Merge pull request #202 from DeadlySatwik/issue4

Added solution to Day-02 q001

Author: Dheeraj-06

Problems/Mathematics/Day-02/sol/Satwik_Santosh/Solution1.cpp

@@ -0,0 +1,100 @@
+/*
+Problem Statement:
+Hossam and Hazem want to count the number of interesting pairs (i, j) such that:
+1. 1 <= i, j <= n
+2. i != j
+3. |a[i] - a[j]| == max(|a[p] - a[q]|) for all 1 <= p, q <= n.
+
+---------------------------------------
+Approach:
+1.  Find the maximum and minimum values in the array. Let them be maxi and mini.
+2.  The maximum absolute difference is diff = maxi - mini.
+3.  We need to find pairs (a[i], a[j]) such that |a[i] - a[j]| = diff.
+4.  Case 1: If maxi == mini (all elements are same), then any pair (i, j) with i != j works.
+    The count is n * (n - 1).
+5.  Case 2: If maxi != mini, we need one element to be maxi and the other to be mini.
+    Count the occurrences of maxi (cntmax) and mini (cntmin).
+    The number of pairs is 2 * cntmin * cntmax (since order matters.
+
+----------------------------------------
+Time Complexity: O(n) - find min, max and their counts.
+Space Complexity: O(n) - store the input array.
+
+----------------------------------------
+Example:
+Input:
+5
+6 2 3 8 1
+
+Process:
+1. mini = 1, maxi = 8.
+2. diff = 7.
+3. cntmin (1) = 1.
+4. cntmax (8) = 1.
+5. Result = 2 * 1 * 1 = 2.
+
+Output:
+2
+*/
+
+#include <bits/stdc++.h>
+using namespace std;
+#define ll long long
+#define vll vector<ll>
+#define out(x) cout << (x) << endl
+#define outr(x)            \
+    {                      \
+        cout << x << endl; \
+        return;            \
+    }
+
+void solve()
+{
+    ll n;
+    cin >> n;
+    vll a(n);
+    int mini = INT_MAX;
+    int maxi = INT_MIN;
+
+    for (int i = 0; i < n; i++)
+    {
+        cin >> a[i];
+        if (a[i] < mini)
+            mini = a[i];
+        if (a[i] > maxi)
+            maxi = a[i];
+    }
+
+    if (mini == maxi)
+    {
+        cout <<  n * (n - 1) << endl;
+        return;
+    }
+
+    ll cntmin = 0;
+    ll cntmax = 0;
+    for (int x : a)
+    {
+        if (x == mini)
+            cntmin++;
+        if (x == maxi)
+            cntmax++;
+    }
+
+    cout << 2*cntmin*cntmax << endl;
+}
+
+int main()
+{
+    ios_base::sync_with_stdio(false);
+    cin.tie(NULL);
+    int t;
+    cin >> t;
+    while (t--)
+    {
+        solve();
+    }
+    return 0;
+}
+
+//submission link: https://codeforces.com/problemset/submission/1771/355269691