Merge cd58e64 into 89aabde

algorithms/dp/OptimalBST.py

@@ -0,0 +1,54 @@
+'''Construct a binary search tree of all keys such that the total cost of all the searches is as small as possible.'''
+
+######   O(N^3)  ######
+
+from itertools import accumulate
+
+
+def dp(a,acc,n):
+    cost = [[float('inf')]*n for i in range(n)]
+    st = [[0]*n for i in range(n)]
+
+    for i in range(n):
+        cost[i][i] = a[i][1]
+
+    for l in range(2,n+1):
+        for i in range(n-l+1):
+            j = i+l-1
+            for r in range(i,j+1):
+
+                if i!=0:
+                    c =  (lambda r:cost[i][r-1] if r>i else 0)(r) + (lambda r:cost[r+1][j] if r<j else 0)(r) + acc[j] - acc[i-1]
+                else:
+                    c = (lambda r: cost[i][r - 1] if r > i else 0)(r) + (lambda r: cost[r + 1][j] if r < j else 0)(r) + acc[j]
+                if c<cost[i][j]:
+                    cost[i][j]=c
+                    st[i][j]=r
+    ans = []
+    prStruct(a,0,n-1,st,ans)
+    return ans
+    #return cost[0][n-1]
+
+def prStruct(a,i,j,st,ans):
+    if j<i:
+        return
+    elif i==j:
+         ans.append(a[i][0])
+         return
+    else:
+        ans.append(a[st[i][j]][0])
+        prStruct(a,i,st[i][j]-1,st,ans)
+        prStruct(a,st[i][j]+1,j,st,ans)
+
+
+
+keys = [12, 20, 10, 22]
+wt = [34, 30, 50, 5]
+n=4
+a = list(sorted(zip(keys,wt),key=lambda x:x[0]))
+
+acc = list(accumulate([i[1] for i in a]))
+
+ans = dp(a,acc,4)
+
+print(*ans)