Optimal BST

Author: coderick14

OptimalBST.cpp

@@ -0,0 +1,51 @@
+#include <bits/stdc++.h>
+#define N 10
+using namespace std;
+
+int cost[N][N], obst[N][N], prefix[N];
+
+void findOptimalBST(int keys[], int freq[], int n) {
+    int i,j,l,r;
+    /*precompute prefix sums*/
+    prefix[0] = freq[0];
+    for(i=1; i<n; i++) {
+        prefix[i] = prefix[i-1] + freq[i];
+    }
+
+    /*
+     * If key[i] is the only node in the tree, cost will be the freq[i]*1
+     * since key[i] will be the root(with depth = 0) and it'll be visited freq[i] times
+    */
+    for(i=0; i<n; i++) {
+        cost[i][i] = freq[i];
+        obst[i][i] = i;   
+    }
+    for(l=2; l<=n; l++) {
+        for(i=0; i<=n-l+1; i++) {
+            j = i+l-1;
+            cost[i][j] = INT_MAX;
+            /*Calculate cost for each element in [i,j] as the root and take the minimum*/
+            for(r=i; r<=j; r++) {
+                int c = ((r>i)?cost[i][r-1]:0) +
+                        ((r<j)?cost[r+1][j]:0) +
+                        (prefix[j] - (i-1>=0?prefix[i-1]:0));
+                if(c < cost[i][j]) {
+                    cost[i][j] = c;
+                    obst[i][j] = r;
+                }
+            }
+        }
+    }
+}
+
+int main() {
+    int i,n;
+    cin>>n; //number of nodes in the tree
+    int keys[n], freq[n];
+    for(i=0; i<n; i++) {
+        cin>>keys[i]>>freq[i];
+    }
+    findOptimalBST(keys, freq, n);
+    cout<<"Optimal cost = "<<cost[0][n-1]<<endl;
+    return 0;
+}