Solution to Money Sums Problem Dynamic Programming

Money Sums.cpp

@@ -0,0 +1,26 @@
+#include <bits/stdc++.h>
+using namespace std;
+#define int long long int 
+int32_t main()
+{
+    int n; cin>>n;
+    int arr[n], sum=0;
+    for(int i=0; i<n; ++i) cin>>arr[i],sum+=arr[i];
+    vector<vector<bool>> dp(2,vector<bool>(sum+1,false));
+    dp[0][0]=true;
+    dp[1][0]=true;
+    // Optimised DP Space Complexity O(n) since only result of previous state was required 
+    for(int i=1; i<=n; ++i)
+    {
+        for(int j=1; j<=sum; ++j)
+        {
+            if(arr[i-1]<=j) dp[i%2][j]=(dp[(i-1)%2][j]||dp[(i-1)%2][j-arr[i-1]]);
+            else dp[i%2][j]=dp[(i-1)%2][j];
+        }
+    }
+    vector<int> vec;
+    for(int j=1; j<=sum; ++j) if(dp[n%2][j]) vec.push_back(j);
+    cout<<vec.size()<<"\n";
+    for(auto i: vec) cout<<i<<" ";
+    return 0;
+}