Create 494. Target Sum.cpp

494. Target Sum.cpp

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+//*************************** Approach 1 *****************
+class Solution {
+public:
+    int solve(vector<int>& nums, int &target, int i, int sum, unordered_map<string, int>& memo) {
+        if (i == nums.size()) {
+            return sum == target ? 1 : 0;
+        }
+
+        // Create a unique key for the current state
+        string key = to_string(i) + "," + to_string(sum);
+
+        // Check if the result is already computed
+        if (memo.find(key) != memo.end()) {
+            return memo[key];
+        }
+
+        // Compute the result recursively
+        int plus = solve(nums, target, i + 1, sum + nums[i], memo);
+        int minus = solve(nums, target, i + 1, sum - nums[i], memo);
+
+        // Store the result in the memo
+        memo[key] = plus + minus;
+
+        return memo[key];
+    }
+
+    int findTargetSumWays(vector<int>& nums, int target) {
+        unordered_map<string, int> memo;
+        return solve(nums, target, 0, 0, memo);
+    }
+};
+
+
+// ************************** Approach 2 ***************************************
+
+class Solution {
+public:
+    int S;
+    int solve(vector<int>& nums, int &target, int i, int sum, vector<vector<int>>& t) {
+        if(i == nums.size()) {
+            return sum == target ? 1 : 0;
+        }
+
+        if(t[i][sum+S] != INT_MIN) {
+            return t[i][sum+S];
+        }
+        int plus  = solve(nums, target, i+1, sum+nums[i], t);
+        int minus = solve(nums, target, i+1, sum-nums[i], t);
+
+        return t[i][sum+S] = plus+minus;
+    }
+
+    int findTargetSumWays(vector<int>& nums, int target) {
+        int n = nums.size();
+        S = accumulate(begin(nums), end(nums), 0);
+        vector<vector<int>> t(n, vector<int>(2*S+1, INT_MIN));
+        return solve(nums, target, 0, 0, t);
+    }
+};
+
+// *************************** Approach 3 *************************
+
+class Solution {
+public:
+    int S;
+    int solve(vector<int>& nums, int &target, int i, int sum, vector<vector<int>>& t) {
+        if(i == nums.size()) {
+            return sum == target ? 1 : 0;
+        }
+
+        if(t[i][sum+S] != INT_MIN) {
+            return t[i][sum+S];
+        }
+        int plus  = solve(nums, target, i+1, sum+nums[i], t);
+        int minus = solve(nums, target, i+1, sum-nums[i], t);
+
+        return t[i][sum+S] = plus+minus;
+    }
+
+    int findTargetSumWays(vector<int>& nums, int target) {
+        int n = nums.size();
+        S = accumulate(begin(nums), end(nums), 0);
+        vector<vector<int>> t(n, vector<int>(2*S+1, INT_MIN));
+        return solve(nums, target, 0, 0, t);
+    }
+};
+
+// ************************** Approach 3 ***************************
+
+class Solution {
+public:
+    int t[21][1001];
+    int subsetSum(vector<int>& nums, int n, int s) {
+        if(t[n][s] != -1)
+            return t[n][s];
+        if(s == 0)
+            return 1;
+        if(n == 0)
+            return 0;
+        if(nums[n-1] == 0)
+            return t[n][s] = subsetSum(nums, n-1, s);
+
+        if(nums[n-1] <= s)
+            return t[n][s] = subsetSum(nums, n-1, s-nums[n-1]) + subsetSum(nums, n-1, s);
+        else
+            return t[n][s] = subsetSum(nums, n-1, s);
+    }
+
+    int findTargetSumWays(vector<int>& nums, int target) {
+        memset(t, -1, sizeof(t));
+        int sum   = accumulate(begin(nums), end(nums), 0);
+        auto lambda = [&](const int& x) {
+            return x == 0;
+        };
+        int zeros = count_if(begin(nums), end(nums), lambda);
+        if(target > sum)
+            return 0;
+
+        if((sum-target) %2 != 0)
+            return 0;
+
+        int s1 = (sum-target)/2;
+        return pow(2, zeros)*subsetSum(nums, nums.size(), s1);
+
+    }
+};
+
+//**************************** Approach 4 ******************************
+
+class Solution {
+public:
+    int subsetSum(vector<int>& nums, int s) {
+        int n = nums.size();
+        vector<vector<int>> t(n+1, vector<int>(s+1));
+
+        for(int col = 0; col < s+1; col++) t[0][col] = 0;
+        for(int row = 0; row < n+1; row++) t[row][0] = 1;
+
+        for(int i = 1; i<n+1; i++) {
+            for(int j = 1; j<s+1; j++) {
+                if(nums[i-1] == 0)
+                    t[i][j] = t[i-1][j];
+                else if(nums[i-1] <= j)
+                    t[i][j] = t[i-1][j-nums[i-1]] + t[i-1][j];
+                else
+                    t[i][j] = t[i-1][j];
+            }
+        }
+
+        return t[n][s];
+    }
+
+    int findTargetSumWays(vector<int>& nums, int target) {
+        int sum   = accumulate(begin(nums), end(nums), 0);
+        auto lambda = [&](const int& x) {
+            return x == 0;
+        };
+        int zeros = count_if(begin(nums), end(nums), lambda);
+        if(target > sum)
+            return 0;
+
+        if((sum-target) %2 != 0)
+            return 0;
+
+        int s1 = (sum-target)/2;
+        /*
+            You could also do like this :
+            if((sum + target)%2 != 0)
+                return 0;
+        
+            int s1 = (sum + target)/2;
+            But since, target can be negative also as per Leetcode (they have recently changed the constraints), 
+            you need to do :
+            target = abs(target); before finding s1 and the if condition above
+        */
+        return pow(2, zeros)*subsetSum(nums, s1);
+    }
+};