## 题目描述：

LeetCode 494. Target sum

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.

## 题目大意：

• 给定数组长度为正数并且不会超过20。
• 元素之和不会超过1000。
• 输出答案确保在32位整数范围内。

## Python代码：

class Solution(object):
def findTargetSumWays(self, nums, S):
"""
:type nums: List[int]
:type S: int
:rtype: int
"""
dp = collections.Counter()
dp[0] = 1
for n in nums:
ndp = collections.Counter()
for sgn in (1, -1):
for k in dp.keys():
ndp[k + n * sgn] += dp[k]
dp = ndp
return dp[S]

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