CountTriplets.cpp

DSA/Cpp/CountTriplets.cpp

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+
+// C++ program to count Triplets such that at
+// least one of the numbers can be written
+// as sum of the other two
+#include<bits/stdc++.h>
+using namespace std;
+
+    // Function to count the number of ways to choose the triples..
+    // 
+    int countWays(int arr[], int n)
+    {
+        // compute the max value in the array and create frequency array of size max_val + 1.
+
+        // We can also use HashMap to store frequencies. We have used an array to keep remaining code simple.
+        int max_val = 0;
+        for (int i = 0; i < n; i++)
+            max_val = max(max_val, arr[i]);
+        int freq[max_val + 1]={0};
+        for (int i = 0; i < n; i++)
+            freq[arr[i]]++;
+
+        int ans = 0; // stores the number of ways
+
+        // Case 1: 0, 0, 0
+        ans += freq[0] * (freq[0] - 1) * (freq[0] - 2) / 6;
+
+        // Case 2: 0, x, x
+        for (int i = 1; i <= max_val; i++)
+            ans += freq[0] * freq[i] * (freq[i] - 1) / 2;
+
+        // Case 3: x, x, 2*x
+        for (int i = 1; 2 * i <= max_val; i++)
+            ans += freq[i] * (freq[i] - 1) / 2 * freq[2 * i];
+
+        // Case 4: x, y, x + y
+        // iterate through all pairs (x, y)
+        for (int i = 1; i <= max_val; i++) {
+            for (int j = i + 1; i + j <= max_val; j++)
+                ans += freq[i] * freq[j] * freq[i + j];
+        }
+
+        return ans;
+    }
+
+    int main()
+    {
+      int n;
+      cin>>n;
+      int arr[n];
+      for(int i=0;i<n;i++){
+      cin>>arr[i];
+      }
+        cout<<(countWays(arr, n));
+        return 0;
+    }