Divide N into K parts in the form (X, 2X, … , KX) for some value of X
Given a positive integer N and K, the task is to divide N into K parts such that the first part has a value X, the second part is 2X, and so on for some value of X. If such division is not possible then print -1.
Input: N = 10, K = 4
Output: 1 2 3 4
If we take 1 as first number second number will be 2 third number will be 3 times first which is 3 and the last number will be 4 times third number so last number is 4. We can note that sum=1+2+3+4=10 which is the required sum.
Input N = 10, K = 3
Distributing N in 3 parts with given constraint is not possible.
Approach: To solve the problem mentioned above let’s to understand it’s mathematical implementation. Let the division be X1, X2, X3 up to XK where the second integer is X1 * 2, third one is X1 * 3 and the Kth one is X1 * K.
We know that,
=> , where ( 1 + 2 + 3 + … + K) =
So to solve the problem we have to follow the steps given below:
- Calculate the value of K * (K + 1) and divide 2 * N by K * (K + 1) in order to get value of X1.
- If X1 is not an integer in the above step then print -1 as there is no such division is possible.
- To get the value of X2 we will multiply X1 by 2. Similarly, to get XK multiply X1 with K.
- After finding all teh values print them.
Below is the implementation of above approach:
1 2 3 4
Time Complexity: O(K)
Auxiliary Space: O(1)
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