So I have a vector with n one digit elements. I want to make m digit numbers using these elements. m and n will be given by user.
For example:
If the original vector is {0,1,2,3,4,5,6,7,8}, I want the new vector to be {012,345,678}.
So instead of 9 one digit elements, we now have 3 three-digit elements. Once again, the user gives the value of n and m.
Now I have been able to do this by converting the elements to a string and appending them. But the problem is that the array size needs to be very large (about 3 million long).
When I use my logic for this long value, it takes ages to compile. This is what I have currently.
vector<string> list_generator(int *array,int m, int combinations)
{
string ryan, temp;
stringstream aStream;
vector<string> lexicographic;
while (next_permutation(array, array + m))
{
for (int i = 0; i < m; i = i + m)
{
for (unsigned int j = i; j < m+ 1; j++)
aStream << array[i];
temp = aStream.str();
ryan.append(temp);
aStream.str("");
}
lexicographic.push_back(ryan);
ryan.clear();
}
return (lexicographic);
}
Is there a faster way to do this.
Related
As I was looking through some string hash fucntions, I came across this one (code below). The function processes the string four bytes at a time, and interprets each of the four-byte chunks as a single long integer value. The integer values for the four-byte chunks are added together. In the end, the resulting sum is converted to the range 0 to M-1 using the modulus operator.
The following is the function code :
// Use folding on a string, summed 4 bytes at a time
long sfold(String s, int M) {
int intLength = s.length() / 4;
long sum = 0;
for (int j = 0; j < intLength; j++) {
char c[] = s.substring(j * 4, (j * 4) + 4).toCharArray();
long mult = 1;
for (int k = 0; k < c.length; k++) {
sum += c[k] * mult;
mult *= 256;
}
}
char c[] = s.substring(intLength * 4).toCharArray();
long mult = 1;
for (int k = 0; k < c.length; k++) {
sum += c[k] * mult;
mult *= 256;
}
return(Math.abs(sum) % M);
}
The confusion for me is this chunk of code, especially the first line.
char c[] = s.substring(intLength * 4).toCharArray();
long mult = 1;
for (int k = 0; k < c.length; k++) {
sum += c[k] * mult;
mult *= 256;
To my knowledge, the substring function used in this line takes as argument : begin index inclusive, The substring will start from the specified beginIndex and it will extend to the end of the string.
For the sake of example, let's assume we want to hash the following string : aaaabbbb. In this case intLength is going to be 2 (second line of function code). Replacing the value of intlength in s.substring(intLength * 4).toCharArray() will give us s.substring(8).toCharArray() which means string index is out of bounds given the string to be hashed has 8 characters.
I don't quite understand what's going on !
This hash function is awful, but to answer your question:
There is no IndexOutOfBoundsException, because "aaaabbbb".substring(8) is ""
The purpose of that last loop is to deal with leftovers when the string length isn't a multiple of 4. When s is "aaaabbbbcc", for example, then intLength == 2, and s.substring(8) is "cc".
I'm facing difficulty in understanding O(sum) complexity solution of coin changing problem.
The problem statement is:
You are given a set of coins A. In how many ways can you make sum B assuming you have infinite amount of each coin in the set.
NOTE:
Coins in set A will be unique. Expected space complexity of this problem is O(B).
The solution is:
int count( int S[], int m, int n )
{
int table[n+1];
memset(table, 0, sizeof(table));
table[0] = 1;
for(int i=0; i<m; i++)
for(int j=S[i]; j<=n; j++)
table[j] += table[j-S[i]];
return table[n];
}
can someone explain me this code.?
First, let's identify the parameters and variables used in the function:
Parameters:
S contain the denomination of all m coins. i.e. Each element contain the value of each coin.
m represents the number of coin denominations. Essentially, it's the length of array S.
n represents the sum B to be achieved.
Variables:
table: Element i in array table contains the number of ways sum i can be achieved with the given coins. table[0] = 1 because there is a single way to achieve a sum of 0 (not using any coin).
i loops through each coin.
Logic:
The number of ways to achieve a sum j = sum of the following:
number of ways to achieve a sum of j - S[0]
number of ways to achieve a sum of j - S[1]
...
number of ways to achieve a sum of j - S[m-1] (S[m-1] is the value of the mth coin)
I did not completely decipher nor validate the rest of the code, but I hope this is a step in the right direction.
Added comments to code:
#include <stdio.h>
#include <string.h>
int count( int S[], int m, int n )
{
int table[n+1];
memset(table, 0, sizeof(table));
table[0] = 1;
for(int i=0; i<m; i++) // Loop through all of the coins
for(int j=S[i]; j<=n; j++) // Achieve sum j between the value of S[i] and n.
table[j] += table[j-S[i]]; // Add to the number of ways to achieve sum j the number of ways to achieve sum j - S[i]
return table[n];
}
int main() {
int S[] = {1, 2};
int m = 2;
int n = 3;
int c = count(S, m, n);
printf("%d\n", c);
}
Notes:
The code avoids repeats: 3 = 1+1+1, 1+2 (2 ways instead of 3 if 2+1 was considered.
No dependence on the order of the coins in term of value.
Find the substring of length n that repeats a maximum number of times in a given string.
Input: abbbabbbb# 2
Output: bb
My solution:
public static String mrs(String s, int m) {
int n = s.length();
String[] suffixes = new String[n-m+1];
for (int i = 0; i < n-m+1; i++) {
suffixes[i] = s.substring(i, i+m);
}
Arrays.sort(suffixes);
String ans = "", tmp=suffixes[0].substring(0,m);
int cnt = 1, max=0;
for (int i = 0; i < n-m; i++) {
if (suffixes[i].equals(suffixes[i+1])){
cnt++;
}else{
if(cnt>max){
max = cnt;
ans =tmp;
}
cnt=0;
tmp = suffixes[i];
}
}
return ans;
}
Can it be done better than the above O(nm) time and O(n) space solution?
For a string of length L and a given length k (not to mess up with n and m which the question interchanges at times), we can compute polynomial hashes of all substrings of length k in O(L) (see Wikipedia for some elaboration on this subproblem).
Now, if we map the hash values to the number of times they occur, we get the value which occurs most frequently in O(L) (with a HashMap with high probability, or in O(L log L) with a TreeMap).
After that, just take the substring which got the most frequent hash as the answer.
This solution does not take hash collisions into account.
The idea is to just reduce the probability of collisions enough for the application (if it's too high, use multiple hashes, for example).
If the application demands that we absolutely never give a wrong answer, we can check the answer in O(L) with another algorithm (KMP, for example), and re-run the whole solution with a different hash function as long as the answer turns out to be wrong.
We need to find the maximum element in an array which is also equal to product of two elements in the same array. For example [2,3,6,8] , here 6=2*3 so answer is 6.
My approach was to sort the array and followed by a two pointer method which checked whether the product exist for each element. This is o(nlog(n)) + O(n^2) = O(n^2) approach. Is there a faster way to this ?
There is a slight better solution with O(n * sqrt(n)) if you are allowed to use O(M) memory M = max number in A[i]
Use an array of size M to mark every number while you traverse them from smaller to bigger number.
For each number try all its factors and see if those were already present in the array map.
Here is a pseudo code for that:
#define M 1000000
int array_map[M+2];
int ans = -1;
sort(A,A+n);
for(i=0;i<n;i++) {
for(j=1;j<=sqrt(A[i]);j++) {
int num1 = j;
if(A[i]%num1==0) {
int num2 = A[i]/num1;
if(array_map[num1] && array_map[num2]) {
if(num1==num2) {
if(array_map[num1]>=2) ans = A[i];
} else {
ans = A[i];
}
}
}
}
array_map[A[i]]++;
}
There is an ever better approach if you know how to find all possible factors in log(M) this just becomes O(n*logM). You have to use sieve and backtracking for that
#JerryGoyal 's solution is correct. However, I think it can be optimized even further if instead of using B pointer, we use binary search to find the other factor of product if arr[c] is divisible by arr[a]. Here's the modification for his code:
for(c=n-1;(c>1)&& (max==-1);c--){ // loop through C
for(a=0;(a<c-1)&&(max==-1);a++){ // loop through A
if(arr[c]%arr[a]==0) // If arr[c] is divisible by arr[a]
{
if(binary_search(a+1, c-1, (arr[c]/arr[a]))) //#include<algorithm>
{
max = arr[c]; // if the other factor x of arr[c] is also in the array such that arr[c] = arr[a] * x
break;
}
}
}
}
I would have commented this on his solution, unfortunately I lack the reputation to do so.
Try this.
Written in c++
#include <vector>
#include <algorithm>
using namespace std;
int MaxElement(vector< int > Input)
{
sort(Input.begin(), Input.end());
int LargestElementOfInput = 0;
int i = 0;
while (i < Input.size() - 1)
{
if (LargestElementOfInput == Input[Input.size() - (i + 1)])
{
i++;
continue;
}
else
{
if (Input[i] != 0)
{
LargestElementOfInput = Input[Input.size() - (i + 1)];
int AllowedValue = LargestElementOfInput / Input[i];
int j = 0;
while (j < Input.size())
{
if (Input[j] > AllowedValue)
break;
else if (j == i)
{
j++;
continue;
}
else
{
int Product = Input[i] * Input[j++];
if (Product == LargestElementOfInput)
return Product;
}
}
}
i++;
}
}
return -1;
}
Once you have sorted the array, then you can use it to your advantage as below.
One improvement I can see - since you want to find the max element that meets the criteria,
Start from the right most element of the array. (8)
Divide that with the first element of the array. (8/2 = 4).
Now continue with the double pointer approach, till the element at second pointer is less than the value from the step 2 above or the match is found. (i.e., till second pointer value is < 4 or match is found).
If the match is found, then you got the max element.
Else, continue the loop with next highest element from the array. (6).
Efficient solution:
2 3 8 6
Sort the array
keep 3 pointers C, B and A.
Keeping C at the last and A at 0 index and B at 1st index.
traverse the array using pointers A and B till C and check if A*B=C exists or not.
If it exists then C is your answer.
Else, Move C a position back and traverse again keeping A at 0 and B at 1st index.
Keep repeating this till you get the sum or C reaches at 1st index.
Here's the complete solution:
int arr[] = new int[]{2, 3, 8, 6};
Arrays.sort(arr);
int n=arr.length;
int a,b,c,prod,max=-1;
for(c=n-1;(c>1)&& (max==-1);c--){ // loop through C
for(a=0;(a<c-1)&&(max==-1);a++){ // loop through A
for(b=a+1;b<c;b++){ // loop through B
prod=arr[a]*arr[b];
if(prod==arr[c]){
System.out.println("A: "+arr[a]+" B: "+arr[b]);
max=arr[c];
break;
}
if(prod>arr[c]){ // no need to go further
break;
}
}
}
}
System.out.println(max);
I came up with below solution where i am using one array list, and following one formula:
divisor(a or b) X quotient(b or a) = dividend(c)
Sort the array.
Put array into Collection Col.(ex. which has faster lookup, and maintains insertion order)
Have 2 pointer a,c.
keep c at last, and a at 0.
try to follow (divisor(a or b) X quotient(b or a) = dividend(c)).
Check if a is divisor of c, if yes then check for b in col.(a
If a is divisor and list has b, then c is the answer.
else increase a by 1, follow step 5, 6 till c-1.
if max not found then decrease c index, and follow the steps 4 and 5.
Check this C# solution:
-Loop through each element,
-loop and multiply each element with other elements,
-verify if the product exists in the array and is the max
private static int GetGreatest(int[] input)
{
int max = 0;
int p = 0; //product of pairs
//loop through the input array
for (int i = 0; i < input.Length; i++)
{
for (int j = i + 1; j < input.Length; j++)
{
p = input[i] * input[j];
if (p > max && Array.IndexOf(input, p) != -1)
{
max = p;
}
}
}
return max;
}
Time complexity O(n^2)
I'm trying to write an algorithm that will generate all strings of length nm, with exactly n of each number 1, 2, ... m,
For instance all strings of length 6, with exactly two 1's, two 2's and two 3's e.g. 112233, 121233,
I managed to do this with just 1's and 2's using a recursive method, but can't seem to get something that works when I introduce 3's.
When m = 2, the algorithm I have is:
generateAllStrings(int len, int K, String str)
{
if(len == 0)
{
output(str);
}
if(K > 0)
{
generateAllStrings(len - 1, K - 1, str + '2');
}
if(len > K)
{
generateAllStrings(len - 1, K, str + '1');
}
}
I've tried inserting similar conditions for the third number but the algorithm doesn't give a correct output. After that I wouldn't even know how to generalise for 4 numbers and above.
Is recursion the right thing to do? Any help would be appreciated.
One option would be to list off all distinct permutations of the string 111...1222...2...nnn....n. There are nice algorithms for enumerating all distinct permutations of a string in time proportional to the length of the string, and they'd probably be a good way to go about solving this problem.
To use a simple recursive algorithm, give each recursion the permutation so far (variable perm), and the number of occurances of each digit that is still available (array count).
Run the code snippet to generate all unique permutations for n=2 and m=4 (set: 11223344).
function permutations(n, m) {
var perm = "", count = []; // start with empty permutation
for (var i = 0; i < m; i++) count[i] = n; // set available number for each digit = n
permute(perm, count); // start recursion with "" and [n,n,n...]
function permute(perm, count) {
var done = true;
for (var i = 0; i < count.length; i++) { // iterate over all digits
if (count[i] > 0) { // more instances of digit i available
var c = count.slice(); // create hard copy of count array
--c[i]; // decrement count of digit i
permute(perm + (i + 1), c); // add digit to permutation and recurse
done = false; // digits left over: not the last step
}
}
if (done) document.write(perm + "<BR>"); // no digits left: complete permutation
}
}
permutations(2, 4);
You can easily do this using DFS (or BFS alternatively). We can define an graph such that each node contains one string and a node is connected to any node that holds a string with a pair of int swaped in comparison to the original string. This graph is connected, thus we can easily generate a set of all nodes; which will contain all strings that are searched:
set generated_strings
list nodes
nodes.add(generateInitialString(N , M))
generated_strings.add(generateInitialString(N , M))
while(!nodes.empty())
string tmp = nodes.remove(0)
for (int i in [0 , N * M))
for (int j in distinct([0 , N * M) , i))
string new = swap(tmp , i , j)
if (!generated_strings.contains(new))
nodes.add(new)
generated_strings.add(new)
//generated_strings now contains all strings that can possibly be generated.