### ganesh_6's blog

By ganesh_6, history, 15 months ago,

I know Nim Game, Nim Sum (xor sum) and the theorem, lemmas behind that. Also, I solved the https://cses.fi/problemset/task/1730 After solving that, I moved to https://cses.fi/problemset/task/1098 I could not figure out the solution. So, I found one solution online and could not figure out the nuances behind the working of the algorithm. I can see that he has used a[i]%4 which is used for one pile game to find out the winner. However, in this case he combined Nim Game 1 algorithm and 1 pile game algorithm to derive the solution. Please explain the reason behind working of this?

#include<bits/stdc++.h>
using namespace std;

string solve(int n, vector<int> heaps){
for(int i=0;i<n;i++)
{
heaps[i]%=4;
}
int xr=0;
for(int i=0;i<n;i++)
{
xr^=heaps[i];
}
if(xr)
{
return "first";
}
else{
return "second";
}
}


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 » 15 months ago, # |   0 tl;dr: The terms for you to google are Grundy numbers and the Sprague-Grundy theorem.I wrote a blog explaining this a few years ago: https://codeforces.com/blog/entry/66040Jump to "Extension on Nim and Grundy Numbers"I do intend to rewrite this blog sometime this year since my college-level writing is not the best. But if you find it unsatisfactory, you can just google for other articles using the above keywords