through it for a second pass. (These pointers could also be obtained from the previous pass by incrementing once, twice, and three times per four iterations in the previous traversal.)
For the randomization pass, traverse again and swap pointers 0 and 2 and pointers 1 and 3 with 50% probability. (Do either both swap operations or neither; just one swap will split the list in two.)
Here is some example code. It looks like it could be a little more random, but I suppose a few more passes could do the trick. Anyway, analyzing the algorithm is more difficult than writing it :vP . Apologies for the lack of indentation; I just punched it into ideone in the browser.
http://ideone.com/9I7mx
#include <iostream>
#include <cstdlib>
#include <ctime>
using namespace std;
struct list_node {
int v;
list_node *n;
list_node( int inv, list_node *inn )
: v( inv ), n( inn) {}
};
int main() {
srand( time(0) );
// initialize the list and 4 pointers at even intervals
list_node *n_first = new list_node( 0, 0 ), *n = n_first;
list_node *p[4];
p[0] = n_first;
for ( int i = 1; i < 20; ++ i ) {
n = new list_node( i, n );
if ( i % (20/4) == 0 ) p[ i / (20/4) ] = n;
}
// intervals must be coprime to list length!
p[2] = p[2]->n;
p[3] = p[3]->n;
// turn it into a circular list
n_first->n = n;
// swap the pointers around to reshape the circular list
// one swap cuts a circular list in two, or joins two circular lists
// so perform one cut and one join, effectively reordering elements.
for ( int i = 0; i < 20; ++ i ) {
list_node *p_old[4];
copy( p, p + 4, p_old );
p[0] = p[0]->n;
p[1] = p[1]->n;
p[2] = p[2]->n;
p[3] = p[3]->n;
if ( rand() % 2 ) {
swap( p_old[0]->n, p_old[2]->n );
swap( p_old[1]->n, p_old[3]->n );
}
}
// you might want to turn it back into a NULL-terminated list
// print results
for ( int i = 0; i < 20; ++ i ) {
cout << n->v << ", ";
n = n->n;
}
cout << '\n';
}
For the case when N is really big (so it doesn't fit your memory), you can do the following (a sort of Knuth's 3.4.2P):
j = N
k = random between 1 and j
traverse the input list, find k-th item and output it; remove the said item from the sequence (or mark it somehow so that you won't consider it at the next traversal)
decrease j and return to 2 unless j==0
output the rest of the list
Beware that this is O(N^2), unless you can ensure random access in the step 3.
In case the N is relatively small, so that N items fit into the memory, just load them into array and shuffle, like #Mitch proposes.
If you know both N and n, I think you can do it simply. It's fully random, too. You only iterate through the whole list once, and through the randomized part each time you add a node. I think that's O(n+NlogN) or O(n+N^2). I'm not sure. It's based upon updating the conditional probability that a node is selected for the random portion given what happened to previous nodes.
Determine the probability that a certain node will be selected for the random portion given what happened to previous nodes (p=(N-size)/(n-position) where size is number of nodes previously chosen and position is number of nodes previously considered)
If node is not selected for random part, move to step 4. If node is selected for the random part, randomly choose place in random part based upon the size so far (place=(random between 0 and 1) * size, size is again number of previous nodes).
Place the node where it needs to go, update the pointers. Increment size. Change to looking at the node that previously pointed at what you were just looking at and moved.
Increment position, look at the next node.
I don't know C, but I can give you the pseudocode. In this, I refer to the permutation as the first elements that are randomized.
integer size=0; //size of permutation
integer position=0 //number of nodes you've traversed so far
Node head=head of linked list //this holds the node at the head of your linked list.
Node current_node=head //Starting at head, you'll move this down the list to check each node, whether you put it in the list.
Node previous=head //stores the previous node for changing pointers. starts at head to avoid asking for the next field on a null node
While ((size not equal to N) or (current_node is not null)){ //iterating through the list until the permutation is full. We should never pass the end of list, but just in case, I include that condition)
pperm=(N-size)/(n-position) //probability that a selected node will be in the permutation.
if ([generate a random decimal between 0 and 1] < pperm) //this decides whether or not the current node will go in the permutation
if (j is not equal to 0){ //in case we are at start of list, there's no need to change the list
pfirst=1/(size+1) //probability that, if you select a node to be in the permutation, that it will be first. Since the permutation has
//zero elements at start, adding an element will make it the initial node of a permutation and percent chance=1.
integer place_in_permutation = round down([generate a random decimal between 0 and 1]/pfirst) //place in the permutation. note that the head =0.
previous.next=current_node.next
if(place_in_permutation==0){ //if placing current node first, must change the head
current_node.next=head //set the current Node to point to the previous head
head=current_node //set the variable head to point to the current node
}
else{
Node temp=head
for (counter starts at zero. counter is less than place_in_permutation-1. Each iteration, increment counter){
counter=counter.next
} //at this time, temp should point to the node right before the insertion spot
current_node.next=temp.next
temp.next=current_node
}
current_node=previous
}
size++ //since we add one to the permutation, increase the size of the permutation
}
j++;
previous=current_node
current_node=current_node.next
}
You could probably increase the efficiency if you held on to the most recently added node in case you had to add one to the right of it.
Similar to Vlad's answer, here is a slight improvement (statistically):
Indices in algorithm are 1 based.
Initialize lastR = -1
If N <= 1 go to step 6.
Randomize number r between 1 and N.
if r != N
4.1 Traverse the list to item r and its predecessor.
If lastR != -1
If r == lastR, your pointer for the of the r'th item predecessor is still there.
If r < lastR, traverse to it from the beginning of the list.
If r > lastR, traverse to it from the predecessor of the lastR'th item.
4.2 remove the r'th item from the list into a result list as the tail.
4.3 lastR = r
Decrease N by one and go to step 2.
link the tail of the result list to the head of the remaining input list. You now have the original list with the first N items permutated.
Since you do not have random access, this will reduce the traversing time you will need within the list (I assume that by half, so asymptotically, you won't gain anything).
O(NlogN) easy to implement solution that does not require extra storage:
Say you want to randomize L:
is L has 1 or 0 elements you are done
create two empty lists L1 and L2
loop over L destructively moving its elements to L1 or L2 choosing between the two at random.
repeat the process for L1 and L2 (recurse!)
join L1 and L2 into L3
return L3
Update
At step 3, L should be divided into equal sized (+-1) lists L1 and L2 in order to guaranty best case complexity (N*log N). That can be done adjusting the probability of one element going into L1 or L2 dynamically:
p(insert element into L1) = (1/2 * len0(L) - len(L1)) / len(L)
where
len(M) is the current number of elements in list M
len0(L) is the number of elements there was in L at the beginning of step 3
There is an algorithm takes O(sqrt(N)) space and O(N) time, for a singly linked list.
It does not generate a uniform distribution over all permutation sequence, but it can gives good permutation that is not easily distinguishable. The basic idea is similar to permute a matrix by rows and columns as described below.
Algorithm
Let the size of the elements to be N, and m = floor(sqrt(N)). Assuming a "square matrix" N = m*m will make this method much clear.
In the first pass, you should store the pointers of elements that is separated by every m elements as p_0, p_1, p_2, ..., p_m. That is, p_0->next->...->next(m times) == p_1 should be true.
Permute each row
For i = 0 to m do:
Index all elements between p_i->next to p_(i+1)->next in the link list by an array of size O(m)
Shuffle this array using standard method
Relink the elements using this shuffled array
Permute each column.
Initialize an array A to store pointers p_0, ..., p_m. It is used to traverse the columns
For i = 0 to m do
Index all elements pointed A[0], A[1], ..., A[m-1] in the link list by an array of size m
Shuffle this array
Relink the elements using this shuffled array
Advance the pointer to next column A[i] := A[i]->next
Note that p_0 is an element point to the first element and the p_m point to the last element. Also, if N != m*m, you may use m+1 separation for some p_i instead. Now you get a "matrix" such that the p_i point to the start of each row.
Analysis and randomness
Space complexity: This algorithm need O(m) space to store the start of row. O(m) space to store the array and O(m) space to store the extra pointer during column permutation. Hence, time complexity is ~ O(3*sqrt(N)). For N = 1000000, it is around 3000 entries and 12 kB memory.
Time complexity: It is obviously O(N). It either walk through the "matrix" row by row or column by column
Randomness: The first thing to note is that each element can go to anywhere in the matrix by row and column permutation. It is very important that elements can go to anywhere in the linked list. Second, though it does not generate all permutation sequence, it does generate part of them. To find the number of permutation, we assume N=m*m, each row permutation has m! and there is m row, so we have (m!)^m. If column permutation is also include, it is exactly equal to (m!)^(2*m), so it is almost impossible to get the same sequence.
It is highly recommended to repeat the second and third step by at least one more time to get an more random sequence. Because it can suppress almost all the row and column correlation to its original location. It is also important when your list is not "square". Depends on your need, you may want to use even more repetition. The more repetition you use, the more permutation it can be and the more random it is. I remember that it is possible to generate uniform distribution for N=9 and I guess that it is possible to prove that as repetition tends to infinity, it is the same as the true uniform distribution.
Edit: The time and space complexity is tight bound and is almost the same in any situation. I think this space consumption can satisfy your need. If you have any doubt, you may try it in a small list and I think you will find it useful.
The list randomizer below has complexity O(N*log N) and O(1) memory usage.
It is based on the recursive algorithm described on my other post modified to be iterative instead of recursive in order to eliminate the O(logN) memory usage.
#include <stdlib.h>
#include <stdio.h>
#include <string.h>
typedef struct node {
struct node *next;
char *str;
} node;
unsigned int
next_power_of_two(unsigned int v) {
v--;
v |= v >> 1;
v |= v >> 2;
v |= v >> 4;
v |= v >> 8;
v |= v >> 16;
return v + 1;
}
void
dump_list(node *l) {
printf("list:");
for (; l; l = l->next) printf(" %s", l->str);
printf("\n");
}
node *
array_to_list(unsigned int len, char *str[]) {
unsigned int i;
node *list;
node **last = &list;
for (i = 0; i < len; i++) {
node *n = malloc(sizeof(node));
n->str = str[i];
*last = n;
last = &n->next;
}
*last = NULL;
return list;
}
node **
reorder_list(node **last, unsigned int po2, unsigned int len) {
node *l = *last;
node **last_a = last;
node *b = NULL;
node **last_b = &b;
unsigned int len_a = 0;
unsigned int i;
for (i = len; i; i--) {
double pa = (1.0 + RAND_MAX) * (po2 - len_a) / i;
unsigned int r = rand();
if (r < pa) {
*last_a = l;
last_a = &l->next;
len_a++;
}
else {
*last_b = l;
last_b = &l->next;
}
l = l->next;
}
*last_b = l;
*last_a = b;
return last_b;
}
unsigned int
min(unsigned int a, unsigned int b) {
return (a > b ? b : a);
}
randomize_list(node **l, unsigned int len) {
unsigned int po2 = next_power_of_two(len);
for (; po2 > 1; po2 >>= 1) {
unsigned int j;
node **last = l;
for (j = 0; j < len; j += po2)
last = reorder_list(last, po2 >> 1, min(po2, len - j));
}
}
int
main(int len, char *str[]) {
if (len > 1) {
node *l;
len--; str++; /* skip program name */
l = array_to_list(len, str);
randomize_list(&l, len);
dump_list(l);
}
return 0;
}
/* try as: a.out list of words foo bar doz li 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
*/
Note that this version of the algorithm is completely cache unfriendly, the recursive version would probably perform much better!
If both the following conditions are true:
you have plenty of program memory (many embedded hardwares execute directly from flash);
your solution does not suffer that your "randomness" repeats often,
Then you can choose a sufficiently large set of specific permutations, defined at programming time, write a code to write the code that implements each, and then iterate over them at runtime.