Create solution.cpp

Author: milandungrani

DP/minimized cost of binnary search tree/solution.cpp

@@ -0,0 +1,95 @@
+#include<iostream>
+#include<string>
+#include<vector>
+#include<math.h>
+#include <bits/stdc++.h>
+#define ll long long
+
+using namespace std;
+vector<ll> level[10000];
+void print(vector<vector<ll> > p,ll i,ll j,ll* a,ll l)     //print function
+{
+    if(i>j) return ;
+
+    print(p,i,p[i][j]-1,a,l+1);             //recursion go to left side
+    level[l].push_back(a[p[i][j]]);
+    print(p,p[i][j]+1,j,a,l+1);             //recursion go to right side
+}
+
+int main()
+{
+    ll n;
+    cin >>n;
+    pair<ll,ll> a[n];
+    ll b[n];
+    for(ll i=0; i<n; i++)
+    {
+        cin >> a[i].first >>a[i].second;
+    }
+    sort(a,a+n);
+    for(ll i=0; i<n; i++)
+    {
+        b[i]=a[i].first;
+    }
+    ll sum[n+1];
+    sum[0]=0;
+    for(ll i=0; i<n; i++)
+    {
+        sum[i+1]=sum[i]+a[i].second; //pre-calculating sum of cost instead of calling sum() again and again
+    }
+    ll dp[n][n];
+
+    vector<vector<ll> > p;
+
+    for(ll i=0; i<n; i++)     //initialize all values of dp array to zero
+    {
+        vector<ll> t;
+        for(ll j=0; j<n; j++)
+        {
+            dp[i][j]=0;
+            t.push_back(-1);
+        }
+        p.push_back(t);
+    }
+
+    for(ll k=0; k<n; k++)
+    {
+        ll i=0;
+        for(ll j=k; j<n; j++)
+        {
+            ll min=LONG_LONG_MAX;
+            for(ll m=j; m>=i; m--)
+            {
+                ll temp1=0,temp2=0;
+                if(i<m) temp1=dp[i][m-1];
+                if(m<j) temp2=dp[m+1][j];
+
+                ll temp=temp1 + temp2 + (sum[j+1]-sum[i]); //taking all possibilities for minimum cost
+                if(min>=temp)
+                {
+                    min=temp;
+                    p[i][j]=m;
+                }
+            }
+            dp[i][j]=min;             //dp value set as minimum value
+            i++;
+        }
+    }
+    cout<<"Minimum Cost : "<<dp[0][n-1]<<endl<<endl;  //at dp[0][n-1] total minimum cost stored
+
+    cout<<"Optimal BST with minimum cost as under : "<<endl<<endl;
+
+    print(p,0,n-1,b,0);    //print function
+    ll i=0;
+    while(level[i].size())   //printing level of BST
+    {
+        cout<< "Level "<<i+1<<": ";
+        for (std::vector<ll>::const_iterator j = level[i].begin(); j != level[i].end(); ++j)
+        {
+            std::cout << *j <<" ";
+        }
+        cout<<endl;
+        i++;
+    }
+    return 0;
+}