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.
Difficulty:Medium
Category:Dynamic-Programming, Depth-First-Search
Analyze
Solution
Solution 1: DFS
class Solution {
public:
int findTargetSumWays(vector<int>& nums, int S) {
int sum = 0, ans = 0;
for (int& i : nums) sum += i;
if (sum < abs(S)) return 0;
dfs(nums, 0, S, ans);
return ans;
}
private:
void dfs(vector<int>& nums, int index, int s, int& ans) {
if (index == nums.size()) {
if (s == 0) ++ans;
return;
}
dfs(nums, index + 1, s - nums[index], ans);
dfs(nums, index + 1, s + nums[index], ans);
}
};