I'm trying to implement a game where the viable moves are down-left and down-right.
The parameter for the function is for the size of the array, so if you pass 4 it will be a 4 by 4 array.
The starting position is the top row from any column. Every element in the array is a number in the range 1-100, taken from a file. I need to find the resulting value for the most profitable route from any starting column.
My current implementation will compare the right position and left position and move to whichever is higher. The problem is, for example, if the left position is lower in value than the right, but the left position will provide more profit in the long run since it can access higher value elements, my algorithm fails.
Here is a demo:
84 (53) 40 62
*42* 14 [41] 57
76 *47* 80 [95]
If we start at number 53. The numbers enclosed in * are the moves that my algorithm will take, but the numbers enclosed in [] are the moves my algorithm should take.
This is my code:
import java.util.ArrayList;
import java.util.Scanner;
public class bestPathGame{
private int[][] grid;
private int n;
public bestPathGame(int num){
Scanner input = new Scanner(System.in);
n = num;
grid = new int[n][n];
for(int i = 0; i < n; i++){
for(int j = 0; j < n; j++){
grid[i][j] = input.nextInt();
}
}
}
public static void main(String[] args){
bestPathGame obj = new bestPathGame(Integer.parseInt(args[0]));
obj.bestPath();
}
private boolean moveLeftBetter(int r,int c){
if(c <= 0){
return false;
} else if (c >= n -1 ){
return true;
}
return grid[r][c-1] > grid[r][c+1];
}
public void bestPath(){
ArrayList<Integer> allOptions = new ArrayList<>();
for(int k = 0; k < n; k++){
int row = 0;
int col = k;
int collection = grid[row][col];
while(row < n - 1){
row += 1;
if(moveLeftBetter(row,col)){
col-=1;
} else{
col+=1;
}
collection += grid[row][col];
}
allOptions.add(collection);
}
System.out.println(allOptions.stream().reduce((a,b)->Integer.max(a,b)).get());
}
}
Greedy algorithm vs Dynamic programming
There's an issue with the logic of your solution.
Basically, what you are implemented is a called a greedy algorithm. At each step of iteration, you are picking a result that optimal locally, assuming that this choice will lead to the optimal global result. I.e. your code is based on the assumption that by choosing a local maximum between the two columns, you will get the correct global maximum.
As a consequence, your code in the bestPath() method almost at each iteration will discard a branch of paths based on only one next value. This approach might lead to incorrect results, especially with large matrixes.
Greedy algorithms are rarely able to give an accurate output, usually their result is somewhat close but not precise. As an upper-hand, they run fast, typically in O(n) time.
For this problem, you need to use a dynamic programming (DP).
In short, DP is an enhanced brute-force approach which cashes the results and reuses them instead of recalculating the same values multiple times. And as well, as a regular brute-force DP algorithms are always checking all possible combinations.
There are two major approaches in dynamic programming: tabulation and memoization (take a look at this post for more information).
Tabulation
While implementing a tabulation first you need to create an array which then need to be prepopulated (completely or partially). Tabulation is also called the bottom-up approach because calculation start from the elementary edge cases. Every possible outcome is being computed based on the previously obtained values while iterating over this array. The final result will usually be stored in the last cell (in this case in the last row).
To implement the tabulation, we need to create the matrix of the same size, and copy all the values from the given matrix into it. Then row by row every cell will be populated with the maximum possible profit that could be obtained by reaching this cell from the first row.
I.e. every iteration will produce a solution for a 2D-array, that continuously increases by one row at each step. It'll start from the array that consists of only one first row (no changes are needed), then to get the profit for every cell in the second row it's values has to be combined with the best values from the first row (that will be a valid solution for 2D-array of size 2 * n), and so on. That way, solution gradually develops, and the last row will contain the maximum results for every cell.
That how the code will look like:
public static int getMaxProfitTabulation(int[][] matrix) {
int[][] tab = new int[matrix.length][matrix.length];
for (int row = 0; row < tab.length; row++) { // populating the tab to preserve the matrix intact
tab[row] = Arrays.copyOf(matrix[row], matrix[row].length);
}
for (int row = 1; row < tab.length; row++) {
for (int col = 0; col < tab[row].length; col++) {
if (col == 0) { // index on the left is invalid
tab[row][col] += tab[row - 1][col + 1];
} else if (col == matrix[row].length - 1) { // index on the right is invalid
tab[row][col] += tab[row - 1][col - 1];
} else {
tab[row][col] += Math.max(tab[row - 1][col - 1], tab[row - 1][col + 1]); // max between left and right
}
}
}
return getMax(tab);
}
Helper method responsible for extracting the maximum value from the last row (if you want to utilize streams for that, use IntStream.of(tab[tab.length - 1]).max().orElse(-1);).
public static int getMax(int[][] tab) {
int result = -1;
for (int col = 0; col < tab[tab.length - 1].length; col++) {
result = Math.max(tab[tab.length - 1][col], result);
}
return result;
}
Memoization
The second option is to use Memoization, also called the top-down approach.
As I said, DP is an improved brute-force algorithm and memoization is based on the recursive solution that generates all possible outcomes, that is enhanced by adding a HashMap that stores all previously calculated results for every cell (i.e. previously encountered unique combination of row and column).
Recursion starts with the first row and the base-case of recursion (condition that terminates the recursion and is represented by a simple edge-case for which output is known in advance) for this task is when the recursive call hits the last row row == matrix.length - 1.
Otherwise, HashMap will be checked whether it already contains a result. And if it not the case all possible combination will be evaluated and the best result will be placed into the HashMap in order to be reused, and only the then the method returns.
Note that tabulation is usually preferred over memoization, because recursion has significant limitations, especially in Java. But recursive solutions are sometimes easier to came up with, so it's completely OK to use it when you need to test the idea or to prove that an iterative solution is working correctly.
The implementation will look like that.
public static int getMaxProfitMemoization(int[][] matrix) {
int result = 0;
for (int i = 0; i < matrix[0].length; i++) {
result = Math.max(result, maxProfitHelper(matrix, 0, i, new HashMap<>()));
}
return result;
}
public static int maxProfitHelper(int[][] matrix, int row, int col,
Map<String, Integer> memo) {
if (row == matrix.length - 1) { // base case
return matrix[row][col];
}
String key = getKey(row, col);
if (memo.containsKey(key)) { // if cell was already encountered result will be reused
return memo.get(key);
}
int result = matrix[row][col]; // otherwise result needs to be calculated
if (col == matrix[row].length - 1) { // index on the right is invalid
result += maxProfitHelper(matrix, row + 1, col - 1, memo);
} else if (col == 0) { // index on the left is invalid
result += maxProfitHelper(matrix, row + 1, col + 1, memo);
} else {
result += Math.max(maxProfitHelper(matrix, row + 1, col - 1, memo),
maxProfitHelper(matrix, row + 1, col + 1, memo));
}
memo.put(key, result); // placing result in the map
return memo.get(key);
}
public static String getKey(int row, int col) {
return row + " " + col;
}
Method main() and a matrix-generator used for testing purposes.
public static void main(String[] args) {
int[][] matrix = generateMatrix(100, new Random());
System.out.println("Tabulation: " + getMaxProfitTabulation(matrix));
System.out.println("Memoization: " + getMaxProfitMemoization(matrix));
}
public static int[][] generateMatrix(int size, Random random) {
int[][] result = new int[size][size];
for (int row = 0; row < result.length; row++) {
for (int col = 0; col < result[row].length; col++) {
result[row][col] = random.nextInt(1, 101);
}
}
return result;
}
Related
I came across this problem in class and I'm stuck on it. I did plenty of research but I'm not being able to fix my code.
I need to create a matrix and find the smallest value in the row of the largest value (I believe this element is called minimax). I'm trying to do with a simple 3 x 3 matrix. What I have so far:
Scanner val = new Scanner(System.in);
int matrizVal[][] = new int[3][3];
for (int a = 0; a < matrizVal.length; a++) {
for (int b = 0; b < matrizVal.length; b++) {
System.out.print("(" + a + ", " + b + "): ");
matrizVal[a][b] = val.nextInt();
}
}
int largest = matrizVal[0][0];
int largestrow = 0;
int arr[] = new int[2];
for (int row = 0; row < matrizVal.length; row++){
for (int col = 0; col < matrizVal.length; col++){
if (largest < matrizVal[row][col]){
largest = matrizVal[row][col];
largestrow = row;
}
}
}
To find the so called minimax element I decided to create a for each loop and get all the values of largestrow except the largest one.
for (int i : matrizVal[largestrow]){
if (i != largest){
System.out.print(i);
}
}
Here's where I'm stuck! I'd simply like to 'sort' this integer and take the first value and that'd be the minimax. I'm thinking about creating an array of size [matrizVal.length - 1], but not sure if it's gonna work.
I did a lot of research on the subject but nothing seems to help. Any tips are welcome.
(I don't think it is but I apologize if it's a duplicate)
Given the code you have provided, matrizVal[largestrow] should be the row of the matrix that contains the highest valued element.
Given that your task is to extract the smallest value in this array, there are a number of options.
If you want to simply extract the minimum value, a naive approach would go similarly to how you determined the maximum value, just with one less dimension.
For example:
int min = matrizVal[largestrow][0];
for (int i = 0; i < matrizVal.length; i++) {
if (matrizVal[largestrow][i] < min) {
min = matrizVal[largestrow][i];
}
}
// min will be the target value
Alternatively, if you want to sort the array such that the first element of the array is always the smallest, first ensure that you're making a copy of the array so as to avoid mutating the original matrix. Then feel free to use any sorting algorithm of your choice. Arrays.sort() should probably suffice.
You can simplify your approach by scanning each row for the maximum and minimum values in that row and then deciding what to do with those values based on the maximum value found in previous rows. Something like this (untested) should work:
int largestValue = Integer.MIN_VALUE;
int smallestValue = 0; // anything, really
for (int[] row : matrizVal) {
// First find the largest and smallest value for this row
int largestRowValue = Integer.MIN_VALUE;
int smallestRowValue = Integer.MAX_VALUE;
for (int val : row) {
smallestRowValue = Math.min(smallestRowValue, val);
largestRowValue = Math.max(largestRowValue, val);
}
// now check whether we found a new highest value
if (largestRowValue > largestValue) {
largestValue = largestRowValue;
smallestValue = smallestRowValue;
}
}
This doesn't record the row index, since it didn't sound like you needed to find that. If you do, then replace the outer enhanced for loop with a loops that uses an explicit index (as with your current code) and record the index as well.
I wouldn't bother with any sorting, since that (1) destroys the order of the original data (or introduces the expense of making a copy) and (2) has higher complexity than a one-time scan through the data.
You may want to consider a different alternative using Java 8 Stream :
int[] maxRow = Arrays.stream(matrizVal).max(getCompertator()).get();
int minValue = Arrays.stream(maxRow).min().getAsInt();
where getCompertator() is defined by:
private static Comparator<? super int[]> getCompertator() {
return (a1, a2)->
Integer.compare(Arrays.stream(a1).max().getAsInt(),
Arrays.stream(a2).max().getAsInt()) ;
}
Note that it may not give you the (undefined) desired output if two rows include the same highest value .
This is an implementation of the 0-1 Knapsack Problem. The problem statement goes like this,
You're given two arrays, one containing the weights of a set of items and the other containing values for the respective weights. You're provided a max weight. Within the constraint of staying under the max weight, determine the maximum value that you can obtain by selecting or not selecting the set of items.
The values and the weight list will always be of the same size.
This is my solution, which generally works fine(not on edge cases).
public static int getCombination(int[] weights, int[] values, int maxWeight){
int[][] memo = new int[weights.length][maxWeight + 1];
for (int i = 0; i < memo.length; i++) {
for(int j=0; j < memo[i].length; j++){
if(j == 0){
memo[i][j] = 0;
}else if(weights[i] > j){
if(i == 0) memo[i][j] = 0;
else memo[i][j] = memo[i-1][j];
}else{
if(i == 0){
memo[i][j] = values[i];
}
else{
memo[i][j] = Integer.max((values[i] + memo[i-1][j- weights[i]]), memo[i-1][j]);
}
}
}
}
return memo[weights.length -1][maxWeight];
}
Now I want to re-write this complete logic in a declarative manner using Java 8 Streams and lambdas. Can someone help me with that.
Since your for loop based solution is completely fine, streams do not add much value here if you only convert the for loops to forEach streams.
You get more out of using streams, if you use IntStream and the toArray method, because you can concentrate on calculating the value based on row and column index, and not care about filling it into the array.
int[][] memo = IntStream.range(0, rows)
.mapToObj(r -> IntStream.range(0, cols)
.map(c -> computeValue(r, c))
.toArray())
.toArray(int[rows][cols]::new);
Here, we create an array for each row, and then put those into a 2D-array at the end. As you can see, the toArray() methods take care of filling the arrays.
Actually, now that I looked at your method to calculate the values more closely, I realize that streams might be difficult if not impossible to use in this case. The problem is that you need values from previous columns and rows to calculate the current value. This is not possible in my solution precisely because we only create the arrays at the end. More specifically, my approach is stateless, i.e. you do not remember the result of previous iterations.
You could see if you can use Stream.reduce() to achieve your goal instead.
BTW, your approach is fine. If you don't want to parallelize this, you are good to go.
Here's a possible starting point to create the indices into your array:
int rows = 3;
int cols = 4;
int[][] memo = new int[rows][cols];
IntStream.range(0, rows * cols).forEach(n -> {
int i = n / cols;
int j = n % cols;
System.out.println("(" + i + "," + j + ")");
});
I am trying to create shopping lists from a collection of products, where the returned shopping list should be optimized for cost as well as to meet another condition.
For example, let's say that I want to create shopping lists based on the energy content of the products. When the user enters a total sum, the returned shopping list should try to max out the kcal content while keeping the total sum at or around the sum specified by the user.
I've gotten so far as to create the collection of products, and all products are stored as objects with fields holding nutritional values and price etc. The kcal-value is also stored as a member variable in each product's object.
At first I considered looping through all combinations of products, sort out those that are way out of the price interval, and then return the one with the highest kcal content. But as the numbers of products available increases this soon becomes a non-viable option I think.
I now wonder if there is any algorithm to solve this problem, if not, is there any way to easily implement this?
I did something similiar with Dynamic Programming Wikipedia article on Dynamic Programming
In the following costs and values should be arrays of the same length. The length of the possible items to choose from. The capacity is the maximum sum of all the costs of items you choose. It returns an array of booleans of the same length determining whether to take the item or not.
The idea is to create a table with the solutions to sub-problems that can then be used to solve a bigger problem. The sub-problems just solve the same problem but with a smaller list, initially with only one item. The table contains the best value you can get with the first i items for each weight up to the maximum. As you add one potential item to the list you add its value to the previous solution for that allowed weight minus the weight your adding and check if that is better than the previous solution without the last item. Once the last row is created you can tell which items to take by checking for where there are differences in the values in that last row.
public boolean[] solve(int[] values, int[] costs, int capacity) {
boolean take[] = new boolean[values.length];
int min_cost = Integer.MAX_VALUE;
for (int i = 0; i < values.length; i++) {
if (costs[i] < min_cost) {
min_cost = costs[i];
}
}
int table[][] = new int[values.length][capacity + 1 - min_cost];
for (int i = 0; i < values.length; i++) {
int v = values[i];
int w = costs[i];
for (int j = 0; j < capacity - min_cost + 1; j++) {
int prev_value = 0;
int new_value = 0;
if (i > 0) {
prev_value = table[i - 1][j];
if (w <= j + min_cost) {
if (w <= j) {
new_value = table[i - 1][j - w] + v;
} else {
new_value = v;
}
}
} else if (w <= j + min_cost) {
new_value = v;
}
table[i][j] = Math.max(prev_value, new_value);
}
}
int index = capacity - min_cost;
for (int i = values.length - 1; i > 0 && index >= 0; i--) {
if (table[i][index] != table[i - 1][index]) {
take[i] = true;
index -= costs[i];
if (index < 0) {
System.err.println("index = " + index);
}
} else {
take[i] = false;
}
}
take[0] = index >= 0 && table[0][index] != 0;
return take;
}
I'm trying to make an encryption program where the user enters a message and then converts the "letters into numbers".
For example the user enters a ABCD as his message. The converted number would be 1 2 3 4 and the numbers are stored into a one dimensional integer array. What I want to do is be able to put it into a 2x2 matrix with the use of two dimensional arrays.
Here's a snippet of my code:
int data[] = new int[] {10,20,30,40};
*for(i=0;i<2;i++)
{
for(j=0;j<2;j++)
{
for (int ctr=0; ictr<data.length(); ictr++){
a[i][j] = data[ctr];}
}
}
I know there's something wrong with the code but I am really lost.
How do I output it as the following?
10 20
30 40
(instead of just 10,20,30,40)
Here's one way of doing it. It's not the only way. Basically, for each cell in the output, you calculate the corresponding index of the initial array, then do the assignment.
int data[] = new int[] {10, 20, 30, 40, 50, 60};
int width = 3;
int height = 2;
int[][] result = new int[height][width];
for(int i = 0; i < height; i++) {
for(int j = 0; j < width; j++) {
result[i][j] = data[i * width + j];
}
}
Seems like you want to output a 2xn matrix while still having the values stored in a one-dimensional array. If that's the case then you can to this:
Assume the cardinality m of your set of values is known. Then, since you want it to be 2 rows, you calculate n=ceil(m/2), which will be the column count for your 2xn matrix. Note that if m is odd then you will only have n-1 values in your second row.
Then, for your array data (one-dimension array) which stores the values, just do
for(i=0;i<2;i++) // For each row
{
for(j=0;j<n;j++) // For each column,
// where index is baseline+j in the original one-dim array
{
System.out.print(data[i*n+j]);
}
}
But make sure you check the very last value for an odd cardinality set. Also you may want to do Integer.toString() to print the values.
Your code is close but not quite right. Specifically, your innermost loop (the one with ctr) doesn't accomplish much: it really just repeatedly sets the current a[i][j] to every value in the 1-D array, ultimately ending up with the last value in the array in every cell. Your main problem is confusion around how to work ctr into those loops.
There are two general approaches for what you are trying to do here. The general assumption I am making is that you want to pack an array of length L into an M x N 2-D array, where M x N = L exactly.
The first approach is to iterate through the 2D array, pulling the appropriate value from the 1-D array. For example (I'm using M and N for sizes below):
for (int i = 0, ctr = 0; i < M; ++ i) {
for (int j = 0; j < N; ++ j, ++ ctr) {
a[i][j] = data[ctr];
}
} // The final value of ctr would be L, since L = M * N.
Here, we use i and j as the 2-D indices, and start ctr at 0 and just increment it as we go to step through the 1-D array. This approach has another variation, which is to calculate the source index explicitly rather than using an increment, for example:
for (int i = 0; i < M; ++ i) {
for (int j = 0; j < N; ++ j) {
int ctr = i * N + j;
a[i][j] = data[ctr];
}
}
The second approach is to instead iterate through the 1-D array, and calculate the destination position in the 2-D array. Modulo and integer division can help with that:
for (int ctr = 0; ctr < L; ++ ctr) {
int i = ctr / N;
int j = ctr % N;
a[i][j] = data[ctr];
}
All of these approaches work. Some may be more convenient than others depending on your situation. Note that the two explicitly calculated approaches can be more convenient if you have to do other transformations at the same time, e.g. the last approach above would make it very easy to, say, flip your 2-D matrix horizontally.
check this solution, it works for any length of data
public class ArrayTest
{
public static void main(String[] args)
{
int data[] = new int[] {10,20,30,40,50};
int length,limit1,limit2;
length=data.length;
if(length%2==0)
{
limit1=data.length/2;
limit2=2;
}
else
{
limit1=data.length/2+1;
limit2=2;
}
int data2[][] = new int[limit1][limit2];
int ctr=0;
//stores data in 2d array
for(int i=0;i<limit1;i++)
{
for(int j=0;j<limit2;j++)
{
if(ctr<length)
{
data2[i][j] = data[ctr];
ctr++;
}
else
{
break;
}
}
}
ctr=0;
//prints data from 2d array
for(int i=0;i<limit1;i++)
{
for(int j=0;j<limit2;j++)
{
if(ctr<length)
{
System.out.println(data2[i][j]);
ctr++;
}
else
{
break;
}
}
}
}
}
Hey I'm having trouble getting my code to compare the integers of a given row or column and block to make sure there are no duplicates within those parameters. I don't know if it would be a good idea separating the three contraints in 3 different methods or just trying to attempt to do all at once.
public static rowCheck(int[][] nsudokuBoard) {
for (int i =0; i < 9; i++) {
for (int j = 0; j < 9; j++) {
// (nsudokuBoard)
}
}
}
this is my code im starting. before you guys bash on me for not even being able to compile this im stuck on how to compare all the values of a row of the 2d array.
You can compare all the values of the 2d array as shown in the code below:
void validate(final int[][] nsudokuBoard) {
final int width = nsudokuBoard[0].length;
final int depth = nsudokuBoard.length;
for (int i = 0; i < width; i++) {
int j = i;
int reference = nsudokuBoard[i][j];
do {
if (j < width) {
int current = nsudokuBoard[i][j];
if (current == reference) {
// invalid entry found do something
}
}
if (j < depth) {
// note reversed indexes
int current = nsudokuBoard[j][i];
if (current == reference) {
// invalid entry found do something
}
}
++j;
} while ((j >= width) || (j >= depth));
}
}
I haven't tried to compile this code, but it should give you an idea of how to accomplish your task. I would suggest that rather than passing in int[][] sudokuBoard that you should define a class which encapsulates the concept of a SudokuSquare and pass in SudokuSquare[][] , that way your validate method can return a List<SudokuSquare> containing all the offending entries.
I'll show how you might do it for one row, and then you can figure out the rest. I'm assuming your values are 1 through 9 inclusive, and that you don't have any zeroes or any "unfilled entries."
boolean isRowValid(int[][] grid, int row) {
boolean[] seen = new boolean[9];
int row; // chosen somewhere else
for (int col = 0; col < 9; col++) {
if (seen[grid[row][col] - 1]) { // if we've seen this value before in this row
return false; // there is a duplicate, and this is a bad sudoku
}
seen[grid[row][col] - 1] = true; // mark us as having seen this element
}
return true; // we're all good
}
return true; // this row is fine
make a class Cell with fields row,col,block,value; then make a class Matrix with field cells = cell[], fill matrix.
make a class checker with main method Matrix matrix = init(int[][]) and check(matrix), where init(ยท) fills the matrix.
boolean ok = check(matrix) where check(Matrix) does if(!rowcheck())return false; if(!colcheck()) return false etc;
create some methods like getrows(), getrow(r) and for(Cell cell: matrix.values()) to filter out the ones you want.
a bit tedious but i have done it and it is solid as rock.
As a note, filtering over matrix may seem stupid but computers are fast and the problem is O(1) since it is 9x9.