Let G(V, E) an undirected graph with positive edge weights. Dijkstra's single-source shortest path algorithm can be implemented using the binary heap data structure with time complexity:

Consider the following C - function:

double foo(int n){
 int i;
 double sum;
 if(n == 0) return 1.0;
 sum = 0.0;
 for (i = 0; i < n; i++){
  sum += foo(i);
 }
 return sum;
}

The space complexity of the above function is:

Consider the following C - function:

double foo(int n){
 int i;
 double sum;
 if(n == 0) return 1.0;
 sum = 0.0;
 for (i = 0; i < n; i++){
  sum += foo(i);
 }
 return sum;
}

Suppose we modify the above function foo() and store the values of foo(i), $$0 \le i \le n$$, as and when they are computed. With this modification, the time complexity for function foo() is significantly reduced. The space complexity of the modified function would be:

A Priority-Queue is implemented as a Max-Heap. Initially, it has 5 elements. The level-order traversal of the heap is given below:
10, 8, 5, 3, 2
Two new elements '1' and '7' are inserted in the heap in that order, The level order traversal of the heap after the insertion of the elements is: