Colorful Numbers

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Objective: Given a number, find out whether its colorful or not.

Colorful Number: When in a given number, product of every digit of a sub-sequence are different. That number is called Colorful Number. See Example

Example:

Given Number : 3245
Output : Colorful
Number 3245 can be broken into parts like 3 2 4 5 32 24 45 324 245.
this number is a colorful number, since product of every digit of a sub-sequence are different.
That is, 3 2 4 5 (3*2)=6 (2*4)=8 (4*5)=20, (3*2*4)= 24 (2*4*5)= 40

Given Number : 326
Output : Not Colorful.
326 is not a colorful number as it generates 3 2 6 (3*2)=6 (2*6)=12.

Reference : http://www.careercup.com/question?id=4863869499473920

Approach:

  • Insert all the digits into hast table
  • Create a powerset of digits except empty set (Power Set)
  • Multiply all the digits in the individual powerset and insert into Hash Table.
  • If any point, number already present in the Hash table, return false

Code:


import java.util.Arrays;
import java.util.Hashtable;
public class ColorfulNumbers {
Hashtable<Integer, Integer> ht = new Hashtable<>();
boolean [] used; // for creating powerset, every digit, either
//it will be selected or not
public int [] getdigits(int Number){
int length = String.valueOf(Number).length();
int A [] = new int [length];
int counter = length–1; //start filling from the end
while(Number>0){
int x = Number%10;
Number = Number/10;
A[counter]=x;
counter—;
}
return A;
}
public boolean getColorFul(int Number){
ht.clear();
int [] A = getdigits(Number);
used = new boolean[A.length];
return powerSet(A, used, 0);
}
public boolean powerSet(int [] A, boolean [] used, int x){
if(x==used.length–1){
used[x] = false;
boolean b = insertInHash(A, used);
if(b){
used[x] = true;
return insertInHash(A, used);
}else{
return false;
}
}
used[x] = false;
boolean p = powerSet(A, used, x+1);
used[x] = true;
return p & powerSet(A, used, x+1);
}
public boolean insertInHash(int [] A, boolean [] used){
int Sum=0;
for(int i = 0;i<used.length;i++){
if(used[i]){
if(Sum==0){
Sum =A[i];
}
else{
Sum*=A[i];
}
}
}
if(ht.containsKey(Sum)){
return false;
}else{
ht.put(Sum, 1);
return true;
}
}
public static void main(String[] args) {
ColorfulNumbers c = new ColorfulNumbers();
System.out.println(" 326 Colorful?? " + c.getColorFul(326));
System.out.println(" 3245 Colorful?? " + c.getColorFul(3245));
}
}

view raw

ColorfulNumbers.java

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Output:

326 Colorful?? false
3245 Colorful?? true

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