【NOIP 2004】虫食算

因为一天机房都是断网状态，校内的小V评测这道题总显示Unaccept，所以下午放学后就和xiaoyimi晚上回家自习，来做一做这道题。

搜索+剪枝优化：

一开始我是顺着低位向高位填数，这么暴力在Vijos上有90分，如果NOIP能得这么多分我也甘心就写这个暴力吧

#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
int s1[27], s2[27], an[27], ans[27], n;
bool vis[27], pd = 0;
inline void dfs1(int, int);
inline void dfs3(int tmp, int delta) {
	int c = an[tmp];
	if (ans[c] == -1) {
		int num = (ans[s1[tmp]] + ans[s2[tmp]] + delta), mo = num % n;
		if (!vis[mo]) {
			vis[mo] = 1;
			ans[c] = mo;
			dfs1(tmp + 1, num / n);
			if (pd) return;
			vis[mo] = 0;
			ans[c] = -1;
		}
	} else {
		int num = (ans[s1[tmp]] + ans[s2[tmp]] + delta);
		if (ans[c] == num % n)
			dfs1(tmp + 1, num / n);
		if (pd) return;;
	}
}
inline void dfs2(int tmp, int delta) {
	int c = s2[tmp];
	if (ans[c] == -1) {
		for(int i = 0; i < n; ++i)
			if (!vis[i]) {
				vis[i] = 1;
				ans[c] = i;
				dfs3(tmp, delta);
				if (pd) return;
				vis[i] = 0;
				ans[c] = -1;
			}
	} else {
		dfs3(tmp, delta);
		if (pd) return;
	}
}
inline void dfs1(int tmp, int delta) {
	if (tmp > n){
		if (delta == 0)
			pd = 1;
		return;
	}
	int c = s1[tmp];
	if (ans[c] == -1) {
		for(int i = 0; i < n; ++i)
			if (!vis[i]) {
				vis[i] = 1;
				ans[c] = i;
				dfs2(tmp, delta);
				if (pd) return;
				vis[i] = 0;
				ans[c] = -1;
			}
	} else {
		dfs2(tmp, delta);
		if (pd) return;
	}
}
int main() {
	scanf("%d\n", &n);
	char c;
	for(int i = n; i > 0; --i) {
		c = getchar();
		s1[i] = c - 'A';
	}
	scanf("\n");
	for(int i = n; i > 0; --i) {
		c = getchar();
		s2[i] = c - 'A';
	}
	scanf("\n");
	for(int i = n; i > 0; --i) {
		c = getchar();
		an[i] = c - 'A';
	}
	for(int i = 0; i < n; ++i)
		ans[i] = -1;
	dfs1(1, 0);
	for(int i = 0; i < n; ++i)
		printf("%d ",ans[i]);
	return 0;
}

正解：先扫出字母出现的先后顺序，在这个扫出的序列上暴力，每次暴力后简单的扫一遍整个等式进行$check$，这是我写的唯一的也是最重要的剪枝，能过掉那组T掉的数据：

输入

20 
NLHFIEASBRQJOGKMDPCT 
NQGPSIIGKDMFDCBFMQSO 
PNKNTOLHEIJHFGJKHJGG

输出

18 14 0 9 15 17 7 13 12 16 1 10 4 2 8 5 11 3 6 19

AC代码：

#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
int s1[27], s2[27], an[27], ans[27], n, tb[27], tn = 0;
bool vis[27], pan = 0;
inline void mktb(int x) {
	if (!vis[x]){
		vis[x] = 1;
		tb[++tn] = x;
	}
}
inline bool pd() {
	bool p = 0;
	int delta = 0;
	for(int i = 1; i <= n; ++i){
		int a = ans[s1[i]], b = ans[s2[i]], c = ans[an[i]];
		if (a == -1 || b == -1) {
			p = 1;
		} else {
			if (c == -1) {
				if (p) {
					if (a + b == n-1)
						p = 1;
					else
						p = 0, delta = (a + b) / n;
				} else {
					p = 0;
					delta = (a + b + delta) /n;
				}
			} else {
				if (p) {
					if ((a + b) % n == c) {
						p = 0;
						delta = (a + b) / n;
					} else if ((a + b + 1) % n == c) {
						p = 0;
						delta = (a + b + 1) / n;
					} else
						return 1;
				} else {
					if ((a + b + delta) % n != c)
						return 1;
					else {
						p = 0;
						delta = (a + b + delta) / n;
					}
				}
			}
		}
	}
	if (!p && delta == 1)
		return 1;
	else
		return 0;
}
inline void dfs(int tmp) {
	if (pd())
		return;
	if (tmp > n) {
		pan = 1;
		return;
	}
	for(int i = 0; i < n; ++i)
		if (!vis[i]) {
			vis[i] = 1;
			ans[tb[tmp]] = i;
			dfs(tmp + 1);
			if (pan)
				return;
			vis[i] = 0;
			ans[tb[tmp]] = -1;
		}
}
int main() {
	scanf("%d\n", &n);
	char c;
	for(int i = n; i > 0; --i) {
		c = getchar();
		s1[i] = c - 'A';
	}
	scanf("\n");
	for(int i = n; i > 0; --i) {
		c = getchar();
		s2[i] = c - 'A';
	}
	scanf("\n");
	for(int i = n; i > 0; --i) {
		c = getchar();
		an[i] = c - 'A';
	}
	for(int i = 1; i <= n; ++i) {
		mktb(s1[i]);
		mktb(s2[i]);
		mktb(an[i]);
	}
	for(int i = 0; i < n; ++i)
		vis[i] = 0, ans[i] = -1;
	dfs(1);
	for(int i = 0; i < n; ++i)
		printf("%d ",ans[i]);
	return 0;
}

没了，，，xyx和我玩了一下午的棋盘类游戏，SG什么的真的不会啊，省选要爆0了TwT