P1850 [NOIP2016 提高组] 换教室

https://www.luogu.com.cn/record/95239669

Luogu/P1850/P1850.cpp

@@ -0,0 +1,92 @@
+#include <iostream>
+#include <algorithm>
+#include <cstring>
+#include <iomanip>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+const int N = 2005,
+          V = 305;
+
+int n, m, v, e, c[N], d[N], g[V][V];
+double p[N], f[N][N][2], ans = 1e9;
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    cin >> n >> m >> v >> e;
+
+    memset(g, 0x3f, sizeof(g));
+
+    for (int i = 1; i <= n; i++) {
+        cin >> c[i];
+    }
+
+    for (int i = 1; i <= n; i++) {
+        cin >> d[i];
+    }
+
+    for (int i = 1; i <= n; i++) {
+        cin >> p[i];
+    }
+
+    for (int i = 1; i <= v; i++) {
+        g[i][i] = 0;
+    }
+
+    for (int i = 1, a, b, w; i <= e; i++) {
+        cin >> a >> b >> w;
+
+        g[a][b] = g[b][a] = std::min(g[a][b], w);
+    }
+
+    for (int k = 1; k <= v; k++) {
+        for (int i = 1; i <= v; i++) {
+            for (int j = 1; j <= v; j++) {
+                g[i][j] = std::min(g[i][j], g[i][k] + g[k][j]);
+            }
+        }
+    }
+
+    for (int i = 1; i <= n; i++) {
+        for (int j = 0; j <= m; j++) {
+            f[i][j][0] = f[i][j][1] = 1e9;
+        }
+    }
+
+    f[1][0][0] = f[1][1][1] = 0;
+
+    for (int i = 2; i <= n; i++) {
+        for (int j = 0; j <= std::min(m, i); j++) {
+            f[i][j][0] = std::min(
+                f[i - 1][j][0]
+                    + g[c[i - 1]][c[i]],
+                f[i - 1][j][1]
+                    + p[i - 1] * g[d[i - 1]][c[i]]
+                    + (1.0 - p[i - 1]) * g[c[i - 1]][c[i]]);
+
+            if (j) {
+                f[i][j][1] = std::min(
+                    f[i - 1][j - 1][0]
+                        + p[i] * g[c[i - 1]][d[i]]
+                        + (1.0 - p[i]) * g[c[i - 1]][c[i]],
+                    f[i - 1][j - 1][1]
+                        + p[i - 1] * p[i] * g[d[i - 1]][d[i]]
+                        + (1.0 - p[i - 1]) * p[i] * g[c[i - 1]][d[i]]
+                        + p[i - 1] * (1.0 - p[i]) * g[d[i - 1]][c[i]]
+                        + (1.0 - p[i - 1]) * (1.0 - p[i]) * g[c[i - 1]][c[i]]);
+            }
+        }
+    }
+
+    for (int i = 0; i <= m; i++) {
+        ans = std::min({ans, f[n][i][0], f[n][i][1]});
+    }
+
+    cout << std::fixed << std::setprecision(2) << ans << endl;
+
+    return 0;
+}