Optimal_Binary_Search_Tree

Optimal_Binary_Search_Tree/Optimal_Binary_Search_Tree.c

@@ -0,0 +1,75 @@
+#include <stdio.h>
+#include <stdlib.h>
+#include <limits.h> 
+
+// EXAMPLE
+//Input:  keys[] = {10, 12, 34}, freq[] = {54, 10, 4}
+//There can be following possible BSTs
+//    10                12                 34         10              34
+//      \             /    \              /             \            /
+//      12          10     34           12               34         10  
+//        \                            /                 /           \
+//         34                        10                12             12  
+//     I               II             III             IV             V
+//  
+//Cost of the optimal BST (1 BST) is  = 86
+
+int sum(int freq[], int i, int j) 
+{ 
+    int count= 0; 
+    for (int k = i; k <=j; k++) 
+       count += freq[k]; 
+    return count; 
+} 
+
+int minCostBST(int keys[], int freq[], int size)
+{
+   int cost[size][size];
+   for (int i = 0; i < size; i++)    
+      cost[i][i] = freq[i]; // freq is assigned to the diagonal elements of 2-D array cost.
+
+   for (int leng=2; leng<=size; leng++) 
+    {
+        for (int i=0; i<=size-leng+1; i++) 
+          {   
+             int j = i+leng-1;
+             cost[i][j] = INT_MAX;    
+             // One by one consider all elements as root
+             for (int r=i; r<=j; r++) 
+             {
+               //comparing with the cost and update cost if needed
+               int c = ((r > i)?cost[i][r-1]:0)+((r < j)?cost[r+1][j]:0)+sum(freq, i, j);
+               if (c < cost[i][j])
+                  cost[i][j] = c;
+             }
+          }
+     }
+   return cost[0][size-1];
+}
+
+int main() 
+{   
+    int size,i;
+    printf("Enter the numbers of keys ");
+    scanf("%d",&size);
+    int keys[size]; 
+    int freq[size];
+    printf("Enter the data elements ");
+    for ( i=0;i<size;i++)
+       scanf("%d",&keys[i]);
+    printf("Enter the frequencies ");
+    for (i=0;i<size;i++)
+       scanf("%d",&freq[i]);
+
+    printf("Cost of Optimal Binary search tree is  %d ",minCostBST(keys, freq, size));  
+
+    return 0; 
+}
+//INPUT:Enter the numbers of keys 3    
+//Enter the data elements 10
+//12
+//34
+//Enter the frequencies 54
+//10
+//4
+//OUTPUT:Cost of Optimal Binary search tree is  86