I want to find a way by which I can map "b m w" to "bmw" and "ali baba" to "alibaba" in both the following examples.
"b m w shops" and "bmw"
I need to determine whether I can write "b m w" as "bmw"
I thought of this approach:
remove spaces from the original string. This gives "bmwshops". And now find the Largest common substring in "bmwshop" and "bmw".
Second example:
"ali baba and 40 thieves" and "alibaba and 40 thieves"
The above approach does not work in this case.
Is there any standard algorithm that could be used?
It sounds like you're asking this question: "How do I determine if string A can be made equal to string B by removing (some) spaces?".
What you can do is iterate over both strings, advancing within both whenever they have the same character, otherwise advancing along the first when it has a space, and returning false otherwise. Like this:
static bool IsEqualToAfterRemovingSpacesFromOne(this string a, string b) {
return a.IsEqualToAfterRemovingSpacesFromFirst(b)
|| b.IsEqualToAfterRemovingSpacesFromFirst(a);
}
static bool IsEqualToAfterRemovingSpacesFromFirst(this string a, string b) {
var i = 0;
var j = 0;
while (i < a.Length && j < b.Length) {
if (a[i] == b[j]) {
i += 1
j += 1
} else if (a[i] == ' ') {
i += 1;
} else {
return false;
}
}
return i == a.Length && j == b.Length;
}
The above is just an ever-so-slightly modified string comparison. If you want to extend this to 'largest common substring', then take a largest common substring algorithm and do the same sort of thing: whenever you would have failed due to a space in the first string, just skip past it.
Did you look at Suffix Array - http://en.wikipedia.org/wiki/Suffix_array
or Here from Jon Bentley - Programming Pearl
Note : you have to write code to handle spaces.
Related
This is a problem from a programming contest that was held recently.
Two strings a[0..n-1] and b[0..n-1] are called cyclic equivalent if and only if there exists an offset d, such that for all 0 <= i < n, a[i] = b[(i + d) mod n].
Given two strings s[0..L-1] and t[0..L-1] with same length L. You need to find the maximum p such that s[0..p-1] and t[0..p-1] are cyclic equivalent.Print 0 if no such valid p exists.
Input
The first line contains an integer T indicating the number of test cases.
For each test case, there are two lines in total. The first line contains s. The second line contains t.
All strings contain only lower case alphabets.
Output
Output T lines in total. Each line should start with "Case #: " and followed by the maximum p. Here "#" is the number of the test case starting from 1.
Constraints
1 ≤ T ≤ 10
1 ≤ L ≤ 1000000
Example
Input:
2
abab
baba
abab
baac
Output:
Case 1: 4
Case 2: 3
Explanation
Case 1, d can be 1.
Case 2, d can be 2.
My approach :
Generate all substrings of S and T in the from S[0...i], T[0...i] and concatenate S[0...i] with itself and check if T is a substring of S[0...i]+S[0...i]. if it a substring then maximum P = i
bool isCyclic( string s, string t ){
string str = s;
str.append(s);
if( str.find(t) != string::npos )
return true;
return false;
}
int main(){
string s, t;
int t1,l, o=1;
scanf("%d", &t1);
while( t1-- ){
cin>>s>>t;
l = min( s.length(), t.length());
int i, maxP = 0;
for( i=1; i<=l; i++ ){
if( isCyclic(s.substr(0,i), t.substr(0,i)) ){
maxP = i;
}
}
printf("Case %d: %d\n", o++, maxP);
}
return 0;
}
I knew that this not the most optimized approach for this problem since i got Time Limit Exceeded.I came to know that prefix function can be used to get an O(n) algorithm. I dont know about prefix function.Could someone explain the O(n) approach ?
Contest link http://www.codechef.com/ACMKGP14/problems/ACM14KP3
Suppose you are given a word
"sunflower"
You can perform only one operation type on it, pick a character and move it to the front.
So for instance if you picked 'f', the word would be "fsunlower".
You can have a series of these operations.
fsunlower (moved f to front)
wfsunloer (moved w to front)
fwsunloer (moved f to front again)
The problem is to get the minimum number of operations required, given the derived word and the original word. So if input strings are "fwsunloer", "sunflower", the output would be 3.
This problem is equivalent to : given String A and B, find the longest suffix of string A that is a sub-sequence of String B. Because, if we know which n - characters need to be moved, we will only need n steps. So what we need to find is the maximum number of character that don't need to be moved, which is equivalent to the longest suffix in A.
So for the given example, the longest suffix is sunlor
Java code:
public static void main(String[] args) {
System.out.println(minOp("ewfsunlor", "sunflower"));
}
public static int minOp(String A, String B) {
int n = A.length() - 1;//Start from the end of String A;
int pos = B.length();
int result = 0;
while (n >= 0) {
int nxt = -1;
for (int i = pos - 1; i >= 0; i--) {
if (B.charAt(i) == A.charAt(n)) {
nxt = i;
break;
}
}
if (nxt == -1) {
break;
}
result++;
pos = nxt;
n--;
}
return B.length() - result;
}
Result:
3
Time complexity O(n) with n is length of String A.
Note: this algorithm is based on an assumption that A and B contains same set of character. Otherwise, you need to check for that before using the function
Given a string S and a set of n substrings. Remove every instance of those n substrings from S so that S is of the minimum length and output this minimum length.
Example 1
S = ccdaabcdbb
n = 2
substrings = ab, cd
Output
2
Explanation:
ccdaabcdbb -> ccdacdbb -> cabb -> cb (length=2)
Example 2
S = abcd
n = 2
substrings = ab,bcd
Output
1
How do I solve this problem ?
A simple Brute-force search algorithm is:
For each substring, try all possible ways to remove it from the string, then recurse.
In Pseudocode:
def min_final_length (input, substrings):
best = len(input)
for substr in substrings:
beg = 0
// find all occurrences of substr in input and recurse
while (found = find_substring(input, substr, from=beg)):
input_without_substr = input[0:found]+input[found+len(substr):len(input)]
best = min(best, min_final_length(input_without_substr,substrings))
beg = found+1
return best
Let complexity be F(S,n,l) where S is the length of the input string, n is the cardinality of the set substrings and l is the "characteristic length" of substrings. Then
F(S,n,l) ~ n * ( S * l + F(S-l,n,l) )
Looks like it is at most O(S^2*n*l).
The following solution would have an complexity of O(m * n) where m = len(S) and n is the number of substring
def foo(S, sub):
i = 0
while i < len(S):
for e in sub:
if S[i:].startswith(e):
S = S[:i] + S[i+len(e):]
i -= 1
break
else: i += 1
return S, i
If you are for raw performance and your string is very large, you can do better than brute force. Use a suffix trie (E.g, Ukkonnen trie) to store your string. Then find each substring (which us done in O(m) time, m being substring length), and store the offsets to the substrings and length in an array.
Then use the offsets and length info to actually remove the substrings by filling these areas with \0 (in C) or another placeholder character. By counting all non-Null characters you will get the minimal length of the string.
This will als handle overlapping substring, e.g. say your string is "abcd", and you have two substrings "ab" and "abcd".
I solved it using trie+dp.
First insert your substrings in a trie. Then define the state of the dp is some string, walk through that string and consider each i (for i =0 .. s.length()) as the start of some substring. let j=i and increment j as long as you have a suffix in the trie (which will definitely land you to at least one substring and may be more if you have common suffix between some substring, for example "abce" and "abdd"), whenever you encounter an end of some substring, go solve the new sub-problem and find the minimum between all substring reductions.
Here is my code for it. Don't worry about the length of the code. Just read the solve function and forget about the path, I included it to print the string formed.
struct node{
node* c[26];
bool str_end;
node(){
for(int i= 0;i<26;i++){
c[i]=NULL;
}
str_end= false;
}
};
class Trie{
public:
node* root;
Trie(){
root = new node();
}
~Trie(){
delete root;
}
};
class Solution{
public:
typedef pair<int,int>ii;
string get_str(string& s,map<string,ii>&path){
if(!path.count(s)){
return s;
}
int i= path[s].first;
int j= path[s].second;
string new_str =(s.substr(0,i)+s.substr(j+1));
return get_str(new_str,path);
}
int solve(string& s,Trie* &t, map<string,int>&dp,map<string,ii>&path){
if(dp.count(s)){
return dp[s];
}
int mn= (int)s.length();
for(int i =0;i<s.length();i++){
string left = s.substr(0,i);
node* cur = t->root->c[s[i]-97];
int j=i;
while(j<s.length()&&cur!=NULL){
if(cur->str_end){
string new_str =left+s.substr(j+1);
int ret= solve(new_str,t,dp,path);
if(ret<mn){
path[s]={i,j};
}
}
cur = cur->c[s[++j]-97];
}
}
return dp[s]=mn;
}
string removeSubstrings(vector<string>& substrs, string s){
map<string,ii>path;
map<string,int>dp;
Trie*t = new Trie();
for(int i =0;i<substrs.size();i++){
node* cur = t->root;
for(int j=0;j<substrs[i].length();j++){
if(cur->c[substrs[i][j]-97]==NULL){
cur->c[substrs[i][j]-97]= new node();
}
cur = cur->c[substrs[i][j]-97];
if(j==substrs[i].length()-1){
cur->str_end= true;
}
}
}
solve(s,t,dp,path);
return get_str(s, path);
}
};
int main(){
vector<string>substrs;
substrs.push_back("ab");
substrs.push_back("cd");
Solution s;
cout << s.removeSubstrings(substrs,"ccdaabcdbb")<<endl;
return 0;
}
This is a question from one of the online coding challenge (which has completed).
I just need some logic for this as to how to approach.
Problem Statement:
We have two strings A and B with the same super set of characters. We need to change these strings to obtain two equal strings. In each move we can perform one of the following operations:
1. swap two consecutive characters of a string
2. swap the first and the last characters of a string
A move can be performed on either string.
What is the minimum number of moves that we need in order to obtain two equal strings?
Input Format and Constraints:
The first and the second line of the input contains two strings A and B. It is guaranteed that the superset their characters are equal.
1 <= length(A) = length(B) <= 2000
All the input characters are between 'a' and 'z'
Output Format:
Print the minimum number of moves to the only line of the output
Sample input:
aab
baa
Sample output:
1
Explanation:
Swap the first and last character of the string aab to convert it to baa. The two strings are now equal.
EDIT : Here is my first try, but I'm getting wrong output. Can someone guide me what is wrong in my approach.
int minStringMoves(char* a, char* b) {
int length, pos, i, j, moves=0;
char *ptr;
length = strlen(a);
for(i=0;i<length;i++) {
// Find the first occurrence of b[i] in a
ptr = strchr(a,b[i]);
pos = ptr - a;
// If its the last element, swap with the first
if(i==0 && pos == length-1) {
swap(&a[0], &a[length-1]);
moves++;
}
// Else swap from current index till pos
else {
for(j=pos;j>i;j--) {
swap(&a[j],&a[j-1]);
moves++;
}
}
// If equal, break
if(strcmp(a,b) == 0)
break;
}
return moves;
}
Take a look at this example:
aaaaaaaaab
abaaaaaaaa
Your solution: 8
aaaaaaaaab -> aaaaaaaaba -> aaaaaaabaa -> aaaaaabaaa -> aaaaabaaaa ->
aaaabaaaaa -> aaabaaaaaa -> aabaaaaaaa -> abaaaaaaaa
Proper solution: 2
aaaaaaaaab -> baaaaaaaaa -> abaaaaaaaa
You should check if swapping in the other direction would give you better result.
But sometimes you will also ruin the previous part of the string. eg:
caaaaaaaab
cbaaaaaaaa
caaaaaaaab -> baaaaaaaac -> abaaaaaaac
You need another swap here to put back the 'c' to the first place.
The proper algorithm is probably even more complex, but you can see now what's wrong in your solution.
The A* algorithm might work for this problem.
The initial node will be the original string.
The goal node will be the target string.
Each child of a node will be all possible transformations of that string.
The current cost g(x) is simply the number of transformations thus far.
The heuristic h(x) is half the number of characters in the wrong position.
Since h(x) is admissible (because a single transformation can't put more than 2 characters in their correct positions), the path to the target string will give the least number of transformations possible.
However, an elementary implementation will likely be too slow. Calculating all possible transformations of a string would be rather expensive.
Note that there's a lot of similarity between a node's siblings (its parent's children) and its children. So you may be able to just calculate all transformations of the original string and, from there, simply copy and recalculate data involving changed characters.
You can use dynamic programming. Go over all swap possibilities while storing all the intermediate results along with the minimal number of steps that took you to get there. Actually, you are going to calculate the minimum number of steps for every possible target string that can be obtained by applying given rules for a number times. Once you calculate it all, you can print the minimum number of steps, which is needed to take you to the target string. Here's the sample code in JavaScript, and its usage for "aab" and "baa" examples:
function swap(str, i, j) {
var s = str.split("");
s[i] = str[j];
s[j] = str[i];
return s.join("");
}
function calcMinimumSteps(current, stepsCount)
{
if (typeof(memory[current]) !== "undefined") {
if (memory[current] > stepsCount) {
memory[current] = stepsCount;
} else if (memory[current] < stepsCount) {
stepsCount = memory[current];
}
} else {
memory[current] = stepsCount;
calcMinimumSteps(swap(current, 0, current.length-1), stepsCount+1);
for (var i = 0; i < current.length - 1; ++i) {
calcMinimumSteps(swap(current, i, i + 1), stepsCount+1);
}
}
}
var memory = {};
calcMinimumSteps("aab", 0);
alert("Minimum steps count: " + memory["baa"]);
Here is the ruby logic for this problem, copy this code in to rb file and execute.
str1 = "education" #Sample first string
str2 = "cnatdeiou" #Sample second string
moves_count = 0
no_swap = 0
count = str1.length - 1
def ends_swap(str1,str2)
str2 = swap_strings(str2,str2.length-1,0)
return str2
end
def swap_strings(str2,cp,np)
current_string = str2[cp]
new_string = str2[np]
str2[cp] = new_string
str2[np] = current_string
return str2
end
def consecutive_swap(str,current_position, target_position)
counter=0
diff = current_position > target_position ? -1 : 1
while current_position!=target_position
new_position = current_position + diff
str = swap_strings(str,current_position,new_position)
# p "-------"
# p "CP: #{current_position} NP: #{new_position} TP: #{target_position} String: #{str}"
current_position+=diff
counter+=1
end
return counter,str
end
while(str1 != str2 && count!=0)
counter = 1
if str1[-1]==str2[0]
# p "cross match"
str2 = ends_swap(str1,str2)
else
# p "No match for #{str2}-- Count: #{count}, TC: #{str1[count]}, CP: #{str2.index(str1[count])}"
str = str2[0..count]
cp = str.rindex(str1[count])
tp = count
counter, str2 = consecutive_swap(str2,cp,tp)
count-=1
end
moves_count+=counter
# p "Step: #{moves_count}"
# p str2
end
p "Total moves: #{moves_count}"
Please feel free to suggest any improvements in this code.
Try this code. Hope this will help you.
public class TwoStringIdentical {
static int lcs(String str1, String str2, int m, int n) {
int L[][] = new int[m + 1][n + 1];
int i, j;
for (i = 0; i <= m; i++) {
for (j = 0; j <= n; j++) {
if (i == 0 || j == 0)
L[i][j] = 0;
else if (str1.charAt(i - 1) == str2.charAt(j - 1))
L[i][j] = L[i - 1][j - 1] + 1;
else
L[i][j] = Math.max(L[i - 1][j], L[i][j - 1]);
}
}
return L[m][n];
}
static void printMinTransformation(String str1, String str2) {
int m = str1.length();
int n = str2.length();
int len = lcs(str1, str2, m, n);
System.out.println((m - len)+(n - len));
}
public static void main(String[] args) {
Scanner scan = new Scanner(System.in);
String str1 = scan.nextLine();
String str2 = scan.nextLine();
printMinTransformation("asdfg", "sdfg");
}
}
Thinking about this question on testing string rotation, I wondered: Is there was such thing as a circular/cyclic hash function? E.g.
h(abcdef) = h(bcdefa) = h(cdefab) etc
Uses for this include scalable algorithms which can check n strings against each other to see where some are rotations of others.
I suppose the essence of the hash is to extract information which is order-specific but not position-specific. Maybe something that finds a deterministic 'first position', rotates to it and hashes the result?
It all seems plausible, but slightly beyond my grasp at the moment; it must be out there already...
I'd go along with your deterministic "first position" - find the "least" character; if it appears twice, use the next character as the tie breaker (etc). You can then rotate to a "canonical" position, and hash that in a normal way. If the tie breakers run for the entire course of the string, then you've got a string which is a rotation of itself (if you see what I mean) and it doesn't matter which you pick to be "first".
So:
"abcdef" => hash("abcdef")
"defabc" => hash("abcdef")
"abaac" => hash("aacab") (tie-break between aa, ac and ab)
"cabcab" => hash("abcabc") (it doesn't matter which "a" comes first!)
Update: As Jon pointed out, the first approach doesn't handle strings with repetition very well. Problems arise as duplicate pairs of letters are encountered and the resulting XOR is 0. Here is a modification that I believe fixes the the original algorithm. It uses Euclid-Fermat sequences to generate pairwise coprime integers for each additional occurrence of a character in the string. The result is that the XOR for duplicate pairs is non-zero.
I've also cleaned up the algorithm slightly. Note that the array containing the EF sequences only supports characters in the range 0x00 to 0xFF. This was just a cheap way to demonstrate the algorithm. Also, the algorithm still has runtime O(n) where n is the length of the string.
static int Hash(string s)
{
int H = 0;
if (s.Length > 0)
{
//any arbitrary coprime numbers
int a = s.Length, b = s.Length + 1;
//an array of Euclid-Fermat sequences to generate additional coprimes for each duplicate character occurrence
int[] c = new int[0xFF];
for (int i = 1; i < c.Length; i++)
{
c[i] = i + 1;
}
Func<char, int> NextCoprime = (x) => c[x] = (c[x] - x) * c[x] + x;
Func<char, char, int> NextPair = (x, y) => a * NextCoprime(x) * x.GetHashCode() + b * y.GetHashCode();
//for i=0 we need to wrap around to the last character
H = NextPair(s[s.Length - 1], s[0]);
//for i=1...n we use the previous character
for (int i = 1; i < s.Length; i++)
{
H ^= NextPair(s[i - 1], s[i]);
}
}
return H;
}
static void Main(string[] args)
{
Console.WriteLine("{0:X8}", Hash("abcdef"));
Console.WriteLine("{0:X8}", Hash("bcdefa"));
Console.WriteLine("{0:X8}", Hash("cdefab"));
Console.WriteLine("{0:X8}", Hash("cdfeab"));
Console.WriteLine("{0:X8}", Hash("a0a0"));
Console.WriteLine("{0:X8}", Hash("1010"));
Console.WriteLine("{0:X8}", Hash("0abc0def0ghi"));
Console.WriteLine("{0:X8}", Hash("0def0abc0ghi"));
}
The output is now:
7F7D7F7F
7F7D7F7F
7F7D7F7F
7F417F4F
C796C7F0
E090E0F0
A909BB71
A959BB71
First Version (which isn't complete): Use XOR which is commutative (order doesn't matter) and another little trick involving coprimes to combine ordered hashes of pairs of letters in the string. Here is an example in C#:
static int Hash(char[] s)
{
//any arbitrary coprime numbers
const int a = 7, b = 13;
int H = 0;
if (s.Length > 0)
{
//for i=0 we need to wrap around to the last character
H ^= (a * s[s.Length - 1].GetHashCode()) + (b * s[0].GetHashCode());
//for i=1...n we use the previous character
for (int i = 1; i < s.Length; i++)
{
H ^= (a * s[i - 1].GetHashCode()) + (b * s[i].GetHashCode());
}
}
return H;
}
static void Main(string[] args)
{
Console.WriteLine(Hash("abcdef".ToCharArray()));
Console.WriteLine(Hash("bcdefa".ToCharArray()));
Console.WriteLine(Hash("cdefab".ToCharArray()));
Console.WriteLine(Hash("cdfeab".ToCharArray()));
}
The output is:
4587590
4587590
4587590
7077996
You could find a deterministic first position by always starting at the position with the "lowest" (in terms of alphabetical ordering) substring. So in your case, you'd always start at "a". If there were multiple "a"s, you'd have to take two characters into account etc.
I am sure that you could find a function that can generate the same hash regardless of character position in the input, however, how will you ensure that h(abc) != h(efg) for every conceivable input? (Collisions will occur for all hash algorithms, so I mean, how do you minimize this risk.)
You'd need some additional checks even after generating the hash to ensure that the strings contain the same characters.
Here's an implementation using Linq
public string ToCanonicalOrder(string input)
{
char first = input.OrderBy(x => x).First();
string doubledForRotation = input + input;
string canonicalOrder
= (-1)
.GenerateFrom(x => doubledForRotation.IndexOf(first, x + 1))
.Skip(1) // the -1
.TakeWhile(x => x < input.Length)
.Select(x => doubledForRotation.Substring(x, input.Length))
.OrderBy(x => x)
.First();
return canonicalOrder;
}
assuming generic generator extension method:
public static class TExtensions
{
public static IEnumerable<T> GenerateFrom<T>(this T initial, Func<T, T> next)
{
var current = initial;
while (true)
{
yield return current;
current = next(current);
}
}
}
sample usage:
var sequences = new[]
{
"abcdef", "bcdefa", "cdefab",
"defabc", "efabcd", "fabcde",
"abaac", "cabcab"
};
foreach (string sequence in sequences)
{
Console.WriteLine(ToCanonicalOrder(sequence));
}
output:
abcdef
abcdef
abcdef
abcdef
abcdef
abcdef
aacab
abcabc
then call .GetHashCode() on the result if necessary.
sample usage if ToCanonicalOrder() is converted to an extension method:
sequence.ToCanonicalOrder().GetHashCode();
One possibility is to combine the hash functions of all circular shifts of your input into one meta-hash which does not depend on the order of the inputs.
More formally, consider
for(int i=0; i<string.length; i++) {
result^=string.rotatedBy(i).hashCode();
}
Where you could replace the ^= with any other commutative operation.
More examply, consider the input
"abcd"
to get the hash we take
hash("abcd") ^ hash("dabc") ^ hash("cdab") ^ hash("bcda").
As we can see, taking the hash of any of these permutations will only change the order that you are evaluating the XOR, which won't change its value.
I did something like this for a project in college. There were 2 approaches I used to try to optimize a Travelling-Salesman problem. I think if the elements are NOT guaranteed to be unique, the second solution would take a bit more checking, but the first one should work.
If you can represent the string as a matrix of associations so abcdef would look like
a b c d e f
a x
b x
c x
d x
e x
f x
But so would any combination of those associations. It would be trivial to compare those matrices.
Another quicker trick would be to rotate the string so that the "first" letter is first. Then if you have the same starting point, the same strings will be identical.
Here is some Ruby code:
def normalize_string(string)
myarray = string.split(//) # split into an array
index = myarray.index(myarray.min) # find the index of the minimum element
index.times do
myarray.push(myarray.shift) # move stuff from the front to the back
end
return myarray.join
end
p normalize_string('abcdef').eql?normalize_string('defabc') # should return true
Maybe use a rolling hash for each offset (RabinKarp like) and return the minimum hash value? There could be collisions though.