<p>You are given an integer array <code>nums</code> and an integer <code>target</code>.</p>

<p>You want to build an <strong>expression</strong> out of nums by adding one of the symbols <code>&#39;+&#39;</code> and <code>&#39;-&#39;</code> before each integer in nums and then concatenate all the integers.</p>

<ul>
	<li>For example, if <code>nums = [2, 1]</code>, you can add a <code>&#39;+&#39;</code> before <code>2</code> and a <code>&#39;-&#39;</code> before <code>1</code> and concatenate them to build the expression <code>&quot;+2-1&quot;</code>.</li>
</ul>

<p>Return the number of different <strong>expressions</strong> that you can build, which evaluates to <code>target</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,1,1,1,1], target = 3
<strong>Output:</strong> 5
<strong>Explanation:</strong> There are 5 ways to assign symbols to make the sum of nums be target 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
+1 + 1 + 1 + 1 - 1 = 3
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [1], target = 1
<strong>Output:</strong> 1
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums.length &lt;= 20</code></li>
	<li><code>0 &lt;= nums[i] &lt;= 1000</code></li>
	<li><code>0 &lt;= sum(nums[i]) &lt;= 1000</code></li>
	<li><code>-1000 &lt;= target &lt;= 1000</code></li>
</ul>

class Solution {
public:
    int offset = 1000;
    int findWays(vector<int>& nums, int target, int index, vector<vector<int>>& dp){
        if(index == 0){
            if(target == 0 && nums[0] == 0){
                return 2; // two ways. both pick and notPick would work
            }
            else if(target == nums[0] || target == 0){
                return 1; // one way only among these two conditions
            }
            return 0;
        }
        if(dp[index][target+offset] != -1){
            return dp[index][target+offset];
        }
        int notPick = findWays(nums, target, index-1, dp);
        int Pick = 0;
        if(target - nums[index] >= 0){
            Pick = findWays(nums, target - nums[index], index-1, dp);
        }

        return dp[index][target+offset] = notPick + Pick;
    }
    int findTargetSumWays(vector<int>& nums, int target) {
        int index = nums.size()-1;
        int sum = 0;
        for(int i=0;i<nums.size();i++){
            sum += nums[i];
        }
        // s1 + s2 == sum
        // s1 - s2 == target
        // s1 = (sum+target)/2
        if((sum + target) % 2 != 0){
            return 0;
        }
        int s1 = (sum + target)/2;
        vector<vector<int>> dp(nums.size(), vector<int>(2001, -1));
        int ans = findWays(nums, s1, index, dp);

        return ans;
    }
};
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