Longest Univalue path in BST - recursion

I'm trying to solve the problem:
Given a binary tree, find the length of the longest path where each node in the path has the same value. This path may or may not pass through the root.
Note: The length of path between two nodes is represented by the number of edges between them.
Sample inputs here
I am getting wrong answer on a large input. My code passes 46 tests but fails after that. I don't understand where I went wrong. Could someone please help.
Here is my code:
class Solution
{
public:
int longestPath = 0;
int findLongestPath(TreeNode *root, int depth)
{
int leftDepth, rightDepth;
leftDepth = rightDepth = 0;
if (root->left != 0 && root->left->val == root->val)
leftDepth = findLongestPath(root->left, depth + 1);
if (root->right != 0 && root->right->val == root->val)
rightDepth = findLongestPath(root->right, depth + 1);
longestPath = max(longestPath, leftDepth + rightDepth);
return max(max(leftDepth, rightDepth), depth);
}
void traverse(TreeNode *root)
{
if (root == 0)
return;
findLongestPath(root, 0);
traverse(root->left);
traverse(root->right);
}
int longestUnivaluePath(TreeNode *root)
{
traverse(root);
return longestPath;
}
};

Related

Why Complete LinkedList Reversed?

For Input 1->2->2->4->5->6->7->8
My output is 8 7 6 5 4 2 2 1 but I don't know why?
LINK OF PROBLEM IS BELOW :
https://practice.geeksforgeeks.org/problems/reverse-a-linked-list-in-groups-of-given-size/1
Reverse a Linked List in groups of given size.
Given a linked list of size N. The task is to reverse every k nodes (where k is an input to the function) in the linked list. If the number of nodes is not a multiple of k then left-out nodes, in the end, should be considered as a group and must be reversed (See Example 2 for clarification).
Example 1:
Input:
LinkedList: 1->2->2->4->5->6->7->8
K = 4
Output: 4 2 2 1 8 7 6 5
Explanation:
The first 4 elements 1,2,2,4 are reversed first
and then the next 4 elements 5,6,7,8. Hence, the
resultant linked list is 4->2->2->1->8->7->6->5.
Example 2:
Input:
LinkedList: 1->2->3->4->5
K = 3
Output: 3 2 1 5 4
Explanation:
The first 3 elements are 1,2,3 are reversed
first and then elements 4,5 are reversed.Hence,
the resultant linked list is 3->2->1->5->4.
Your Task:
You don't need to read input or print anything. Your task is to complete the function reverse() which should reverse the linked list in group of size k and return the head of the modified linked list.
Expected Time Complexity : O(N)
Expected Auxilliary Space : O(1)
Constraints:
1 <= N <= 104
1 <= k <= N
MY CODE BELOW:
//{ Driver Code Starts
#include<bits/stdc++.h>
using namespace std;
struct node
{
int data;
struct node* next;
node(int x){
data = x;
next = NULL;
}
};
/* Function to print linked list */
void printList(struct node *node)
{
while (node != NULL)
{
printf("%d ", node->data);
node = node->next;
}
printf("\n");
}
// } Driver Code Ends
/*
Reverse a linked list
The input list will have at least one element
Return the node which points to the head of the new LinkedList
Node is defined as
struct node
{
int data;
struct node* next;
node(int x){
data = x;
next = NULL;
}
}*head;
*/
class Solution
{
node* reverseHelper(node* head){
node* pre = NULL;
node* curr = head;
while(curr!=NULL){
node* nextTocurr = curr->next;
curr->next = pre;
pre = curr;
curr = nextTocurr;
}
return pre;
}
public:
struct node *reverse (struct node *head, int k)
{
// Complete this method
if(head==NULL|| head->next==NULL){
return head;
}
int count = 0;
node* tail = head;
while(count<k || tail->next!=NULL){
tail = tail->next;
count++;
}
node* head2 = tail->next;
tail->next = NULL;
node* ans = reverseHelper(head);
head->next = reverse(head2,k);
return ans;
}
};
//{ Driver Code Starts.
/* Drier program to test above function*/
int main(void)
{
int t;
cin>>t;
while(t--)
{
struct node* head = NULL;
struct node* temp = NULL;
int n;
cin >> n;
for(int i=0 ; i<n ; i++)
{
int value;
cin >> value;
if(i == 0)
{
head = new node(value);
temp = head;
}
else
{
temp->next = new node(value);
temp = temp->next;
}
}
int k;
cin>>k;
Solution ob;
head = ob.reverse(head, k);
printList(head);
}
return(0);
}
// } Driver Code Ends
The problem is in this loop:
int count = 0;
while(count<k || tail->next!=NULL){
It has two issues:
The loop will continue until the end of the list because the second condition will be true until that end is reached. The logical OR (||) should be a logical AND (&&), because you want both conditions to be true, not just one.
When the previous point is corrected, the loop will still iterate one time too many, because the head node was already considered to be included in the "slice". Correct by initialising count=1.
With those two corrections your code will work as intended.

C Program to Search a Node in Binary Tree

this code is from binary search tree I don't know this code showing same output
I don't know where the problem is occurring I already tried to change the variables but it didn't work
What seems to be the problem? i already tried so many things but still not able to fix the errors.
#include <stdio.h>
#include <stdlib.h>
****// Basic struct of Tree****
struct node
{
int data;
struct node *left;
struct node *right;
};
****// Function to create a new Node****
struct node *createNode(int item)
{
struct node *newNode = malloc(sizeof(struct node));
newNode->left = NULL;
newNode->right = NULL;
newNode->data = item;
return newNode;
}
int search(struct node *root, int value)
{
if (root == NULL)
return 0;
if (root->data == value)
return 1;
if (root->data < value)
return search(root->right, value);
else
return search(root->left, value);
}
int main()
{
**// struct node *root = NULL;**
struct node *root = createNode(1);
root->left = createNode(2);
root->right = createNode(3);
root->left->left = createNode(4);
root->left->right = createNode(5);
root->right->right = createNode(6);
root->left->right->left = createNode(7);
root->left->right->right = createNode(8);
root->right->right->left = createNode(9);
int item = 34;
// Function to find item in the tree
int found = search(root, item);
if (found)
printf("%d value is found in the tree", item);
else
printf("%d value not found", item);
return 0;
}
The problem is that your search function expects to get a binary search tree, but your main program created a binary tree that is not a binary search tree, but this:
1
/ \
2 3
/ \ \
4 5 6
/ \ /
7 8 9
And of course, a search for 34 will anyway return 0, as it does not occur anywhere in this tree. But even if you would search for let's say 8, it would return 0.
Your search code will not work with such a tree. If you would have made a binary search tree, like for instance this one:
6
/ \
2 7
/ \ \
1 4 9
/ \ /
3 5 8
...then it would work when calling search for any value in or not in the tree. For instance, this will print "5 value is found in the tree":
int main()
{
struct node *root = createNode(6);
root->left = createNode(2);
root->right = createNode(7);
root->left->left = createNode(1);
root->left->right = createNode(4);
root->right->right = createNode(9);
root->left->right->left = createNode(3);
root->left->right->right = createNode(5);
root->right->right->left = createNode(8);
int item = 5;
// Function to find item in the tree
int found = search(root, item);
if (found)
printf("%d value is found in the tree", item);
else
printf("%d value not found", item);
return 0;
}
This function is for binary search tree (BST).
int search(struct node *root, int value)
{
if (root == NULL)
return 0;
if (root->data == value)
return 1;
if (root->data < value)
return search(root->right, value);
else
return search(root->left, value);
}
As you need to a program to work on any binary tree.
You can change it to work on an any binary tree.
int search(struct node *root, int value)
{
if (root == NULL)
return 0;
if (root->data == value)
return 1;
return search(root->right, value) || search(root->left, value);
}

Parallelizing Minimax with alpha-beta pruning using MPI

I am currently busy with a project that requires you to use the minimax with AB pruning.
I have successfully implemented a serial version of the program
//Assume maximizing player is WHITE
int minimax_move(int *current_board, int player, int *chosen_move, int alpha, int beta) {
int *moves_list;//capture the moves for a board
int moves_len;
int opponent = BLACK;
if (player == BLACK) {
opponent = WHITE;
}
get_moves_list(current_board,&moves_list,&moves_len,player);
//No Move to be generated
if (moves_list[0] == 0) {
*chosen_move = -1;
} else {
//Remember the best move
int best_move_value = INT_MIN;
int best_move = moves_list[1];
//Try all the moves
for (int i = 1; i <= moves_len; i++) {
int *temp_board = (int *) malloc(sizeof(int) * BOARDSIZE);
copy_board(current_board,temp_board);
apply_move(&temp_board,moves_list[i],player);
//Initial Call to minimax_value
int value = minimax_value(temp_board,player,opponent,1,alpha,beta);
//Remember best move
if (value > best_move_value) {
best_move_value = value;
best_move = moves_list[i];
}
}
//Set the chosen move
*chosen_move = best_move;
printc("Chosen Move is: %d\nFrom %s\n",*chosen_move,get_turn_player(player));
}
return *chosen_move;
}
//original_turn -> maximizing player
//current_turn -> minimizing_player
//Current turn is what alternates the turn player when simulating move look aheads
//The maximizing player is established in minimax_moves
int minimax_value(int *current_state,int original_turn, int current_turn,int depth,int a,int b) {
if (depth == MAXDEPTH || is_game_over(current_state)) {
return evaluate_board(current_state);
}
int *moves_list;
int moves_len;
int opponent = BLACK;
if (current_turn == BLACK) {
opponent = WHITE;
}
get_moves_list(current_state,&moves_list,&moves_len,current_turn);
//if no moves, skip to next player's (opponent) turn
if (moves_list[0] == 0) {
return minimax_value(board,original_turn,opponent,depth+1,a,b);
} else {
//Remember the best move - Setting the limits
//For max player
int best_move_value = INT_MIN;
int alpha = a;
int beta = b;
if (original_turn != current_turn) {
//original_turn -> max player
//current_tunr -> min player
best_move_value = INT_MAX;
}
for (int i = 1; i <= moves_len; i++) {
//Apply a move to the board
int *temp_board = (int *) malloc(sizeof(int) * BOARDSIZE);
copy_board(current_state,temp_board);
apply_move(&temp_board,moves_list[i],current_turn);
//Recursive calls
int value = minimax_value(temp_board,original_turn,opponent,depth+1,alpha,beta);
//Remember best move
//MAX PLAYER
if (original_turn == current_turn) {
if (value > best_move_value) {
best_move_value = value;
}
if (value > alpha) {
alpha = value;
}
} else {
//MIN PLAYER
if (value < best_move_value) {
best_move_value = value;
}
if (value < beta) {
beta = value;
}
}
//Alpha-Beta pruning
printc("ALPHA: %d - BETA: %d\n",alpha,beta);
if (beta <= alpha) {
printc("\n\nPRUNED\n\n");
break;
}
}
return best_move_value;
}
//return -1; ERROR
}
The project requires me to use MPI to parallelize the minimax algorithm. I have no idea where to start. I have read http://www.pressibus.org/ataxx/autre/minimax/node6.html#SECTION00060000000000000000
but am no closer to solving the problem as I do not understand the psuedo-code written.
My idea was to somehow scatter the moves_list generated in minimax_move() amongst (n-1) slave processes where 1 process will be the master process. However, the first call to minimax_move() yields a move_list of length 3, and we can assume that the number of processors that will be used to run the program will be >= 4.
I would appreciate a starting point on how to solve this as I cannot seem to wrap my head around how I would use MPI to parallelize this. It has to be done using MPI.
Ultimately alpha-beta mini-maxing requires you to score every tree generated by a turn and choose the best one. It sounds like your task is to parallelise the calculation of the scores, you should be able to utilise different processors to score different trees.

String Reduction - Programming Contest . Solution needed

I have a question which asks us to reduce the string as follows.
The input is a string having only A, B or C. Output must be length of
the reduced string
The string can be reduced by the following rules
If any 2 different letters are adjacent, these two letters can be
replaced by the third letter.
Eg ABA -> CA -> B . So final answer is 1 (length of reduced string)
Eg ABCCCCCCC
This doesn't become CCCCCCCC, as it can be reduced alternatively by
ABCCCCCCC->AACCCCCC->ABCCCCC->AACCCC->ABCCC->AACC->ABC->AA
as here length is 2 < (length of CCCCCCCC)
How do you go about this problem?
Thanks a lot!
To make things clear: the question states it wants the minimum length of the reduced string. So in the second example above there are 2 solutions possible, one CCCCCCCC and the other AA. So 2 is the answer as length of AA is 2 which is smaller than the length of CCCCCCCC = 8.
The way this question is phrased, there are only three distinct possibilities:
If the string has only one unique character, the length is the same as the length of the string.
2/3. If the string contains more than one unique character, the length is either 1 or 2, always (based on the layout of the characters).
Edit:
As a way of proof of concept here is some grammar and its extensions:
I should note that although this seems to me a reasonable proof for the fact that the length will reduce to either 1 or 2, I am reasonably sure that determining which of these lengths will result is not as trivial as I originally thought ( you would still have to recurse through all options to find it out)
S : A|B|C|()
S : S^
where () denotes the empty string, and s^ means any combination of the previous [A,B,C,()] characters.
Extended Grammar:
S_1 : AS^|others
S_2 : AAS^|ABS^|ACS^|others
S_3 : AAAS^|
AABS^ => ACS^ => BS^|
AACS^ => ABS^ => CS^|
ABAS^ => ACS^ => BS^|
ABBS^ => CBS^ => AS^|
ABCS^ => CCS^ | AAS^|
ACAS^ => ABS^ => CS^|
ACBS^ => AAS^ | BBS^|
ACCS^ => BCS^ => AS^|
The same thing will happen with extended grammars starting with B, and C (others). The interesting cases are where we have ACB and ABC (three distinct characters in sequence), these cases result in grammars that appear to lead to longer lengths however:
CCS^: CCAS^|CCBS^|CCCS^|
CBS^ => AS^|
CAS^ => BS^|
CCCS^|
AAS^: AAAS^|AABS^|AACS^|
ACS^ => BS^|
ABS^ => CS^|
AAAS^|
BBS^: BBAS^|BBBS^|BBCS^|
BCS^ => AS^|
BAS^ => CS^|
BBBS^|
Recursively they only lead to longer lengths when the remaining string contains their value only. However we have to remember that this case also can be simplified, since if we got to this area with say CCCS^, then we at one point previous had ABC ( or consequently CBA ). If we look back we could have made better decisions:
ABCCS^ => AACS^ => ABS^ => CS^
CBACS^ => CBBS^ => ABS^ => CS^
So in the best case at the end of the string when we make all the correct decisions we end with a remaining string of 1 character followed by 1 more character(since we are at the end). At this time if the character is the same, then we have a length of 2, if it is different, then we can reduce one last time and we end up with a length of 1.
You can generalize the result based on individual character count of string. The algo is as follows,
traverse through the string and get individual char count.
Lets say if
a = no# of a's in given string
b = no# of b's in given string
c = no# of c's in given string
then you can say that, the result will be,
if((a == 0 && b == 0 && c == 0) ||
(a == 0 && b == 0 && c != 0) ||
(a == 0 && b != 0 && c == 0) ||
(a != 0 && b == 0 && c == 0))
{
result = a+b+c;
}
else if(a != 0 && b != 0 && c != 0)
{
if((a%2 == 0 && b%2 == 0 && c%2 == 0) ||
(a%2 == 1 && b%2 == 1 && c%2 == 1))
result = 2;
else
result = 1;
}
else if((a == 0 && b != 0 && c != 0) ||
(a != 0 && b == 0 && c != 0) ||
(a != 0 && b != 0 && c == 0))
{
if(a%2 == 0 && b%2 == 0 && c%2 == 0)
result = 2;
else
result = 1;
}
I'm assuming that you are looking for the length of the shortest possible string that can be obtained after reduction.
A simple solution would be to explore all possibilities in a greedy manner and hope that it does not explode exponentially. I'm gonna write Python pseudocode here because that's easier to comprehend (at least for me ;)):
from collections import deque
def try_reduce(string):
queue = deque([string])
min_length = len(string)
while queue:
string = queue.popleft()
if len(string) < min_length:
min_length = len(string)
for i in xrange(len(string)-1):
substring = string[i:(i+2)]
if substring == "AB" or substring == "BA":
queue.append(string[:i] + "C" + string[(i+2):])
elif substring == "BC" or substring == "CB":
queue.append(string[:i] + "A" + string[(i+2):])
elif substring == "AC" or substring == "CA":
queue.append(string[:i] + "B" + string[(i+2):])
return min_length
I think the basic idea is clear: you take a queue (std::deque should be just fine), add your string into it, and then implement a simple breadth first search in the space of all possible reductions. During the search, you take the first element from the queue, take all possible substrings of it, execute all possible reductions, and push the reduced strings back to the queue. The entire space is explored when the queue becomes empty.
Let's define an automaton with the following rules (K>=0):
Incoming: A B C
Current: --------------------------
<empty> A B C
A(2K+1) A(2K+2) AB AC
A(2K+2) A(2K+3) AAB AAC
AB CA CB ABC
AAB BA ACB BC
ABC CCA AAB AAC
and all rules obtained by permutations of ABC to get the complete definition.
All input strings using a single letter are irreducible. If the input string contains at least two different letters, the final states like AB or AAB can be reduced to a single letter, and the final states like ABC can be reduced to two letters.
In the ABC case, we still have to prove that the input string can't be reduced to a single letter by another reduction sequence.
Compare two characters at a time and replace if both adjacent characters are not same. To get optimal solution, run once from start of the string and once from end of the string. Return the minimum value.
int same(char* s){
int i=0;
for(i=0;i<strlen(s)-1;i++){
if(*(s+i) == *(s+i+1))
continue;
else
return 0;
}
return 1;
}
int reduceb(char* s){
int ret = 0,a_sum=0,i=0;
int len = strlen(s);
while(1){
i=len-1;
while(i>0){
if ((*(s+i)) == (*(s+i-1))){
i--;
continue;
} else {
a_sum = (*(s+i)) + (*(s+i-1));
*(s+i-1) = SUM - a_sum;
*(s+i) = '\0';
len--;
}
i--;
}
if(same(s) == 1){
return strlen(s);
}
}
}
int reducef(char* s){
int ret = 0,a_sum=0,i=0;
int len = strlen(s);
while(1){
i=0;
while(i<len-1){
if ((*(s+i)) == (*(s+i+1))){
i++;
continue;
} else {
a_sum = (*(s+i)) + (*(s+i+1));
*(s+i) = SUM - a_sum;
int j=i+1;
for(j=i+1;j<len;j++)
*(s+j) = *(s+j+1);
len--;
}
i++;
}
if(same(s) == 1){
return strlen(s);
}
}
}
int main(){
int n,i=0,f=0,b=0;
scanf("%d",&n);
int a[n];
while(i<n){
char* str = (char*)malloc(101);
scanf("%s",str);
char* strd = strdup(str);
f = reducef(str);
b = reduceb(strd);
if( f > b)
a[i] = b;
else
a[i] = f;
free(str);
free(strd);
i++;
}
for(i=0;i<n;i++)
printf("%d\n",a[i]);
}
import java.io.*;
import java.util.*;
class StringSim{
public static void main(String args[]){
Scanner sc = new Scanner(System.in);
StringTokenizer st = new StringTokenizer(sc.nextLine(), " ");
int N = Integer.parseInt(st.nextToken());
String op = "";
for(int i=0;i<N;i++){
String str = sc.nextLine();
op = op + Count(str) + "\n";
}
System.out.println(op);
}
public static int Count( String str){
int min = Integer.MAX_VALUE;
char pre = str.charAt(0);
boolean allSame = true;
//System.out.println("str :" + str);
if(str.length() == 1){
return 1;
}
int count = 1;
for(int i=1;i<str.length();i++){
//System.out.println("pre: -"+ pre +"- char at "+i+" is : -"+ str.charAt(i)+"-");
if(pre != str.charAt(i)){
allSame = false;
char rep = (char)(('a'+'b'+'c')-(pre+str.charAt(i)));
//System.out.println("rep :" + rep);
if(str.length() == 2)
count = 1;
else if(i==1)
count = Count(rep+str.substring(2,str.length()));
else if(i == str.length()-1)
count = Count(str.substring(0,str.length()-2)+rep);
else
count = Count(str.substring(0,i-1)+rep+str.substring(i+1,str.length()));
if(min>count) min=count;
}else if(allSame){
count++;
//System.out.println("count: " + count);
}
pre = str.charAt(i);
}
//System.out.println("min: " + min);
if(allSame) return count;
return min;
}
}
Wouldn't a good start be to count which letter you have the most of and look for ways to remove it? Keep doing this until we only have one letter. We might have it many times but as long as it is the same we do not care, we are finished.
To avoid getting something like ABCCCCCCC becoming CCCCCCCC.
We remove the most popular letter:
-ABCCCCCCC
-AACCCCCC
-ABCCCCC
-AACCCC
-ABCCC
-AACC
-ABC
-AA
I disagree with the previous poster who states we must have a length of 1 or 2 - what happens if I enter the start string AAA?
import java.util.LinkedList;
import java.util.List;
import java.util.Scanner;
public class Sample {
private static char[] res = {'a', 'b', 'c'};
private char replacementChar(char a, char b) {
for(char c : res) {
if(c != a && c != b) {
return c;
}
}
throw new IllegalStateException("cannot happen. you must've mucked up the resource");
}
public int processWord(String wordString) {
if(wordString.length() < 2) {
return wordString.length();
}
String wordStringES = reduceFromEnd(reduceFromStart(wordString));
if(wordStringES.length() == 1) {
return 1;
}
String wordStringSE = reduceFromStart(reduceFromEnd(wordString));
if(wordString.length() == 1) {
return 1;
}
int aLen;
if(isReduced(wordStringSE)) {
aLen = wordStringSE.length();
} else {
aLen = processWord(wordStringSE);
}
int bLen;
if(isReduced(wordStringES)) {
bLen = wordStringES.length();
} else {
bLen = processWord(wordStringES);
}
return Math.min(aLen, bLen);
}
private boolean isReduced(String wordString) {
int length = wordString.length();
if(length < 2) {
return true;
}
for(int i = 1; i < length; ++i) {
if(wordString.charAt(i) != wordString.charAt(i - 1)) {
return false;
}
}
return wordString.charAt(0) == wordString.charAt(length - 1);
}
private String reduceFromStart(String theWord) {
if(theWord.length() < 2) {
return theWord;
}
StringBuilder buffer = new StringBuilder();
char[] word = theWord.toCharArray();
char curChar = word[0];
for(int i = 1; i < word.length; ++i) {
if(word[i] != curChar) {
curChar = replacementChar(curChar, word[i]);
if(i + 1 == word.length) {
buffer.append(curChar);
break;
}
} else {
buffer.append(curChar);
if(i + 1 == word.length) {
buffer.append(curChar);
}
}
}
return buffer.toString();
}
private String reduceFromEnd(String theString) {
if(theString.length() < 2) {
return theString;
}
StringBuilder buffer = new StringBuilder(theString);
int length = buffer.length();
while(length > 1) {
char a = buffer.charAt(0);
char b = buffer.charAt(length - 1);
if(a != b) {
buffer.deleteCharAt(length - 1);
buffer.deleteCharAt(0);
buffer.append(replacementChar(a, b));
length -= 1;
} else {
break;
}
}
return buffer.toString();
}
public void go() {
Scanner scanner = new Scanner(System.in);
int numEntries = Integer.parseInt(scanner.nextLine());
List<Integer> counts = new LinkedList<Integer>();
for(int i = 0; i < numEntries; ++i) {
counts.add((processWord(scanner.nextLine())));
}
for(Integer count : counts) {
System.out.println(count);
}
}
public static void main(String[] args) {
Sample solution = new Sample();
solution.go();
}
}
This is greedy approach and traversing the path starts with each possible pair and checking the min length.
import java.io.*;
import java.util.*;
class StringSim{
public static void main(String args[]){
Scanner sc = new Scanner(System.in);
StringTokenizer st = new StringTokenizer(sc.nextLine(), " ");
int N = Integer.parseInt(st.nextToken());
String op = "";
for(int i=0;i<N;i++){
String str = sc.nextLine();
op = op + Count(str) + "\n";
}
System.out.println(op);
}
public static int Count( String str){
int min = Integer.MAX_VALUE;
char pre = str.charAt(0);
boolean allSame = true;
//System.out.println("str :" + str);
if(str.length() == 1){
return 1;
}
int count = 1;
for(int i=1;i<str.length();i++){
//System.out.println("pre: -"+ pre +"- char at "+i+" is : -"+ str.charAt(i)+"-");
if(pre != str.charAt(i)){
allSame = false;
char rep = (char)(('a'+'b'+'c')-(pre+str.charAt(i)));
//System.out.println("rep :" + rep);
if(str.length() == 2)
count = 1;
else if(i==1)
count = Count(rep+str.substring(2,str.length()));
else if(i == str.length()-1)
count = Count(str.substring(0,str.length()-2)+rep);
else
count = Count(str.substring(0,i-1)+rep+str.substring(i+1,str.length()));
if(min>count) min=count;
}else if(allSame){
count++;
//System.out.println("count: " + count);
}
pre = str.charAt(i);
}
//System.out.println("min: " + min);
if(allSame) return count;
return min;
}
}
Following NominSim's observations, here is probably an optimal solution that runs in linear time with O(1) space usage. Note that it is only capable of finding the length of the smallest reduction, not the reduced string itself:
def reduce(string):
a = string.count('a')
b = string.count('b')
c = string.count('c')
if ([a,b,c].count(0) >= 2):
return a+b+c
elif (all(v % 2 == 0 for v in [a,b,c]) or all(v % 2 == 1 for v in [a,b,c])):
return 2
else:
return 1
There is some underlying structure that can be used to solve this problem in O(n) time.
The rules given are (most of) the rules defining a mathematical group, in particular the group D_2 also sometimes known as K (for Klein's four group) or V (German for Viergruppe, four group). D_2 is a group with four elements, A, B, C, and 1 (the identity element). One of the realizations of D_2 is the set of symmetries of a rectangular box with three different sides. A, B, and C are 180 degree rotations about each of the axes, and 1 is the identity rotation (no rotation). The group table for D_2 is
|1 A B C
-+-------
1|1 A B C
A|A 1 C B
B|B C 1 A
C|C B A 1
As you can see, the rules correspond to the rules given in the problem, except that the rules involving 1 aren't present in the problem.
Since D_2 is a group, it satisfies a number of rules: closure (the product of any two elements of the group is another element), associativity (meaning (x*y)*z = x*(y*z) for any elements x, y, z; i.e., the order in which strings are reduced doesn't matter), existence of identity (there is an element 1 such that 1*x=x*1=x for any x), and existence of inverse (for any element x, there is an element x^{-1} such that x*x^{-1}=1 and x^{-1}*x=1; in our case, every element is its own inverse).
It's also worth noting that D_2 is commutative, i.e., x*y=y*x for any x,y.
Given any string of elements in D_2, we can reduce to a single element in the group in a greedy fashion. For example, ABCCCCCCC=CCCCCCCC=CCCCCC=CCCC=CC=1. Note that we don't write the element 1 unless it's the only element in the string. Associativity tells us that the order of the operations doesn't matter, e.g., we could have worked from right to left or started in the middle and gotten the same result. Let's try from the right: ABCCCCCCC=ABCCCCC=ABCCC=ABC=AA=1.
The situation of the problem is different because operations involving 1 are not allowed, so we can't just eliminate pairs AA, BB, or CC. However, the situation is not that different. Consider the string ABB. We can't write ABB=A in this case. However, we can eliminate BB in two steps using A: ABB=CB=A. Since order of operation doesn't matter by associativity, we're guaranteed to get the same result. So we can't go straight from ABB to A but we can get the same result by another route.
Such alternate routes are available whenever there are at least two different elements in a string. In particular, in each of ABB, ACC, BAA, BCC, CAA, CBB, AAB, AAC, BBA, BBC, CCA, CCB, we can act as if we have the reduction xx=1 and then drop the 1.
It follows that any string that is not homogeneous (not all the same letter) and has a double-letter substring (AA, BB, or CC) can be reduced by removing the double letter. Strings that contain just two identical letters can't be further reduced (because there is no 1 allowed in the problem), so it seems safe to hypothesize that any non-homogeneous string can be reduced to A, B, C, AA, BB, CC.
We still have to be careful, however, because CCAACC could be turned into CCCC by removing the middle pair AA, but that is not the best we can do: CCAACC=AACC=CC or AA takes us down to a string of length 2.
Another situation we have to be careful of is AABBBB. Here we could eliminate AA to end with BBBB, but it's better to eliminate the middle B's first, then whatever: AABBBB=AABB=AA or BB (both of which are equivalent to 1 in the group, but can't be further reduced in the problem).
There's another interesting situation we could have: AAAABBBB. Blindly eliminating pairs takes us to either AAAA or BBBB, but we could do better: AAAABBBB=AAACBBB=AABBBB=AABB=AA or BB.
The above indicate that eliminating doubles blindly is not necessarily the way to proceed, but nevertheless it was illuminating.
Instead, it seems as if the most important property of a string is non-homogeneity. If the string is homogeneous, stop, there's nothing we can do. Otherwise, identify an operation that preserves the non-homogeneity property if possible. I assert that it is always possible to identify an operation that preserves non-homogeneity if the string is non-homogeneous and of length four or greater.
Proof: if a 4-substring contains two different letters, a third letter can be introduced at a boundary between two different letters, e.g., AABA goes to ACA. Since one or the other of the original letters must be unchanged somewhere within the string, it follows that the result is still non-homogeneous.
Suppose instead we have a 4-substring that has three different elements, say AABC, with the outer two elements different. Then if the middle two elements are different, perform the operation on them; the result is non-homogeneous because the two outermost elements are still different. On the other hand, if the two inner elements are the same, e.g., ABBC, then they have to be different from both outermost elements (otherwise we'd only have two elements in the set of four, not three). In that case, perform either the first or third operation; that leaves either the last two elements different (e.g., ABBC=CBC) or the first two elements different (e.g., ABBC=ABA) so non-homogeneity is preserved.
Finally, consider the case where the first and last elements are the same. Then we have a situation like ABCA. The middle two elements both have to be different from the outer elements, otherwise we'd have only two elements in this case, not three. We can take the first available operation, ABCA=CCA, and non-homogeneity is preserved again.
End of proof.
We have a greedy algorithm to reduce any non-homogeneous string of length 4 or greater: pick the first operation that preserves non-homogeneity; such an operation must exist by the above argument.
We have now reduced to the case where we have a non-homogeneous string of 3 elements. If two are the same, we either have doubles like AAB etc., which we know can be reduced to a single element, or we have two elements with no double like ABA=AC=B which can also be reduced to a single element, or we have three different elements like ABC. There are six permutations, all of which =1 in the group by associativity and commutativity; all of them can be reduced to two elements by any operation; however, they can't possibly be reduced below a homogeneous pair (AA, BB, or CC) since 1 is not allowed in the problem, so we know that's the best we can do in this case.
In summary, if a string is homogeneous, there's nothing we can do; if a string is non-homogeneous and =A in the group, it can be reduced to A in the problem by a greedy algorithm which maintains non-homogeneity at each step; the same if the string =B or =C in the group; finally if a string is non-homogeneous and =1 in the group, it can be reduced by a greedy algorithm which maintains non-homogeneity as long as possible to one of AA, BB or CC. Those are the best we can do by the group properties of the operation.
Program solving the problem:
Now, since we know the possible outcomes, our program can run in O(n) time as follows: if all the letters in the given string are the same, no reduction is possible so just output the length of the string. If the string is non-homogeneous, and is equal to the identity in the group, output the number 2; otherwise output the number 1.
To quickly decide whether an element equals the identity in the group, we use commutativity and associativity as follows: just count the number of A's, B's and C's into the variables a, b, c. Replace a = a mod 2, b = b mod 2, c = c mod 2 because we can eliminate pairs AA, BB, and CC in the group. If none of the resulting a, b, c is equal to 0, we have ABC=1 in the group, so the program should output 2 because a reduction to the identity 1 is not possible. If all three of the resulting a, b, c are equal to 0, we again have the identity (A, B, and C all cancelled themselves out) so we should output 2. Otherwise the string is non-identity and we should output 1.
//C# Coding
using System;
using System.Collections.Generic;
namespace ConsoleApplication1
{
class Program
{
static void Main(string[] args)
{
/*
Keep all the rules in Dictionary object 'rules';
key - find string, value - replace with value
eg: find "AB" , replace with "AA"
*/
Dictionary<string, string> rules = new Dictionary<string, string>();
rules.Add("AB", "AA");
rules.Add("BA", "AA");
rules.Add("CB", "CC");
rules.Add("BC", "CC");
rules.Add("AA", "A");
rules.Add("CC", "C");
// example string
string str = "AABBCCCA";
//output
Console.WriteLine(fnRecurence(rules, str));
Console.Read();
}
//funcation for applying all the rules to the input string value recursivily
static string fnRecurence(Dictionary<string, string> rules,string str)
{
foreach (var rule in rules)
{
if (str.LastIndexOf(rule.Key) >= 0)
{
str = str.Replace(rule.Key, rule.Value);
}
}
if(str.Length >1)
{
int find = 0;
foreach (var rule in rules)
{
if (str.LastIndexOf(rule.Key) >= 0)
{
find = 1;
}
}
if(find == 1)
{
str = fnRecurence(rules, str);
}
else
{
//if not find any exit
find = 0;
str = str;
return str;
}
}
return str;
}
}
}
Here is my C# solution.
public static int StringReduction(string str)
{
if (str.Length == 1)
return 1;
else
{
int prevAns = str.Length;
int newAns = 0;
while (prevAns != newAns)
{
prevAns = newAns;
string ansStr = string.Empty;
int i = 1;
int j = 0;
while (i < str.Length)
{
if (str[i] != str[j])
{
if (str[i] != 'a' && str[j] != 'a')
{
ansStr += 'a';
}
else if (str[i] != 'b' && str[j] != 'b')
{
ansStr += 'b';
}
else if (str[i] != 'c' && str[j] != 'c')
{
ansStr += 'c';
}
i += 2;
j += 2;
}
else
{
ansStr += str[j];
i++;
j++;
}
}
if (j < str.Length)
{
ansStr += str[j];
}
str = ansStr;
newAns = ansStr.Length;
}
return newAns;
}
}
Compare two characters at a time and replace if both adjacent characters are not same. To get optimal solution, run once from start of the string and once from end of the string. Return the minimum value.
Rav solution is :-
int same(char* s){
int i=0;
for(i=0;i<strlen(s)-1;i++){
if(*(s+i) == *(s+i+1))
continue;
else
return 0;
}
return 1;
}
int reduceb(char* s){
int ret = 0,a_sum=0,i=0;
int len = strlen(s);
while(1){
i=len-1;
while(i>0){
if ((*(s+i)) == (*(s+i-1))){
i--;
continue;
} else {
a_sum = (*(s+i)) + (*(s+i-1));
*(s+i-1) = SUM - a_sum;
*(s+i) = '\0';
len--;
}
i--;
}
if(same(s) == 1){
return strlen(s);
}
}
}
int reducef(char* s){
int ret = 0,a_sum=0,i=0;
int len = strlen(s);
while(1){
i=0;
while(i<len-1){
if ((*(s+i)) == (*(s+i+1))){
i++;
continue;
} else {
a_sum = (*(s+i)) + (*(s+i+1));
*(s+i) = SUM - a_sum;
int j=i+1;
for(j=i+1;j<len;j++)
*(s+j) = *(s+j+1);
len--;
}
i++;
}
if(same(s) == 1){
return strlen(s);
}
}
}
int main(){
int n,i=0,f=0,b=0;
scanf("%d",&n);
int a[n];
while(i<n){
char* str = (char*)malloc(101);
scanf("%s",str);
char* strd = strdup(str);
f = reducef(str);
b = reduceb(strd);
if( f > b)
a[i] = b;
else
a[i] = f;
free(str);
free(strd);
i++;
}
for(i=0;i<n;i++)
printf("%d\n",a[i]);
}
#Rav
this code will fail for input "abccaccba".
solution should be only "b"
but this code wont give that. Since i am not getting correct comment place(due to low points or any other reason) so i did it here.
This problem can be solved by greedy approach. Try to find the best position to apply transformation until no transformation exists. The best position is the position with max number of distinct neighbors of the transformed character.
You can solve this using 2 pass.
In the first pass you apply
len = strlen (str) ;
index = 0 ;
flag = 0 ;
/* 1st pass */
for ( i = len-1 ; i > 0 ; i -- ) {
if ( str[i] != str[i-1] ) {
str[i-1] = getChar (str[i], str[i-1]) ;
if (i == 1) {
output1[index++] = str[i-1] ;
flag = 1 ;
break ;
}
}
else output1[index++] = str[i] ;
}
if ( flag == 0 )
output1[index++] = str[i] ;
output1[index] = '\0';
And in the 2nd pass you will apply the same on 'output1' to get the result.
So, One is forward pass another one is backward pass.
int previous = a.charAt(0);
boolean same = true;
int c = 0;
for(int i = 0; i < a.length();++i){
c ^= a.charAt(i)-'a'+1;
if(a.charAt(i) != previous) same = false;
}
if(same) return a.length();
if(c==0) return 2;
else return 1;
import java.util.Scanner;
public class StringReduction {
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
String str = sc.nextLine();
int length = str.length();
String result = stringReduction(str);
System.out.println(result);
}
private static String stringReduction(String str) {
String result = str.substring(0);
if(str.length()<2){
return str;
}
if(str.length() == 2){
return combine(str.charAt(0),str.charAt(1));
}
for(int i =1;i<str.length();i++){
if(str.charAt(i-1) != str.charAt(i)){
String temp = str.substring(0, i-1) + combine(str.charAt(i-1),str.charAt(i)) + str.substring(i+1, str.length());
String sub = stringReduction(temp);
if(sub.length() < result.length()){
result = sub;
}
}
}
return result;
}
private static String combine(char c1, char c2) {
if(c1 == c2){
return "" + c1 + c2;
}
else{
if(c1 == 'a'){
if(c2 == 'b'){
return "" + 'c';
}
if(c2 == 'c') {
return "" + 'b';
}
}
if(c1 == 'b'){
if(c2 == 'a'){
return "" + 'c';
}
if(c2 == 'c') {
return "" + 'a';
}
}
if(c1 == 'c'){
if(c2 == 'a'){
return "" + 'b';
}
if(c2 == 'b') {
return "" + 'a';
}
}
return null;
}
}
}
JAVASCRIPT SOLUTION:
function StringChallenge(str) {
// code goes here
if(str.length == 1) {
return 1;
} else {
let prevAns = str.length;
let newAns = 0;
while(prevAns != newAns) {
prevAns = newAns;
let ansStr = "";
let i = 1;
let j = 0;
while(i < str.length) {
if(str[i] !== str[j]) {
if(str[i] != 'a' && str[j] != 'a') {
ansStr += 'a';
} else if(str[i] != 'b' && str[j] !='b') {
ansStr +='b';
} else if(str[i] != 'c' && str[j] != 'c') {
ansStr += 'c';
}
i += 2;
j += 2;
} else {
ansStr += str[j];
j++;
i++;
}
}
if(j < str.length) {
ansStr += str[j];
}
str = ansStr;
newAns = ansStr.length;
}
return newAns;
}
}

Recursively searching a tree to get the binary coding for a character

Hi im trying to figure out how to recursively search a tree to find a character and the binary code to get to that character. basically the goal is to go find the code for the character and then write it to a file. the file writer part i can do no problem but the real problem is putting the binary code into a string. while im searching for the character. please help!
this is the code for the recursive method:
public String biNum(Frequency root, String temp, String letter)
{
//String temp = "";
boolean wentLeft = false;
if(root.getString() == null && !wentLeft)
{
if(root.left.getString() == null)
{
temp = temp + "0";
return biNum(root.left, temp, letter);
}
if(root.left.getString().equals(letter))
{
return temp = temp + "0";
}
else
{
wentLeft = true;
temp = temp.substring(0, temp.length() - 1);
return temp;
}
}
if(root.getString() == null && wentLeft)
{
if(root.right.getString() == null)
{
temp = temp + "1";
return (biNum(root.right, temp, letter));
}
if(root.right.getString().equals(letter))
{
return temp = temp + "1";
}
else
{
wentLeft = false;
temp = temp.substring(0, temp.length() - 1);
return temp;
}
}
return temp;
}
and this is the Frequency class:
package huffman;
public class Frequency implements Comparable {
private String s;
private int n;
public Frequency left;
public Frequency right;
private String biNum;
private String leaf;
Frequency(String s, int n, String biNum)
{
this.s = s;
this.n = n;
this.biNum = biNum;
}
public String getString()
{
return s;
}
public int getFreq()
{
return n;
}
public void setFreq(int n)
{
this.n = n;
}
public String getLeaf()
{
return leaf;
}
public void setLeaf()
{
this.leaf = "leaf";
}
#Override
public int compareTo(Object arg0) {
Frequency other = (Frequency)arg0;
return n < other.n ? -1 : (n == other.n ? 0 : 1);
}
}
In your updated version, I think you should re-examine return biNum(root.left, temp, letter);. Specifically, what happens if the root node of the entire tree has a left child which is not a leaf (and thus root.left.getString() == null) but the value you seek descends from the right child of the root node of the entire tree.
Consider this tree, for example:
26
/ \
/ \
/ \
11 15
/ \ / \
/ B A \
6 5 6 9
/ \ / \
D \ C sp
3 3 4 5
/ \
E F
2 1
and trace the steps your function will follow looking for the letter C.
Perhaps you should consider traversing the entire tree (and building up the pattern of 1s and 0s as you go) without looking for any specific letter but taking a particular action when you find a leaf node?

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