I have recently come across with this problem,
you have to find an integer from a sorted two dimensional array. But the two dim array is sorted in rows not in columns. I have solved the problem but still thinking that there may be some better approach. So I have come here to discuss with all of you. Your suggestions and improvement will help me to grow in coding. here is the code
int searchInteger = Int32.Parse(Console.ReadLine());
int cnt = 0;
for (int i = 0; i < x; i++)
{
if (intarry[i, 0] <= searchInteger && intarry[i,y-1] >= searchInteger)
{
if (intarry[i, 0] == searchInteger || intarry[i, y - 1] == searchInteger)
Console.WriteLine("string present {0} times" , ++cnt);
else
{
int[] array = new int[y];
int y1 = 0;
for (int k = 0; k < y; k++)
array[k] = intarry[i, y1++];
bool result;
if (result = binarySearch(array, searchInteger) == true)
{
Console.WriteLine("string present inside {0} times", ++ cnt);
Console.ReadLine();
}
}
}
}
Where searchInteger is the integer we have to find in the array. and binary search is the methiod which is returning boolean if the value is present in the single dimension array (in that single row).
please help, is it optimum or there are better solution than this.
Thanks
Provided you have declared the array intarry, x and y as follows:
int[,] intarry =
{
{0,7,2},
{3,4,5},
{6,7,8}
};
var y = intarry.GetUpperBound(0)+1;
var x = intarry.GetUpperBound(1)+1;
// intarry.Dump();
You can keep it as simple as:
int searchInteger = Int32.Parse(Console.ReadLine());
var cnt=0;
for(var r=0; r<y; r++)
{
for(var c=0; c<x; c++)
{
if (intarry[r, c].Equals(searchInteger))
{
cnt++;
Console.WriteLine(
"string present at position [{0},{1}]" , r, c);
} // if
} // for
} // for
Console.WriteLine("string present {0} times" , cnt);
This example assumes that you don't have any information whether the array is sorted or not (which means: if you don't know if it is sorted you have to go through every element and can't use binary search). Based on this example you can refine the performance, if you know more how the data in the array is structured:
if the rows are sorted ascending, you can replace the inner for loop by a binary search
if the entire array is sorted ascending and the data does not repeat, e.g.
int[,] intarry = {{0,1,2}, {3,4,5}, {6,7,8}};
then you can exit the loop as soon as the item is found. The easiest way to do this to create
a function and add a return statement to the inner for loop.
Related
I have been trying to solve this problem :
" You have to travel to different villages to make some profit.
In each village, you gain some profit. But the catch is, from a particular village i, you can only move to a village j if and only if and the profit gain from village j is a multiple of the profit gain from village i.
You have to tell the maximum profit you can gain while traveling."
Here is the link to the full problem:
https://www.hackerearth.com/practice/algorithms/dynamic-programming/introduction-to-dynamic-programming-1/practice-problems/algorithm/avatar-and-his-quest-d939b13f/description/
I have been trying to solve this problem for quite a few hours. I know this is a variant of the longest increasing subsequence but the first thought that came to my mind was to solve it through recursion and then memoize it. Here is a part of the code to my approach. Please help me identify the mistake.
static int[] dp;
static int index;
static int solve(int[] p) {
int n = p.length;
int max = 0;
for(int i = 0;i<n; i++)
{
dp = new int[i+1];
Arrays.fill(dp,-1);
index = i;
max = Math.max(max,profit(p,i));
}
return max;
}
static int profit(int[] p, int n)
{
if(dp[n] == -1)
{
if(n == 0)
{
if(p[index] % p[n] == 0)
dp[n] = p[n];
else
dp[n] = 0;
}
else
{
int v1 = profit(p,n-1);
int v2 = 0;
if(p[index] % p[n] == 0)
v2 = p[n] + profit(p,n-1);
dp[n] = Math.max(v1,v2);
}
}
return dp[n];
}
I have used extra array to get the solution, my code is written in Java.
public static int getmaxprofit(int[] p, int n){
// p is the array that contains all the village profits
// n is the number of villages
// used one extra array msis, that would be just a copy of p initially
int i,j,max=0;
int msis[] = new int[n];
for(i=0;i<n;i++){
msis[i]=p[i];
}
// while iteraring through p, I will check in backward and find all the villages that can be added based on criteria such previous element must be smaller and current element is multiple of previous.
for(i=1;i<n;i++){
for(j=0;j<i;j++){
if(p[i]>p[j] && p[i]%p[j]==0 && msis[i] < msis[j]+p[i]){
msis[i] = msis[j]+p[i];
}
}
}
for(i=0;i<n;i++){
if(max < msis[i]){
max = msis[i];
}
}
return max;
}
I have been working on an exercise from google's dev tech guide. It is called Compression and Decompression you can check the following link to get the description of the problem Challenge Description.
Here is my code for the solution:
public static String decompressV2 (String string, int start, int times) {
String result = "";
for (int i = 0; i < times; i++) {
inner:
{
for (int j = start; j < string.length(); j++) {
if (isNumeric(string.substring(j, j + 1))) {
String num = string.substring(j, j + 1);
int times2 = Integer.parseInt(num);
String temp = decompressV2(string, j + 2, times2);
result = result + temp;
int next_j = find_next(string, j + 2);
j = next_j;
continue;
}
if (string.substring(j, j + 1).equals("]")) { // Si es un bracket cerrado
break inner;
}
result = result + string.substring(j,j+1);
}
}
}
return result;
}
public static int find_next(String string, int start) {
int count = 0;
for (int i = start; i < string.length(); i++) {
if (string.substring(i, i+1).equals("[")) {
count= count + 1;
}
if (string.substring(i, i +1).equals("]") && count> 0) {
count = count- 1;
continue;
}
if (string.substring(i, i +1).equals("]") && count== 0) {
return i;
}
}
return -111111;
}
I will explain a little bit about the inner workings of my approach. It is a basic solution involves use of simple recursion and loops.
So, let's start from the beggining with a simple decompression:
DevTech.decompressV2("2[3[a]b]", 0, 1);
As you can see, the 0 indicates that it has to iterate over the string at index 0, and the 1 indicates that the string has to be evaluated only once: 1[ 2[3[a]b] ]
The core here is that everytime you encounter a number you call the algorithm again(recursively) and continue where the string insides its brackets ends, that's the find_next function for.
When it finds a close brackets, the inner loop breaks, that's the way I choose to make the stop sign.
I think that would be the main idea behind the algorithm, if you read the code closely you'll get the full picture.
So here are some of my concerns about the way I've written the solution:
I could not find a more clean solution to tell the algorithm were to go next if it finds a number. So I kind of hardcoded it with the find_next function. Is there a way to do this more clean inside the decompress func ?
About performance, It wastes a lot of time by doing the same thing again, when you have a number bigger than 1 at the begging of a bracket.
I am relatively to programming so maybe this code also needs an improvement not in the idea, but in the ways It's written. So would be very grateful to get some suggestions.
This is the approach I figure out but I am sure there are a couple more, I could not think of anyone but It would be great if you could tell your ideas.
In the description it tells you some things that you should be awared of when developing the solutions. They are: handling non-repeated strings, handling repetitions inside, not doing the same job twice, not copying too much. Are these covered by my approach ?
And the last point It's about tets cases, I know that confidence is very important when developing solutions, and the best way to give confidence to an algorithm is test cases. I tried a few and they all worked as expected. But what techniques do you recommend for developing test cases. Are there any softwares?
So that would be all guys, I am new to the community so I am open to suggestions about the how to improve the quality of the question. Cheers!
Your solution involves a lot of string copying that really slows it down. Instead of returning strings that you concatenate, you should pass a StringBuilder into every call and append substrings onto that.
That means you can use your return value to indicate the position to continue scanning from.
You're also parsing repeated parts of the source string more than once.
My solution looks like this:
public static String decompress(String src)
{
StringBuilder dest = new StringBuilder();
_decomp2(dest, src, 0);
return dest.toString();
}
private static int _decomp2(StringBuilder dest, String src, int pos)
{
int num=0;
while(pos < src.length()) {
char c = src.charAt(pos++);
if (c == ']') {
break;
}
if (c>='0' && c<='9') {
num = num*10 + (c-'0');
} else if (c=='[') {
int startlen = dest.length();
pos = _decomp2(dest, src, pos);
if (num<1) {
// 0 repetitions -- delete it
dest.setLength(startlen);
} else {
// copy output num-1 times
int copyEnd = startlen + (num-1) * (dest.length()-startlen);
for (int i=startlen; i<copyEnd; ++i) {
dest.append(dest.charAt(i));
}
}
num=0;
} else {
// regular char
dest.append(c);
num=0;
}
}
return pos;
}
I would try to return a tuple that also contains the next index where decompression should continue from. Then we can have a recursion that concatenates the current part with the rest of the block in the current recursion depth.
Here's JavaScript code. It takes some thought to encapsulate the order of operations that reflects the rules.
function f(s, i=0){
if (i == s.length)
return ['', i];
// We might start with a multiplier
let m = '';
while (!isNaN(s[i]))
m = m + s[i++];
// If we have a multiplier, we'll
// also have a nested expression
if (s[i] == '['){
let result = '';
const [word, nextIdx] = f(s, i + 1);
for (let j=0; j<Number(m); j++)
result = result + word;
const [rest, end] = f(s, nextIdx);
return [result + rest, end]
}
// Otherwise, we may have a word,
let word = '';
while (isNaN(s[i]) && s[i] != ']' && i < s.length)
word = word + s[i++];
// followed by either the end of an expression
// or another multiplier
const [rest, end] = s[i] == ']' ? ['', i + 1] : f(s, i);
return [word + rest, end];
}
var strs = [
'2[3[a]b]',
'10[a]',
'3[abc]4[ab]c',
'2[2[a]g2[r]]'
];
for (const s of strs){
console.log(s);
console.log(JSON.stringify(f(s)));
console.log('');
}
I am writing a Maximum Value Knapsack algorithm. It takes in a Knapsack object with Items that have a value and cost. I declare a 2D array for calculating the max value. For the base cases I have set the zeroth row values to 0 and zeroth column values to 0. I am running into trouble when I grab an item in the knapsack because when I want to grab the zeroth item, I am really grabbing the first item in the knapsack and am consequently getting the wrong values in the 2D array. Can someone check out my code and see what I am missing?
public static double MaximumKnapsack(Knapsack knapsack) {
int numItems = knapsack.getNumOfItems();
int budget = (int) knapsack.getBudget();
double[][] DP = new double[numItems+1][budget+1];
boolean taken = false;
for (int i = 0; i < numItems + 1; i++) {
for (int b = 0; b < budget + 1; b++) {
if (i == 0 || b == 0) {
DP[i][b] = 0;
}
else
{
Item item = knapsack.getItem(i);
if (item.getCost() > b) {
DP[i][b] = DP[i-1][b];
}
else
{
DP[i][b] = Math.max(DP[i-1][b-(int) item.getCost()] + item.getValue(),
DP[i-1][b]);
if (DP[i][b] == DP[i-1][b-(int) item.getCost()] + item.getValue() && item.getCost() != 0.0) {
taken = true;
}
}
}
}
taken = false;
}
return DP[numItems][budget];
}
I think the problem is in
Item item = knapsack.getItem(i);
beacuse your loop will start with i = 1. You should use:
Item item = knapsack.getItem(i-1);
We need to find the maximum element in an array which is also equal to product of two elements in the same array. For example [2,3,6,8] , here 6=2*3 so answer is 6.
My approach was to sort the array and followed by a two pointer method which checked whether the product exist for each element. This is o(nlog(n)) + O(n^2) = O(n^2) approach. Is there a faster way to this ?
There is a slight better solution with O(n * sqrt(n)) if you are allowed to use O(M) memory M = max number in A[i]
Use an array of size M to mark every number while you traverse them from smaller to bigger number.
For each number try all its factors and see if those were already present in the array map.
Here is a pseudo code for that:
#define M 1000000
int array_map[M+2];
int ans = -1;
sort(A,A+n);
for(i=0;i<n;i++) {
for(j=1;j<=sqrt(A[i]);j++) {
int num1 = j;
if(A[i]%num1==0) {
int num2 = A[i]/num1;
if(array_map[num1] && array_map[num2]) {
if(num1==num2) {
if(array_map[num1]>=2) ans = A[i];
} else {
ans = A[i];
}
}
}
}
array_map[A[i]]++;
}
There is an ever better approach if you know how to find all possible factors in log(M) this just becomes O(n*logM). You have to use sieve and backtracking for that
#JerryGoyal 's solution is correct. However, I think it can be optimized even further if instead of using B pointer, we use binary search to find the other factor of product if arr[c] is divisible by arr[a]. Here's the modification for his code:
for(c=n-1;(c>1)&& (max==-1);c--){ // loop through C
for(a=0;(a<c-1)&&(max==-1);a++){ // loop through A
if(arr[c]%arr[a]==0) // If arr[c] is divisible by arr[a]
{
if(binary_search(a+1, c-1, (arr[c]/arr[a]))) //#include<algorithm>
{
max = arr[c]; // if the other factor x of arr[c] is also in the array such that arr[c] = arr[a] * x
break;
}
}
}
}
I would have commented this on his solution, unfortunately I lack the reputation to do so.
Try this.
Written in c++
#include <vector>
#include <algorithm>
using namespace std;
int MaxElement(vector< int > Input)
{
sort(Input.begin(), Input.end());
int LargestElementOfInput = 0;
int i = 0;
while (i < Input.size() - 1)
{
if (LargestElementOfInput == Input[Input.size() - (i + 1)])
{
i++;
continue;
}
else
{
if (Input[i] != 0)
{
LargestElementOfInput = Input[Input.size() - (i + 1)];
int AllowedValue = LargestElementOfInput / Input[i];
int j = 0;
while (j < Input.size())
{
if (Input[j] > AllowedValue)
break;
else if (j == i)
{
j++;
continue;
}
else
{
int Product = Input[i] * Input[j++];
if (Product == LargestElementOfInput)
return Product;
}
}
}
i++;
}
}
return -1;
}
Once you have sorted the array, then you can use it to your advantage as below.
One improvement I can see - since you want to find the max element that meets the criteria,
Start from the right most element of the array. (8)
Divide that with the first element of the array. (8/2 = 4).
Now continue with the double pointer approach, till the element at second pointer is less than the value from the step 2 above or the match is found. (i.e., till second pointer value is < 4 or match is found).
If the match is found, then you got the max element.
Else, continue the loop with next highest element from the array. (6).
Efficient solution:
2 3 8 6
Sort the array
keep 3 pointers C, B and A.
Keeping C at the last and A at 0 index and B at 1st index.
traverse the array using pointers A and B till C and check if A*B=C exists or not.
If it exists then C is your answer.
Else, Move C a position back and traverse again keeping A at 0 and B at 1st index.
Keep repeating this till you get the sum or C reaches at 1st index.
Here's the complete solution:
int arr[] = new int[]{2, 3, 8, 6};
Arrays.sort(arr);
int n=arr.length;
int a,b,c,prod,max=-1;
for(c=n-1;(c>1)&& (max==-1);c--){ // loop through C
for(a=0;(a<c-1)&&(max==-1);a++){ // loop through A
for(b=a+1;b<c;b++){ // loop through B
prod=arr[a]*arr[b];
if(prod==arr[c]){
System.out.println("A: "+arr[a]+" B: "+arr[b]);
max=arr[c];
break;
}
if(prod>arr[c]){ // no need to go further
break;
}
}
}
}
System.out.println(max);
I came up with below solution where i am using one array list, and following one formula:
divisor(a or b) X quotient(b or a) = dividend(c)
Sort the array.
Put array into Collection Col.(ex. which has faster lookup, and maintains insertion order)
Have 2 pointer a,c.
keep c at last, and a at 0.
try to follow (divisor(a or b) X quotient(b or a) = dividend(c)).
Check if a is divisor of c, if yes then check for b in col.(a
If a is divisor and list has b, then c is the answer.
else increase a by 1, follow step 5, 6 till c-1.
if max not found then decrease c index, and follow the steps 4 and 5.
Check this C# solution:
-Loop through each element,
-loop and multiply each element with other elements,
-verify if the product exists in the array and is the max
private static int GetGreatest(int[] input)
{
int max = 0;
int p = 0; //product of pairs
//loop through the input array
for (int i = 0; i < input.Length; i++)
{
for (int j = i + 1; j < input.Length; j++)
{
p = input[i] * input[j];
if (p > max && Array.IndexOf(input, p) != -1)
{
max = p;
}
}
}
return max;
}
Time complexity O(n^2)
For the Longest Common Subsequence of 2 Strings I have found plenty examples online and I believe that I understand the solution.
What I don't understand is, what is the proper way to apply this problem for N Strings? Is the same solution somehow applied? How? Is the solution different? What?
This problem becomes NP-hard when input has arbitrary number of strings. This problem becomes tractable only when input has fixed number of strings. If input has k strings, we could apply the same DP technique in by using a k dimensional array to stored optimal solutions of sub-problems.
Reference: Longest common subsequence problem
To find the Longest Common Subsequence (LCS) of 2 strings A and B, you can traverse a 2-dimensional array diagonally like shown in the Link you posted. Every element in the array corresponds to the problem of finding the LCS of the substrings A' and B' (A cut by its row number, B cut by its column number). This problem can be solved by calculating the value of all elements in the array.
You must be certain that when you calculate the value of an array element, all sub-problems required to calculate that given value has already been solved. That is why you traverse the 2-dimensional array diagonally.
This solution can be scaled to finding the longest common subsequence between N strings, but this requires a general way to iterate an array of N dimensions such that any element is reached only when all sub-problems the element requires a solution to has been solved.
Instead of iterating the N-dimensional array in a special order, you can also solve the problem recursively. With recursion it is important to save the intermediate solutions, since many branches will require the same intermediate solutions. I have written a small example in C# that does this:
string lcs(string[] strings)
{
if (strings.Length == 0)
return "";
if (strings.Length == 1)
return strings[0];
int max = -1;
int cacheSize = 1;
for (int i = 0; i < strings.Length; i++)
{
cacheSize *= strings[i].Length;
if (strings[i].Length > max)
max = strings[i].Length;
}
string[] cache = new string[cacheSize];
int[] indexes = new int[strings.Length];
for (int i = 0; i < indexes.Length; i++)
indexes[i] = strings[i].Length - 1;
return lcsBack(strings, indexes, cache);
}
string lcsBack(string[] strings, int[] indexes, string[] cache)
{
for (int i = 0; i < indexes.Length; i++ )
if (indexes[i] == -1)
return "";
bool match = true;
for (int i = 1; i < indexes.Length; i++)
{
if (strings[0][indexes[0]] != strings[i][indexes[i]])
{
match = false;
break;
}
}
if (match)
{
int[] newIndexes = new int[indexes.Length];
for (int i = 0; i < indexes.Length; i++)
newIndexes[i] = indexes[i] - 1;
string result = lcsBack(strings, newIndexes, cache) + strings[0][indexes[0]];
cache[calcCachePos(indexes, strings)] = result;
return result;
}
else
{
string[] subStrings = new string[strings.Length];
for (int i = 0; i < strings.Length; i++)
{
if (indexes[i] <= 0)
subStrings[i] = "";
else
{
int[] newIndexes = new int[indexes.Length];
for (int j = 0; j < indexes.Length; j++)
newIndexes[j] = indexes[j];
newIndexes[i]--;
int cachePos = calcCachePos(newIndexes, strings);
if (cache[cachePos] == null)
subStrings[i] = lcsBack(strings, newIndexes, cache);
else
subStrings[i] = cache[cachePos];
}
}
string longestString = "";
int longestLength = 0;
for (int i = 0; i < subStrings.Length; i++)
{
if (subStrings[i].Length > longestLength)
{
longestString = subStrings[i];
longestLength = longestString.Length;
}
}
cache[calcCachePos(indexes, strings)] = longestString;
return longestString;
}
}
int calcCachePos(int[] indexes, string[] strings)
{
int factor = 1;
int pos = 0;
for (int i = 0; i < indexes.Length; i++)
{
pos += indexes[i] * factor;
factor *= strings[i].Length;
}
return pos;
}
My code example can be optimized further. Many of the strings being cached are duplicates, and some are duplicates with just one additional character added. This uses more space than necessary when the input strings become large.
On input: "666222054263314443712", "5432127413542377777", "6664664565464057425"
The LCS returned is "54442"