Merge pull request #1551 from elcabalero/patch-12

Update target_sum.cpp to match time complexity in C++

Author: Ahmad-A0

cpp/neetcode_150/14_2-d_dynamic_programming/target_sum.cpp

@@ -8,7 +8,9 @@
     Time: O(n x target)
     Space: O(n x target)
 */
-
+/* 
+// This solution adds a logn complexity for each insertion and search inside
+// of the map (since it is implemented as a tree).
 class Solution {
 public:
     int findTargetSumWays(vector<int>& nums, int target) {
@@ -32,3 +34,33 @@ class Solution {
         return dp[{i, total}];
     }
 };
+*/
+// Faster solution using a (n x maxSum*2) matrix.
+// sumCap is the sum over all the nums array elements, and is
+// used both for initializing the array (as an INT_MAX), and
+// as an offset to sum to the currSum, in order to match the
+// array's 0-indexing (otherwise it would've tried to access the 
+// -1 element of the array, for example).
+// O(n x target) time.
+// O(n x maxSum*2) space.
+class Solution {
+public:
+    int findTargetSumWays(vector<int>& nums, int target) {
+        int sumCap = accumulate(nums.begin(), nums.end(), 0) + 1;
+        vector<vector<int>> DP(nums.size(), vector<int>(sumCap * 2, sumCap));
+        return backtrack(nums, target, sumCap, 0, 0, DP);        
+    }
+private:
+    int backtrack(vector<int>& nums, int target, int sumCap, int currSum, int idx, vector<vector<int>>& DP){
+        if (idx == nums.size())
+            return currSum == target ? 1 : 0;
+        
+        if (DP[idx][currSum + sumCap] != sumCap)
+            return DP[idx][currSum + sumCap];
+        
+        DP[idx][currSum + sumCap] = backtrack(nums, target, sumCap, currSum + nums[idx], idx + 1, DP) +
+                            backtrack(nums, target, sumCap, currSum - nums[idx], idx + 1, DP);
+        
+        return DP[idx][currSum + sumCap];
+    }
+};