Target Sum
Question
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:
- The length of the given array is positive and will not exceed 20.
- The sum of elements in the given array will not exceed 1000.
- Your output answer is guaranteed to be fitted in a 32-bit integer.
Answer
这道题刚开始看到时是想着用动态规划来做，但是没想出转移方程，就打算用递归来做，把所有的都列一遍。代码：
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,超时了，所以决定做个记忆化，保存下计算过的值。
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.
