feat: add slope trick

src/7-misc/dp_opt.cpp

@@ -131,4 +131,25 @@ int main() {
     f(i, 0, n, 0, n);
   // output
   cout << dp[m][n];
-}
+}
+
+// 4. Slope Trick
+// PROBLEM: You are given the array containing n integers.
+// At one turn you can pick any element and increase or decrease it by 1.
+// The goal is the make the array strictly increasing by making the minimum possible number of operations.
+// TIME COMPLEXITY: O(n log(n))
+ll slope_trick(vector<ll> a) {
+  ll ret = 0;
+  priority_queue<ll> pq;
+  for (int i = 0; i < sz(a); i++) {
+    a[i] -= i; // Change strictly increasing condition to non-decreasing condition
+    pq.push(a[i]);
+
+    if (pq.top() > a[i]) {
+      ret += pq.top() - a[i];
+      pq.pop();
+      pq.push(a[i]);
+    }
+  }
+  return ret;
+}