howSum.cpp

#include <iostream>
#include <map>
#include <vector>
using namespace std;
// Time Complexity is O(n*m^2) And Space Complexity is O(m*m)
vector<int> howSum(int *ar,int n,int sum,map<int,vector<int>> &mp){
    if (sum==0){
        vector<int> v;
        v.push_back(0);
        return v;
    }
    if (sum<0){
        return vector<int>();
    }
    if (mp.count(sum)!=0){
        return mp[sum];
    }
    for (int i = 0; i < n; ++i) {
        int rem = sum-ar[i];
        mp[rem] = howSum(ar,n,rem,mp);
        if (!mp[rem].empty()){
            mp[rem].push_back(ar[i]);
            return mp[rem];
        }
    }
    mp[sum] = vector<int>();
    return mp[sum];
}
// Time Complexity is O(n*m^2) And Space Complexity is O(m*m)
vector<int> howSum2(int *ar,int n,int sum){
    vector<int> *dp = new vector<int>[sum+1];
    dp[0].push_back(0);

    for (int i = 1; i <=sum ; ++i) {
        if (dp[i].empty()){
            for (int j = 0; j < n; ++j) {
                if (i>=ar[j] && !dp[i-ar[j]].empty()){
                    dp[i] = dp[i-ar[j]];
                    dp[i].push_back(ar[j]);
                }
            }
        }
    }
    return dp[sum];
}
int main(){
    cout<<"Enter The value of n:\n";
    int n;
    cin>>n;
    cout<<"Enter The value of array:\n";
    int *ar = new int[n];
    for (int i = 0; i < n; ++i) {
        cin>>ar[i];
    }
    cout<<"Enter The value of sum:\n";
    int sum;
    cin>>sum;
    map<int,vector<int>> mp;
    vector<int> v =howSum(ar,n,sum,mp);
    cout<<"Using Top Down Approach:\n";
    if (!v.empty()) {
        for (int i = 1; i < v.size(); ++i) {
            cout<<v[i]<<" ";
        }
    } else{
        cout<<"Not Possible";
    }
    cout<<"\nUsing Bottom Up Approach:\n";
    v =howSum2(ar,n,sum);
    if (!v.empty()) {
        for (int i = 1; i < v.size(); ++i) {
            cout<<v[i]<<" ";
        }
    } else{
        cout<<"Not Possible";
    }
}