Leetcode 494.Target Sum(第十五週作業)

先貼原題：

You are given a list of non-negative integers, a1, a2, …, an, and a target, S. Now you have 2 symbols + and -. For each integer, you should choose one from + and - as its new symbol.

Find out how many ways to assign symbols to make sum of integers equal to target S. Example 1:

Input: nums is [1, 1, 1, 1, 1], S is 3. 
Output: 5
Explanation: 

-1+1+1+1+1 = 3
+1-1+1+1+1 = 3
+1+1-1+1+1 = 3
+1+1+1-1+1 = 3
+1+1+1+1-1 = 3

There are 5 ways to assign symbols to make the sum of nums be target 3.

Note:

1. The length of the given array is positive and will not exceed 20.
2. The sum of elements in the given array will not exceed 1000.
3. Your output answer is guaranteed to be fitted in a 32-bit integer.

這道題剛開始看到時是想着用動態規劃來做，但是沒想出轉移方程，就打算用遞歸來做，把所有的都列一遍。代碼：

class Solution(object):
    count = 0
    def findTargetSumWays(self, nums, S):
        """ :type nums: List[int] :type S: int :rtype: int """
        length = len(nums)
        def helper(currsum, pos):
            if pos == length:
                if currsum == S: self.count+=1
            else:
                helper(currsum+nums[pos], pos+1)
                helper(currsum-nums[pos], pos+1)
        helper(0, 0)
        return self.count

But unfortunately,超時了，所以決定做個記憶化，保存下計算過的值。

class Solution(object):
    def findTargetSumWays(self, nums, S):
        """ :type nums: List[int] :type S: int :rtype: int """
        length = len(nums)
        import sys
        dp = [[-sys.maxint]*2001 for i in range(length)]
        def helper(currsum, pos):
            if pos == length:
                return 1 if currsum == S else 0
            else:
                if dp[pos][currsum+1000] != -sys.maxint:
                    return dp[pos][currsum+1000]
                add = helper(currsum+nums[pos], pos+1)
                sub = helper(currsum-nums[pos], pos+1)
                dp[pos][currsum+1000] = add + sub
                return dp[pos][currsum+1000]
        return helper(0, 0)

Solved.