Police Chase-CSES graph Section

(https://cses.fi/problemset/task/1695/) .This problem involves minimum no of edges to be removed in order to prevent thief from reaching vertex 1 to n.
Actually i am stuck at the part where we have to find the edges.
From what i was doing i thought total edges to be removed would be equal to total augmenting paths but unable to find which edges . please help @carre @ssjgz @everule1 @ssrivastava990

anybody??

https://cp-algorithms.com/graph/edmonds_karp.html#toc-tgt-5

thanks but i have seen that can u elaborate more.
Actually i am taking capacity of each edge as 1 but when i am finding any augmenting path i am decreasing the capacity by one due to which that path cannot be used more.But how to find which particular edge on that path is critical edge

Well, you just have to use DFS from 1, on unused edges. All edges between the nodes you visit on this dfs, and the ones you dont, are the cut edges.

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but how will that give the minimum
consider
1 2
1 3
2 4
4 5
4 6
here we need to remove only 2-4 how would the above will give this

It will give you 1 -> 2 as the only edge which is also correct.

sorry there was also an edge between 3 and 2
thanks for help till now as i am new to flows please can u tell what changes should to my code .
Link to code https://cses.fi/paste/049adcd6790c036f11c565/

if u want explanation of anyhting in the code i will tell u . Basically it is edmond karp only

What I see is you are finding a path, and then breaking the last edge of the path. That is the same as removing k edges from node n. That is not necessarily even a cut. Construct the cut how I described it.

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Thanks i will try to implement can u explain the above more elaboratly or with the help of a good example