POJ 1704 Georgia and Bob (Tiered Nim game), pojnim

POJ 1704 Georgia and Bob (Tiered Nim game), pojnim

Time Limit:1000 MS   Memory Limit:10000 K Total Submissions:11357   Accepted:3749 Description Georgia and Bob decide to play a self-defined Ted game. they draw a row of grids on paper, number the grids from left to right by 1, 2, 3 ,..., and place N chessmen on different grids, as shown in the following figure for example: Georgia and Bob move the chessmen in turn. every time a player will choose a chessman, and move it to the left without going over any other chessmen or keep ss the left edge. the player can freely choose number of steps the chessman moves, with the constraint that the chessman must be moved at least ONE step and one grid can at most contains ONE single chessman. the player who cannot make a move loses the game. Georgia always plays first since "Lady first ". suppose that Georgia and Bob both do their best in the game, I. e ., if one of them knows a way to win the game, he or she will be able to carry it out. Given the initial positions of the n chessmen, can you predict who will finally win the game? Input The first line of the input contains a single integer T (1 <= T <= 20), the number of test cases. then T cases follow. each test case contains two lines. the first line consists of one integer N (1 <= N <= 1000), indicating the number of chessmen. the second line contains N different integers P1, P2... pn (1 <= Pi <= 10000), which are the initial positions of the n chessmen. Output For each test case, prints a single line, "Georgia will win", if Georgia will win the game; "Bob will win", if Bob will win the game; otherwise 'Not sure '. Sample Input 231 2 381 5 6 7 9 12 14 17 Sample Output Bob will winGeorgia will win Source POJ Monthly -- 2004.07.18

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This practice is really 666. I don't know how std came up.

First, we come up with a mandatory defeat: that is, there are only two vertices that are adjacent to each other.

Then we can sort all vertices and bind them to each other. In this way, if A moves the first vertex, B can move the second vertex to the same number of steps.

In this way, the order problem is solved.

Then we will consider how to solve the game problem.

Here is a fairy operation

Take the distance between two points as a pile of stones, and then ask Nim.

 

# Include <cstdio> # include <algorithm> # include <cstring> using namespace std; const int MAXN = 1e4 + 10, INF = 1e9 + 10; inline int read () {char c = getchar (); int x = 0, f = 1; while (c <'0' | c> '9 ') {if (c = '-') f =-1; c = getchar () ;}while (c> = '0' & c <= '9 ') {x = x * 10 + c-'0'; c = getchar ();} return x * f;} int a [MAXN]; int main () {# ifdef WIN32 freopen (". in "," r ", stdin); # else # endif int QwQ = read (); while (QwQ --) {int N = read (); for (int I = 1; I <= N; I ++) a [I] = read (); sort (a + 1, a + N + 1 ); int ans; if (N & 1) // odd {ans = a [1]-1; for (int I = 3; I <= N; I + = 2) ans = ans ^ (a [I]-a [I-1]-1);} else {ans = a [2]-a [1]-1; for (int I = 4; I <= N; I + = 2) ans = ans ^ (a [I]-a [I-1]-1);} if (ans) printf ("Georgia will win \ n"); else printf ("Bob will win \ n");} return 0 ;}