Develop Reference

Input and Output help in topological sorting

public class Problem3 {
public static void main (String [] args){
Scanner sc= new Scanner (System.in);
System.out.println("Enter no. of Islands");
int n= sc.nextInt();
Graph g = new Graph (n);
System.out.println("Enter no. of one-way bridges");
int m= sc.nextInt();
System.out.println("Enter no. of island you want to be intially on");
int r= sc.nextInt();
try{ for (int i=0; i<m;i++){
System.out.println("This one-way bridge connects between");
int u = sc.nextInt();
int v = sc.nextInt();
if(u == v || u>n || v>n){ throw new Bounds("");}
else{ g.addEgde(u-1, v-1);}
}
g.topoSort();}
catch(IndexOutOfBoundsException e){
System.out.println("Please enter a valid input!");
}
catch(Bounds e){
System.out.println("Please enter a valid input!");
}
}
public static class Bounds extends Exception{
public Bounds (String message){
super(message);
}}
static class Graph {
int V;
LinkedList<Integer>[] adjList;
Graph(int V) {
this.V = V;
adjList = new LinkedList[V];
for (int i = 0; i < V; i++) {
adjList[i] = new LinkedList<>();
}
}
public void addEgde(int u, int v) {
adjList[u].addFirst(v);
}
public void topoSort() {
boolean[] visited = new boolean[V];
stack stack = new stack();
for (int i = 0; i < V; i++) {
if (!visited[i]) {
topoSortRE(i, visited, stack);
}
}
System.out.println("Topological Sort: ");
int size = stack.size();
for (int i = 0; i <size ; i++) {
System.out.print(stack.pop()+ 1 + " ");
}
}
public void topoSortRE(int s, boolean[] visited, stack stack) {
visited[s] = true;
for (int i = 0; i < adjList[s].size(); i++) {
int vertex = adjList[s].get(i);
if (!visited[vertex])
topoSortRE(vertex, visited, stack);
}
stack.push(s);
}}}
The following code is an attempt to solve the following problem:
There are many islands that are connected by one-way bridges, that is, if a bridge connects
islands a and b, then you can only use the bridge to go from a to b but you cannot travel back
by using the same. If you are on island a, then you select (uniformly and randomly) one of
the islands that are directly reachable from a through the one-way bridge and move to that
island. You are stuck on an island if you cannot move any further. It is guaranteed that if
there is a directed path from one island to the second there is no path that leads from the
second back to the first. In other words the formed graph is a Directed Acyclic Graph.
Find the island that you are most likely to get stuck on; that is the island that you can
possibly reach with the maximum number of paths from all other islands.
Input format:
First line: Three integers n (the number of islands), m (the number of one-way bridges), and r
(the index of the island you are initially on)
Next m lines: Two integers ui and vi representing a one-way bridge from island ui to vi.
Output format:
Print the index of the island that you are most likely to get stuck on. If there are multiple
islands, then print them in the increasing order of indices (space separated values in a single
line).
Sample input
5, 7, 1
(1, 2)
(1, 3)
(1, 4)
(1, 5)
(2, 4)
(2, 5)
(3, 4)
Sample output
4
I wrote the code to topologically sort the graph but I am having issues with how to make the input r the intial island and also how to make the output be the most probable island to be stuck on. I know that the island I'm most likely to be stuck on is the island that has the most indegrees and no outdegrees but don't know how to implement that.

For each node make a value (real number) representing probability that you will reach it from your starting island. At first, set this value for initial node to 1 and 0 for other nodes.
During the topological sort, when you're in node v, add its probability value divided by number of neighbors to each neighbor's value (in other words, since you know that the probability of getting to v is v.value, then the probability of reaching its neighbor should be increased by v.value * ppb of choosing this neighbor, that is 1 / #_of_neighbors). In this way, whenever you're in some node during topological sort, its value will be equal to the total probability of reaching it.
Your answer is an ending island (node with outdegree 0) with largest value.
Your topological sort seems wrong, you're doing something that looks like DFS. In topological sort you want to visit each vertex after visiting all vertices with an edge ending in it.
About implementation, I changed your DFS into topological sort and added those probabilities I've talked about. I left the part about choosing best ending vertex to you, I don't think doing all the work for someone is educational in any way. Also, I do not guarantee that my changes below do not contain any spelling mistakes, etc. I did my best, but I have not run this code.
static class Graph {
int V;
LinkedList<Integer>[] adjList;
Graph(int V) {
this.V = V;
adjList = new LinkedList[V];
probability = new double[V];
for (int i = 0; i < V; i++) {
adjList[i] = new LinkedList<>();
}
}
public void addEgde(int u, int v) {
adjList[u].addFirst(v);
}
public void topoSort(int start) {
double[] probability;
probability[start] = 1;
int[] indegree = new int[V];
stack stack = new stack();
for (int i = 0; i < V; i++) {
probability[i] = 0;
for (int j = 0; j < adjList[i].size(); ++j) {
indegree[adjList[i][j]] += 1;
}
}
probability[start] = 1;
for(int i = 0; i < V; ++i)
{
if(indegree[i] == 0)
stack.push(i);
}
while(stack.size())
{
int v = stack.pop();
for (int i = 0; i < adjList[v].size(); ++i)
{
indegree[adjList[v][i]] -= 1;
probability[adjList[v][i]] += probability[v] / (double)(adjList[v].size());
if(indegree[adjList[v][i]] == 0)
stack.push(adjList[v][i]);
}
}
//probability array now contains all probabilities to visit each node
}
}
}

Finding biggest area of adjacent numbers in a matrix using DFS algorithm

I am learning programming on my own with a book for beginners. My last task after chapter Arrays is to :
// Find the biggest area of adjacent numbers in this matrix:
int[][] matrix = {
{1,3,2,2,2,4},
{3,3,3,2,4,4},
{4,3,1,2,3,3}, // --->13 times '3';
{4,3,1,3,3,1},
{4,3,3,3,1,1}
As a hint I have - use DFS or BFS algorithm. After I read about them and saw many their implementations I got the idea but it was just too overwhelming for a beginner. I found the solution for my task and after I runned the program many times I understood how it works and now I can solve the problem on my own. Although, I am happy that this solution helped me to learn about recursion, I am wondering can the following code be modified in iterative way and if so can you give me hints how to do it? Thank you in advance.
public class Practice {
private static boolean[][] visited = new boolean[6][6];
private static int[] dx = {-1,1,0,0};
private static int[] dy = {0,0,-1,1};
private static int newX;
private static int newY;
public static void main(String[] args){
// Find the biggest area of adjacent numbers in this matrix:
int[][] matrix = {
{1,3,2,2,2,4},
{3,3,3,2,4,4},
{4,3,1,2,3,3}, // --->13 times '3';
{4,3,1,3,3,1},
{4,3,3,3,1,1}
};
int current = 0;
int max = 0;
for (int rows = 0; rows < matrix.length;rows++){
for(int cols = 0; cols < matrix[rows].length;cols++){
if (visited[rows][cols] == false){
System.out.printf("Visited[%b] [%d] [%d] %n", visited[rows]
[cols],rows,cols);
current = dfs(matrix,rows,cols,matrix[rows][cols]);
System.out.printf("Current is [%d] %n", current);
if(current > max){
System.out.printf("Max is : %d %n ", current);
max = current;
}
}
}
}
System.out.println(max);
}
static int dfs(int[][] matrix,int x, int y, int value){
if(visited[x][y]){
System.out.printf("Visited[%d][%d] [%b] %n",x,y,visited[x][y]);
return 0;
} else {
visited[x][y] = true;
int best = 0;
int bestX = x;
int bestY = y;
for(int i = 0; i < 4;i++){
//dx = {-1,1,0,0};
//dy = {0,0,-1,1};
int modx = dx[i] + x;
System.out.printf(" modx is : %d %n", modx);
int mody = dy[i] + y;
System.out.printf(" mody is : %d %n", mody);
if( modx == -1 || modx >= matrix.length || mody == -1 || mody >=
matrix[0].length){
continue;
}
if(matrix[modx][mody] == value){
System.out.printf("Value is : %d %n",value);
int v = dfs(matrix,modx,mody,value);
System.out.printf(" v is : %d %n",v);
best += v;
System.out.printf("best is %d %n",best);
}
newX = bestX;
System.out.printf("newX is : %d %n",newX);
newY = bestY;
System.out.printf("newY is : %d %n",newY);
}
System.out.printf("Best + 1 is : %d %n ",best + 1);
return best + 1;
}
}
}

If you look on the Wikipedia page for Depth-first search under the pseudocode section, they have an example of a iterative verision of the DFS algorithm. Should be able to figure out a solution from there.
*Edit
To make it iterative, you can do the following:
procedure DFS-iterative(matrix, x, y):
let S be a stack
let value = 0
if !visited[v.x, v.y]
S.push(position(x,y))
while S is not empty
Position v = S.pop()
value += 1
for all valid positions newPosition around v
S.push(newPosition)
return value
Everytime you would call the dfs() method in the recursive method, you should be calling S.push(). You can create class Position as follows
class Position{
int x;
int y;
public Position(int x, int y){
this.x = x;
this.y = y;
}
//getters and setters omitted for brevity
}
and use the built in java class java.util.Stack to make it easy.
Stack<Position> s = new Stack<Position>();
If you want to use BFS instead of DFS, you can simple change the Stack to a Queue and you will get the desired result. This link has a very nice explanation of stacks and queues and may prove useful as you learn about the topic.

I assume you are looking for a BFS solution, since you already have a working DFS, and BFS is iterative while DFS is recursive (or at least, is easier to implement recursively).
The (untested) BFS code to measure a region's size could be:
public static int regionSize(int[][] matrix,
int row, int col, HashSet<Point> visited) {
ArrayDeque<Point> toVisit = new ArrayDeque<>();
toVisit.add(new Point(col, row));
int regionColor = matrix[col][row];
int regionSize = 0;
while ( ! toVisit.isEmpty()) {
Point p = toVisit.removeFirst(); // use removeLast() to emulate DFS
if ( ! visited.contains(p)) {
regionSize ++;
visited.add(p);
// now, add its neighbors
for (int[] d : new int[][] {{1, 0}, {0, 1}, {-1, 0}, {0, -1}}) {
int nx = p.x + d[0];
int ny = p.y + d[1];
if (nx >= 0 && nx < matrix[0].length
&& ny >= 0 && ny < matrix.length
&& matrix[ny][nx] == regionColor) {
toVisit.addLast(new Point(nx, ny)); // add neighbor
}
}
}
}
return regionSize;
}
Note that you can change a (queue-based) BFS into an iterative DFS by changing a single line. In a recursive DFS, you would be using the program stack to keep track of toVisit intead of an explicit stack/deque. You can test this by adding a System.out.println to track the algorithm's progress.
Above, I use a HashSet of Point instead of a boolean[][] array, but feel free to use whichever is easiest for you.

Stock ticker data structure for getting top k stock prices

I am practicing some interview questions and one I came across is a stock ticker data structure problem.
Given a stream of stock prices write a data structure that supports that following operations:
1. StockSticker(int k) : Initialize the size of the ticker.
2. void addOrUpdate(String stock, double price) : Add or update a stock.
3. List<Stock> top(int k) : Get top k stocks.
My idea was to use a HashMap in conjunction with the quickselection algorithm in order to get an average case O(n) complexity for the top(k) function. Would this be an efficient solution when dealing with a stream of values, or is there something better? The only other idea I have would be to use heaps, but I am not sure how to manipulate it in a way to get better than O(n).
Here is my solution:
public class StockTicker {
public class Stock{
String sym;
double price;
public Stock(String s, double val){
this.sym = s;
this.price = val;
}
}
HashMap<String,Stock> st;
HashMap<String,Integer> ind;
int unique;
int max;
Stock[] stocks;
public StockTicker(int k){
this.unique = 0;
this.max = k;
this.st = new HashMap<String, Stock>();
this.ind = new HashMap<String, Integer>();
this.stocks = new Stock[k];
}
public void addOrUpdate(String sym, double price){
if(!st.containsKey(sym)){
Stock stock = new Stock(sym,price);
st.put(sym, stock);
ind.put(sym, unique);
stocks[unique++] = stock;
}
else{
Stock update = st.get(sym);
update.price = price;
}
}
public List<Stock> top(int k){
List<Stock> res = new ArrayList<Stock>();
Stock[] temp = new Stock[max];
for(int i = 0; i < temp.length; i++){
temp[i] = new Stock(stocks[i].sym, stocks[i].price);
}
int top = quickselect(temp, 0, temp.length-1, k);
for(int i = 0; i <= top; i++){
res.add(temp[i]);
}
return res;
}
public int quickselect(Stock[] stocks, int left, int right, int kth){
if(left == right){
return left;
}
int split = partition(stocks, left,right);
if(kth-1 == split){ return split;}
else if(kth-1 > split){ return quickselect(stocks,split + 1, right, kth);}
else { return quickselect(stocks, left , split-1, kth);}
}
public int partition(Stock[] stocks, int left, int right){
int lastIndex = right;
double pivot = stocks[lastIndex].price;
while(left <= right){
while( left <= right && stocks[left].price > pivot ){
left++;
}
while( left <= right && stocks[right].price <= pivot){
right--;
}
if(left <= right && stocks[left].price <= pivot && stocks[right].price > pivot){
swap(stocks,left,right);
}
}
swap(stocks,left,lastIndex);
return left;
}
public void swap(Stock[] stocks, int x, int y){
Stock eleX = stocks[x];
Stock eleY = stocks[y];
stocks[x] = eleY;
stocks[y] = eleX;
}
public Stock getStock(String sym){
return st.get(sym);
}
public static void main(String[] args){
StockTicker ticker = new StockTicker(10);
ticker.addOrUpdate("A", 10.00);
ticker.addOrUpdate("B", 1.00);
ticker.addOrUpdate("C", 9.00);
ticker.addOrUpdate("D", 2.00);
ticker.addOrUpdate("E", 8.00);
ticker.addOrUpdate("F", 3.00);
ticker.addOrUpdate("G", 7.00);
ticker.addOrUpdate("H", 4.00);
ticker.addOrUpdate("I", 6.00);
ticker.addOrUpdate("J", 5.00);
List<Stock> topStocks = ticker.top(5);
for(Stock s: topStocks){
System.out.print(s.sym + ": " + s.price + " ");
}
}
}

You can do better for small k: you can maintain a priority queue, pop the maximum k times and add these elements back to the queue to answer the top k query in O(k log n) time.
In fact, you can answer each query in O(k + log N) time for any value of k, but it would require implementing a custom balanced binary search tree (with a custom tree, you just need to split it by the k-th position), but it can be pretty tedious to implement.

I think this is a classic Priority Queue use case, you just need to handle the logic when new price is coming and you need to change the price of the stock which is already in the queue.
Here's a python solution from official doc:
https://docs.python.org/2/library/heapq.html#priority-queue-implementation-notes
Or a Java implementation of Indexed Priority Queue that is exactly what you need:
https://algs4.cs.princeton.edu/24pq/IndexMinPQ.java.html

printing the turns of a recursive maze solution in Java

So I've been working on the following problem:
I buried my sapphire then started walking. I always walked in a
straight line following a compass direction (N, S, E, W). When I
stopped, I made a 90 degree turn and continued walking. I might have
crossed my path, but I don’t remember. Below are the number of meters
I travelled in each direction. I’m now lost and must abandon this
record while I search for a way out. I’m placing this note under a
rock at my final location. Perhaps some lucky adventurer will decode
my note and retrace my steps to earn the treasure. Unfortunately,
there is no record of where in the ruins the note was found. Instead,
you must write a program to find the treasure. Input The first
line contains two integers X Y, representing the number of rows and
columns in the ruins. Maximum of 20 rows and 50 columns. The next X
lines show a grid map of the space. A period “.” is an empty square. A
hash “#” is a large boulder, marking a square that cannot be entered.
The next line has an integer N, the count of the straight paths
walked. Maximum of 20 paths. The last line contains N integers
separated by spaces, showing the successive path-lengths.. 5 10
####
........#
.#...##.#
...#....#
#### 8 2 4 2 2 2 5 2 1 Output Your program must print the same map, with the location of both the Sapphire (S) and the final
location of the message (F) marked. Also, label every turning point
with successive lowercase letters (if the same point is used more
than once, print the letter for the later turn.) There is only one
route which follows the path-lengths in the list.
####
b.e.a..f#
.#...##.#
c.d#S.Fg#
#
and I have made a recursive method that checks every direction starting from every open position of the maze until it finds the solution, however the output of the problem needs to be the mazes with the turns.
The problem is, when I use a recursive solution and edit the actual char[][] map, it never knows which path will lead to the actual finish, so it will create output like this:
d...d
.....
cbabc
d...d
but instead I would like it to show only one path, like this:
....d
.....
..abc
.....
Here is my incomplete solution:
import java.util.Scanner;
public class SapphireSearch {
private static int rs; // Row Size
private static int cs; // Column Size
private static int sr; // Save row (saves solution row)
private static int sc; // Save col (saves solution col)
private static Direction sd; // Save direction (saves solution dir)
private static char[][] map; // the maze to traverse
private static int n; // number of turns
private static int[] go; // length of the turns
public static void main(String[] args) {
getInput();
for (int r = 0; r < rs; r++)
for (int c = 0; c < cs; c++)
for (Direction d : Direction.values())
solve(sr = r, sc = c, sd = d, 0, false);
}
public static void solve(int r, int c, Direction d, int start,
boolean printing) {
if (isSolid(r, c))
return;
if (printing) {
if (start == 0)
map[r][c] = 'S';
else
map[r][c] = (char) (start - 1 + 'a');
if (start == n) {
map[r][c] = 'F';
return;
}
}
if (start == n - 1 && !printing) {
solve(sr, sc, sd, 0, true);
printArray(map);
System.exit(0);
}
int count = 0;
while (start < go.length && count < go[start]) {
count++;
r += d.dr;
c += d.dc;
if (isSolid(r, c))
return;
}
for (Direction t : d.turn())
solve(r, c, t, start + 1, printing);
}
public static boolean isSolid(int r, int c) {
return map[r][c] == '#';
}
public static void printArray(char[][] o) {
for (int r = 0; r < o.length; r++) {
for (int c = 0; c < o[r].length; c++)
System.out.print(o[r][c]);
System.out.println();
}
}
private static void getInput() {
Scanner s = new Scanner(System.in);
rs = s.nextInt();
cs = s.nextInt();
s.nextLine(); // clear buffer
map = new char[rs][cs];
for (int r = 0; r < rs; r++) {
int c = 0;
char[] f = s.nextLine().trim().toCharArray();
for (char t : f)
map[r][c++] = t;
}
n = s.nextInt();
go = new int[n];
for (int i = 0; i < n; i++)
go[i] = s.nextInt();
}
}
enum Direction {
// deltaR, deltaC
up(-1, 0), down(1, 0), left(0, -1), right(0, 1);
public int dr;
public int dc;
private Direction(int dr, int dc) {
this.dr = dr;
this.dc = dc;
}
public Direction[] turn() {
Direction[] out = new Direction[2];
switch (this) {
case up:
case down:
out[0] = left;
out[1] = right;
break;
case left:
case right:
out[0] = up;
out[1] = down;
}
return out;
}
}
The question is: building upon my recursive solve algorithm, what would be the best way to print the solution path (where it doesn't print out every path it tries to take)?

You need to build up your list of turns as you do the recursive search (I'm just listing the direction here for simplicity but you could store an object with co-ordinates as well for example).
If the path is (N,E,N,W,S) and then save that as you exit.
To do that keep the partial list so far and each recursive call COPY the list so far and add to it.
i.e.:
n
ne
nw Fail
nen
nes Fail
nenw
etc.
At the end you can either return the completed solution or if you need to handle multiple solutions have a final results list of lists that you insert the completed one into.
The key step is to copy the list so far so that recursion branches cannot interfere with each other.

I need an algorithm to get the chromatic number of a graph

Given the adjacency matrix of a graph, I need to obtain the chromatic number (minimum number of colours needed to paint every node of a graph so that adjacent nodes get different colours).
Preferably it should be a java algorithm, and I don't care about performance.
Thanks.
Edit:
recently introduced a fix so the answer is more accurately. now it will recheck his position with his previous positions.
Now a new question comes up. Which will be better to raise his 'number-color'? the node in which i am standing, or the node i am visiting (asking if i am adjacent to it)?
public class Modelacion {
public static void main(String args[]) throws IOException{
// given the matrix ... which i have hidden the initialization here
int[][] matriz = new int[40][40];
int color[] = new int[40];
for (int i = 0 ; i<40;i++)
color[i]=1;
Cromatico c = new Cromatico(matriz, color);
}
}
import java.io.IOException;
public class Cromatico {
Cromatico(int[][]matriz, int[] color, int fila) throws IOException{
for (int i = 0; i<fila;i++){
for (int j = 0 ; j<fila;j++){
if (matriz[i][j] == 1 && color[i] == color [j]){
if (j<i)
color [i] ++;
else
color [j] ++;
}
}
}
int numeroCromatico = 1;
for (int k = 0; k<fila;k++){
System.out.print(".");
numeroCromatico = Math.max(numeroCromatico, color[k]);
}
System.out.println();
System.out.println("el numero cromatico del grafo es: " + numeroCromatico);
}
}

Finding the chromatic number of a graph is NP-Complete (see Graph Coloring). It is NP-Complete even to determine if a given graph is 3-colorable (and also to find a coloring).
The wiki page linked to in the previous paragraph has some algorithms descriptions which you can probably use.
btw, since it is NP-Complete and you don't really care about performance, why don't you try using brute force?
Guess a chromatic number k, try all possibilities of vertex colouring (max k^n possibilities), if it is not colorable, new guess for chromatic number = min{n,2k}. If it is k-colorable, new guess for chromatic number = max{k/2,1}. Repeat, following the pattern used by binary search and find the optimal k.
Good luck!
And to answer your edit.
Neither option of incrementing the color will work. Also, your algorithm is O(n^2). That itself is enough to tell it is highly likely that your algorithm is wrong, even without looking for counterexamples. This problem is NP-Complete!

Super slow, but it should work:
int chromaticNumber(Graph g) {
for (int ncolors = 1; true; ncolors++) {
if (canColor(g, ncolors)) return ncolors;
}
}
boolean canColor(Graph g, int ncolors) {
return canColorRemaining(g, ncolors, 0));
}
// recursive routine - the first colors_so_far nodes have been colored,
// check if there is a coloring for the rest.
boolean canColorRemaining(Graph g, int ncolors, int colors_so_far) {
if (colors_so_far == g.nodes()) return true;
for (int c = 0; c < ncolors; c++) {
boolean ok = true;
for (int v : g.adjacent(colors_so_far)) {
if (v < colors_so_far && g.getColor(v) == c) ok = false;
}
if (ok) {
g.setColor(colors_so_far, c);
if (canColorRemaining(g, ncolors, colors_so_far + 1)) return true;
}
}
return false;
}