P1092 [NOIP2004 提高组] 虫食算

https://www.luogu.com.cn/record/85702831

Luogu/P1092/P1092.cpp

@@ -0,0 +1,115 @@
+#include <iostream>
+#include <map>
+#include <set>
+#include <string>
+#include <vector>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+const int N = 30;
+
+int n;
+bool vis[N];
+std::string s1, s2, s3;
+std::map<char, int> map;
+std::vector<char> chs;
+
+bool check() {
+    for (int i = n - 1; i >= 0; i--) {
+        if (map[s1[i]] != -1 && map[s2[i]] != -1 && map[s3[i]] != -1) {
+            if ((map[s1[i]] + map[s2[i]]) % n != map[s3[i]]
+                && (map[s1[i]] + map[s2[i]] + 1) % n != map[s3[i]]) {
+                return false;
+            }
+        } else if (map[s1[i]] != -1 && map[s2[i]] != -1) {  // map[s3[i]] == -1
+            if (vis[(map[s1[i]] + map[s2[i]]) % n]
+                && vis[(map[s1[i]] + map[s2[i]] + 1) % n]) {
+                return false;
+            }
+        } else if (map[s1[i]] != -1 && map[s3[i]] != -1) {  // map[s2[i]] == -1
+            if (vis[(map[s3[i]] - map[s1[i]] + n) % n]
+                && vis[(map[s3[i]] - map[s1[i]] - 1 + n) % n]) {
+                return false;
+            }
+        } else if (map[s2[i]] != -1 && map[s3[i]] != -1) {  // map[s1[i]] == -1
+            if (vis[(map[s3[i]] - map[s2[i]] + n) % n]
+                && vis[(map[s3[i]] - map[s2[i]] - 1 + n) % n]) {
+                return false;
+            }
+        }
+    }
+
+    return true;
+}
+
+bool check_ans() {
+    int x = 0;
+
+    for (int i = n - 1; i >= 0; i--) {
+        if ((x + map[s1[i]] + map[s2[i]]) % n != map[s3[i]]) {
+            return false;
+        }
+
+        x = (x + map[s1[i]] + map[s2[i]]) / n;
+    }
+
+    return x == 0;
+}
+
+void dfs(int x) {
+    if (x == n) {
+        if (check_ans()) {
+            for (auto o : map) {
+                cout << o.second << ' ';
+            }
+
+            cout << endl;
+
+            exit(0);
+        }
+
+        return;
+    }
+
+    for (int i = n - 1; i >= 0; i--) {
+        if (vis[i]) continue;
+
+        vis[i] = true;
+        map[chs[x]] = i;
+
+        if (check()) dfs(x + 1);
+
+        map[chs[x]] = -1;
+        vis[i] = false;
+    }
+}
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    cin >> n >> s1 >> s2 >> s3;
+
+    for (int i = n - 1; i >= 0; i--) {
+        if (!map.count(s1[i])) {
+            map[s1[i]] = -1;
+            chs.emplace_back(s1[i]);
+        }
+
+        if (!map.count(s2[i])) {
+            map[s2[i]] = -1;
+            chs.emplace_back(s2[i]);
+        }
+
+        if (!map.count(s3[i])) {
+            map[s3[i]] = -1;
+            chs.emplace_back(s3[i]);
+        }
+    }
+
+    dfs(0);
+
+    return 0;
+}