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Time Complexity Calculation
By I_lOVE_ROMAN, history, 14 months ago, In English

For this Problem

1829E - The Lakes

The solution is written in O(n*m)

But How it is possible if there is recursion calls inside the nested solution.

Solution in tutorial is:

https://mirror.codeforces.com/blog/entry/116108 (Problem E)

Please someone help me understand the time complexity?Shouldn't it be O(n*m*n*m).I know we are not checking same grid twice.

Please someone help me.

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14 months ago, # |
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each cell will be visited at most once

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    14 months ago, # ^ |
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    I know that.But I am not understanding if there is recursion calls in that O(n*m) nested loop.Shouldn't it be O(n*m*recursioncalls).

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      14 months ago, # ^ |
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      No. Loop counts do not matter. Its all about sum. Think of it this way.

      """Given a tree with n nodes and a value for each node ai, calculate the sum of values of their children for each node.

      Take a look at this pseudocode.

      vector<int> ans(n+1);

for (int i=1;i<=n;i++) {
    for (int neighbor : edges[node]) {
        if (neighbor!=parent) {
            ans[node]+=a[neighbor];
        }
    }
}

      This piece of code has n loops and it seems like every node can have upto n neighbors so its O(N^2) right? No. Because the sum of neighbor counts of each node is fixed and is linear. So it is O(N).

      The same logic can be applied here.

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