Ultraviolet A 12163-addition-subtraction game (game)

Ultraviolet A 12163-addition-subtraction game

Question Link

Given a directed graph, each node has a ki, and each time the game gives each node A starting value, a position is selected in turn each time, so that it can reach the next node and the value is positive, set the value to-1, select K [I] + 1 at the surrounding node, and then ask who cannot perform the operation or lose. Then, ask the game to win or lose each time.

Idea: first construct the SG function on the graph. Since each node connects up to 15 nodes, You can enumerate which nodes are added with an odd number of times 1, because the even number is equal to no effect, (The first step is to take the second step without any impact), use a State compression, then you can find the SG function based on the state transition, and then each round of the game only needs to consider the NIM and

Code:

#include <cstdio>#include <cstring>#include <algorithm>#include <vector>#include <map>using namespace std;const int MAXS = (1<<15);const int N = 105;int t, n, m, k[N], sg[N], cnt[MAXS];vector<int> g[N];int bitcount(int x) {    int ans = 0;    while (x) {ans += (x&1);x >>= 1;    }    return ans;}int dfs(int u) {    if (sg[u] != -1) return sg[u];    if (g[u].size() == 0) return sg[u] = 0;    for (int i = 0; i < g[u].size(); i++)dfs(g[u][i]);    int maxs = (1<<g[u].size());    map<int, int> vis;    for (int i = 0; i < maxs; i++) {if (cnt[i] > k[u]) continue;if ((cnt[i]^k[u])&1) continue;int x = 0;for (int j = 0; j < g[u].size(); j++) {    if (i&(1<<j))x ^= sg[g[u][j]];}vis[x] = 1;    }    for (int i = 0; ; i++)if (!vis.count(i))    return sg[u] = i;}void getsg() {    memset(sg, -1, sizeof(sg));    for (int i = 0; i < n; i++)dfs(i);}int main() {    for (int i = 0; i < MAXS; i++)cnt[i] = bitcount(i);    int cas = 0;    scanf("%d", &t);    while (t--) {scanf("%d%d", &n, &m);for (int i = 0; i < n; i++)    g[i].clear();int u, v;while (m--) {    scanf("%d%d", &u, &v);    g[u].push_back(v);}for (int i = 0; i < n; i++)    scanf("%d", &k[i]);getsg();scanf("%d", &m);printf("Game#%d:\n", ++cas);int rou = 0;while (m--) {    int sum = 0, x;    for (int i = 0; i < n; i++) {scanf("%d", &x);if (x&1) sum ^= sg[i];    }    printf("Round#%d: %s\n", ++rou, sum == 0 ? "LOSING" : "WINNING");}printf("\n");    }    return 0;}