human
Sum of elements of all partitions of number such that no element is less than K | Function that returns total number of valid partitions of integer N.
Global declaration of 2D dp array which will be later used for memoization.
Initializing 2D dp array with - 1 we will use this 2D array for memoization.
If this subproblem is already previously calculated , then directly return that answer.
If N < K , then no valid partition is possible.
If N is between K to 2 * K then there is only one partition and that is the number N itself.
Initialize answer with 1 as the number N itself is always a valid partition.
For loop to iterate over K to N and find number of possible valid partitions recursively ..
Memoization is done by storing this calculated answer.
Returning number of valid partitions.
Driver code.
Printing total number of valid partitions"
How can the above be solved in Python?

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Give me a code to sum of elements of all partitions of number such that no element is less than K and the other steps required?
assistant
#Here is code to sum of elements of all partitions of number such that no element is less than K and the other steps required.
 def countPartitions ( n , k ) :
	dp = [ [ 0 ] * 201 ] * 201
	for i in range ( n + 1 ) :
		for j in range ( n + 1 ) :
			dp [ i ] [ j ] = - 1
	if ( dp [ n ] [ k ] >= 0 ) :
		return dp [ n ] [ k ]
	if ( n < k ) :
		return 0
	if ( n < 2 * k ) :
		return 1
	answer = 1
	for i in range ( k , n ) :
		answer = ( answer + countPartitions ( n - i , i ) )
	dp [ n ] [ k ] = answer
	return answer
n = 10
k = 3
print ( " Total ▁ Aggregate ▁ sum ▁ of ▁ all ▁ " " Valid ▁ Partitions : ▁ " , countPartitions ( n , k ) * n )