# 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.
``````

``````class Solution {
public:
int findTargetSumWays(vector<int>& nums, int S) {
int res = 0;
helper(nums, S, 0, res);
return res;
}
void helper(vector<int>& nums, long S, int start, int& res) {
if (start >= nums.size()) {
if (S == 0) ++res;
return;
}
helper(nums, S - nums[start], start + 1, res);
helper(nums, S + nums[start], start + 1, res);
}
};
``````

``````class Solution {
public:
int findTargetSumWays(vector<int>& nums, int S) {
vector<unordered_map<int, int>> memo(nums.size());
return helper(nums, S, 0, memo);
}
int helper(vector<int>& nums, long sum, int start, vector<unordered_map<int, int>>& memo) {
if (start == nums.size()) return sum == 0;
if (memo[start].count(sum)) return memo[start][sum];
int cnt1 = helper(nums, sum - nums[start], start + 1, memo);
int cnt2 = helper(nums, sum + nums[start], start + 1, memo);
return memo[start][sum] = cnt1 + cnt2;
}
};
``````

``````class Solution {
public:
int findTargetSumWays(vector<int>& nums, int S) {
int n = nums.size();
vector<unordered_map<int, int>> dp(n + 1);
dp[0][0] = 1;
for (int i = 0; i < n; ++i) {
for (auto &a : dp[i]) {
int sum = a.first, cnt = a.second;
dp[i + 1][sum + nums[i]] += cnt;
dp[i + 1][sum - nums[i]] += cnt;
}
}
return dp[n][S];
}
};
``````

``````class Solution {
public:
int findTargetSumWays(vector<int>& nums, int S) {
unordered_map<int, int> dp;
dp[0] = 1;
for (int num : nums) {
unordered_map<int, int> t;
for (auto a : dp) {
int sum = a.first, cnt = a.second;
t[sum + num] += cnt;
t[sum - num] += cnt;
}
dp = t;
}
return dp[S];
}
};
``````

Github 同步地址：

https://github.com/grandyang/leetcode/issues/494

https://leetcode.com/problems/target-sum/

https://leetcode.com/problems/target-sum/discuss/97371/Java-Short-DFS-Solution

https://leetcode.com/problems/target-sum/discuss/97369/Evolve-from-brute-force-to-dp

https://leetcode.com/problems/target-sum/discuss/97334/Java-(15-ms)-C%2B%2B-(3-ms)-O(ns)-iterative-DP-solution-using-subset-sum-with-explanation

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