Finding the number of subsets with sum equal to k - c++

Question

Can anyone explain me the dynamic algorithm, that finds number of subsets with sum equal to k.
I searched in Google, but cant find any simple explanation! Sorry for my English!
Here is the code:
int numbers[MAX];
int GetmNumberOfSubsets()
{
int dp[MAX];
dp[0] = 1;
int currentSum = 0;
for (int i = 0; i < numbers.length; i++)
{
currentSum += numbers[i];
for (int j = min(sum, currentSum); j >= numbers[i]; j--)
dp[j] += dp[j - numbers[i]];
}
return dp[sum];
}

Answer 1

Your DP solution should be 2-dimensional, 1 dimension for the sum, and 1 dimension for the number of elements.
The recursive formula defining this solution is:
DP(x,i) = 0 x < 0
DP(0,i) = 1
DP(x,0) = 0 x > 0
DP(x,i) = DP(x-numbers[i],i-1) + DP(x,i-1)
And it should be something like:
int dp[MAX+1][sum+1];
int i, x;
for (i = 0; i < MAX+1; i++) {
dp[i][0] = 1;
}
for (x = 1; x < sum+1; x++) {
dp[0][x] = 0
}
for (i = 1; i < MAX+1; i++) {
for (x = 1; x < sum+1; x++) {
dp[i][x] = dp[i-1][x];
if (x >= numbers[i])
dp[i][x] += dp[i][x-numbers[i]];
}
}
return dp[MAX][sum];
(Hope I didn't have minor issues, didn't test it - but it should give you idea how to implement it once recursive formulas are clear)

Answer 2

You can use the following example to find the number of subsets with sum equal to k:
#include <iostream>
using std::cout;
using std::cin;
int count = 0,K;
void noofsubsets(int arr[], int sum, int N){
if(N==0){
if(sum==K)
count++;
return;
}
noofsubsets(arr, sum, N-1);
noofsubsets(arr, sum+arr[N-1], N-1);
}

Answer 3

here is a solution using recursion ...
considering two cases
i) Including first element of an array.
ii) without first array element.
`
def subSetsSumK(arr, v, k) :
if (k == 0) :
for value in v :
print(value, end=" ")
print()
return
if (len(arr)== 0):
return
si=0
v1 = [] + v
v1.append(arr[si])
subSetsSumK(arr[1:], v1, k - arr[si])
subSetsSumK(arr[1:], v, k)
def subSetsSumK(arr, k):
v = []
subSetsSumK(arr,v, k)
# Driver code
arr = [ 2,1,3,2 ]
k_sum = 4
subSetsSumK(arr,k)