leetcode494

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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.

Idea

counting problems, max min problems are always involved with DP.

Code

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class Solution(object):
    def findTargetSumWays(self, nums, S):
        """
        :type nums: List[int]
        :type S: int
        :rtype: int
        """
        # cache[(i, s)] the number of combination sum up to s from nums[i] to nums[n - 1]
        def findTarget(i, s):
            if (i, s) not in cache:
                r = 0
                if i == len(nums): # base case
                    if s == 0: # the top of the figure, where number of solutions is 1.
                        r = 1
                else:
                    r = findTarget(i+1, s-nums[i]) + findTarget(i+1, s+nums[i])
                cache[(i, s)] = r
            return cache[(i, s)]
        cache = {}
        return findTarget(0, S)