ADVANCED DATA STRUCTURES PROGRAM • LEVEL 20 — ADVANCED GRAPH ALGORITHMS
Find Maximum Bipartite Matching
Learn how to find maximum bipartite matching using a clear C program.
PROBLEM UNDERSTANDING
Input and expected output
Sample input
No input required
Sample output
Matching size = 4
COMPLETE C PROGRAM
Complete C implementation
#include <stdio.h>
int augment(int left,int graph[4][4],int seen[],int matched[]){for(int right=0;right<4;right++)if(graph[left][right]&&!seen[right]){seen[right]=1;if(matched[right]<0||augment(matched[right],graph,seen,matched)){matched[right]=left;return 1;}}return 0;}
int main(void)
{
int graph[4][4]={{1,1,0,0},{0,1,1,0},{0,0,1,1},{1,0,0,0}},matched[4]={-1,-1,-1,-1},answer=0;
for(int left=0;left<4;left++){int seen[4]={0};answer+=augment(left,graph,seen,matched);}printf("Matching size = %d\n",answer);return 0;
}CURRENT STEP
Select Start to walk through the important lines.
SELECTED LINE
No line selected
EXPECTED OUTPUT FOR THE SAMPLE
Matching size = 4
Step 0 of 0
PROGRAM EXPLANATION
Algorithm and explanation
- Read the required input values.
- For every left vertex, search an augmenting path that can reroute earlier matches.
- Display the computed result.
For every left vertex, search an augmenting path that can reroute earlier matches.
EFFICIENCY
Time and space complexity
Time complexity
O(VE)
Auxiliary space
O(V + E)
DEBUGGING CHECKLIST
Common mistakes
Check this
Use the correct format specifier for every variable.
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Initialize variables before using their values.
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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.