ADVANCED DATA STRUCTURES PROGRAM • LEVEL 17 — ADVANCED HEAPS
Maintain a Running Median with Two Heaps
Learn how to maintain a running median with two heaps using a clear C program.
PROBLEM UNDERSTANDING
Input and expected output
Sample input
No input required
Sample output
5.0 10.0 5.0 4.0
COMPLETE C PROGRAM
Complete C implementation
#include <stdio.h>
void push_max(int heap[], int *count, int value) { int i = (*count)++; heap[i] = value; while (i && heap[(i-1)/2] < heap[i]) { int t=heap[i]; heap[i]=heap[(i-1)/2]; heap[(i-1)/2]=t; i=(i-1)/2; } }
void push_min(int heap[], int *count, int value) { int i = (*count)++; heap[i] = value; while (i && heap[(i-1)/2] > heap[i]) { int t=heap[i]; heap[i]=heap[(i-1)/2]; heap[(i-1)/2]=t; i=(i-1)/2; } }
int pop_max(int heap[], int *count) { int answer=heap[0]; heap[0]=heap[--(*count)]; for(int i=0;;){int l=2*i+1,r=l+1,b=i;if(l<*count&&heap[l]>heap[b])b=l;if(r<*count&&heap[r]>heap[b])b=r;if(b==i)break;int t=heap[i];heap[i]=heap[b];heap[b]=t;i=b;}return answer; }
int pop_min(int heap[], int *count) { int answer=heap[0]; heap[0]=heap[--(*count)]; for(int i=0;;){int l=2*i+1,r=l+1,b=i;if(l<*count&&heap[l]<heap[b])b=l;if(r<*count&&heap[r]<heap[b])b=r;if(b==i)break;int t=heap[i];heap[i]=heap[b];heap[b]=t;i=b;}return answer; }
void add_value(int value,int lower[],int *lc,int upper[],int *uc){if(!*lc||value<=lower[0])push_max(lower,lc,value);else push_min(upper,uc,value);if(*lc>*uc+1)push_min(upper,uc,pop_max(lower,lc));else if(*uc>*lc)push_max(lower,lc,pop_min(upper,uc));}
int main(void)
{
int stream[] = {5, 15, 1, 3}, lower[10], upper[10], lower_count = 0, upper_count = 0;
for (int i = 0; i < 4; i++) { add_value(stream[i], lower, &lower_count, upper, &upper_count); if (lower_count == upper_count) printf("%.1f", (lower[0] + upper[0]) / 2.0); else printf("%.1f", lower[0] * 1.0); printf("%c", i == 3 ? '\n' : ' '); }
return 0;
}CURRENT STEP
SELECTED LINE
EXPECTED OUTPUT FOR THE SAMPLE
5.0 10.0 5.0 4.0
Step 0 of 0
PROGRAM EXPLANATION
Algorithm and explanation
- Read the required input values.
- Balance a max heap for the lower half with a min heap for the upper half.
- Display the computed result.
Balance a max heap for the lower half with a min heap for the upper half.
EFFICIENCY
Time and space complexity
Time complexity
O(log n) per value
Auxiliary space
O(n)
DEBUGGING CHECKLIST
Common mistakes
Check this
Use the correct format specifier for every variable.
Check this
Initialize variables before using their values.
Check this
Check braces, semicolons and input order carefully.
Try it yourself
Practice: Run the program with the sample input, predict its output, and then test one boundary case of your own.
