ADVANCED DATA STRUCTURES PROGRAM • LEVEL 20 — ADVANCED GRAPH ALGORITHMS

Find Shortest Paths in a Weighted DAG

Learn how to find shortest paths in a weighted dag using a clear C program.

AdvancedAdvanced graphsGraph optimization

PROBLEM UNDERSTANDING

Input and expected output

Sample input

No input required

Sample output

0 5 3 10 7 5

COMPLETE C PROGRAM

Complete C implementation

#include <stdio.h>

int main(void)
{
    int weight[6][6]={{0,5,3,0,0,0},{0,0,2,6,0,0},{0,0,0,7,4,2},{0,0,0,0,-1,1},{0,0,0,0,0,-2},{0,0,0,0,0,0}},order[]={0,1,2,3,4,5},distance[]={0,99,99,99,99,99};
    for(int p=0;p<6;p++){int node=order[p];for(int next=0;next<6;next++)if(weight[node][next]&&distance[node]+weight[node][next]<distance[next])distance[next]=distance[node]+weight[node][next];}
    for(int i=0;i<6;i++){printf("%d%c",distance[i],i==5?'\n':' ');}
    return 0;
}

CURRENT STEP

Select Start to walk through the important lines.

SELECTED LINE

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EXPECTED OUTPUT FOR THE SAMPLE

0 5 3 10 7 5

0%Step 0 of 0

PROGRAM EXPLANATION

Algorithm and explanation

Read the required input values.
Relax outgoing edges once in topological order, which works even with negative weights in a DAG.
Display the computed result.

Relax outgoing edges once in topological order, which works even with negative weights in a DAG.

EFFICIENCY

Time and space complexity

Time complexity

O(V + E)

Auxiliary space

O(V + E)

DEBUGGING CHECKLIST

Common mistakes

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Use the correct format specifier for every variable.

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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.