POJ 1704 Georgia and Bob (ladder game + proof)

POJ 1704 Topics Link

There are the following theorems about ladder game :

Treat all odd steps as n heap stones, make nim, move stones from odd heaps to even heaps as take stones, similarly, when the XOR value is not 0 (self-interest), the initiator will win.

Proof of theorem See this blog: http://blog.csdn.net/kk303/article/details/6692506

The following is the AC code for POJ 1704:

//The pawn can only go left (the leftmost line), can walk any Dogger (>=1)//and the pawn cannot cross the pawn in front of it (the pawn on its left)//each of the squares has a maximum of one piece, indicating that the piece can not go to the position of another piece//convert to Nim: Put the input position in order to calculate the spacing between two adjacent points, the spacing is the maximum number of steps to walk K, as a bunch of k stones//then iterate from the largest position (because of the right), calculating the Nim XOR value of the odd heap#include <iostream>#include<cstdio>#include<algorithm>using namespacestd;intMain () {intT; scanf ("%d",&t);  while(t--)    {        intsum=0, n,a[1005],b[1005]; scanf ("%d",&N); a[0]=0;  for(intI=1; i<=n;i++) scanf ("%d",&A[i]); Sort (A,a+n+1);  for(intI=1; i<=n;i++) B[i]=a[i]-a[i-1]-1; intCnt=0;  for(intI=n;i>0; i--) {CNT++; if(cnt&1) Sum^=B[i]; }        if(sum) printf ("Georgia'll win\n"); Elseprintf"Bob would win\n"); }    return 0;}

POJ 1704 Georgia and Bob (ladder game + proof)