Update form-largest-integer-with-digits-that-add-up-to-target.py

Author: kamyu104

Python/form-largest-integer-with-digits-that-add-up-to-target.py

@@ -8,33 +8,62 @@ def largestNumber(self, cost, target):
         :type target: int
         :rtype: str
         """
-        dp = [0] + [-1]*(target)
+        dp = [0]
         for t in xrange(1, target+1):
+            dp.append(-1)
             for i, c in enumerate(cost):
                 if t-c < 0 or dp[t-c] < 0:
                     continue
                 dp[t] = max(dp[t], dp[t-c]+1)
         if dp[target] < 0:
             return "0"
         result = []
-        for i in reversed(xrange(1, 9)):
+        for i in reversed(xrange(9)):
             while target >= cost[i] and dp[target] == dp[target-cost[i]]+1:
                 target -= cost[i]
-                result.append(i)
+                result.append(i+1)
         return "".join(map(str, result))
 
 
+# Time:  O(t)
+# Space: O(t)
+class Solution2(object):
+    def largestNumber(self, cost, target):
+        """
+        :type cost: List[int]
+        :type target: int
+        :rtype: str
+        """
+        def key(bag):
+            return sum(bag), bag
+        
+        dp = [[0]*9]
+        for t in xrange(1, target+1):
+            dp.append([])
+            for d, c in enumerate(cost):
+                if t < c or not dp[t-c]:
+                    continue
+                curr = dp[t-c][:]
+                curr[~d] += 1
+                if key(curr) > key(dp[t]):
+                    dp[-1] = curr        
+        if not dp[-1]:
+            return "0"
+        return "".join(str(9-i)*c for i, c in enumerate(dp[-1]))
+
+
 # Time:  O(t^2)
 # Space: O(t^2)
-class Solution(object):
+class Solution3(object):
     def largestNumber(self, cost, target):
         """
         :type cost: List[int]
         :type target: int
         :rtype: str
         """
-        dp = [0] + [-1]*(target)
+        dp = [0]
         for t in xrange(1, target+1):
+            dp.append(-1)
             for i, c in enumerate(cost):
                 if t-c < 0:
                     continue