Given an infinite stream of integers, find the k’th largest element at any point of time. It may be assumed that 1 <= k <= n.

Input: stream[] = {10, 20, 11, 70, 50, 40, 100, 5, ...} k = 3 Output: {_, _, 10, 11, 20, 40, 50, 50, ...}

Extra space allowed is O(k).

The idea is to use min heap.

1) Store first k elements in min heap.

2) For every element from (k+1)-th to n-th, do following.

……a) Print root of heap.

……b) If current element is more than root of heap, pop root and insert

// CPP program to find k-th largest element in a // stream after every insertion. #include <bits/stdc++.h> using namespace std; int kthLargest(int stream[], int n, int k) { // Create a min heap and store first k-1 elements // of stream into priority_queue<int, vector<int>, greater<int> > pq; // Push first k elements and print "_" (k-1) times for (int i=0; i<k-1; i++) { pq.push(stream[i]); cout << "_ "; } pq.push(stream[k-1]); for (int i=k; i<n; i++) { // We must insert last element before we // decide last k-th largest output. if (i < n-1) cout << pq.top() << " "; if (stream[i] > pq.top()) { pq.pop(); pq.push(stream[i]); } } // Print last k-th largest element (after // (inserting last element) cout << pq.top(); } // Driver code int main() { int arr[] = {10, 20, 11, 70, 50, 40, 100, 55}; int k = 3; int n = sizeof(arr)/sizeof(arr[0]); kthLargest(arr, n, k); return 0; }

**Output:**

_ _ 10 11 20 40 55

If stream contains elements of non-primitive types, we may define our own compactor function and create a priority_queue accordingly.

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