P1121 环状最大两段子段和

https://www.luogu.com.cn/record/84279869

Luogu/P1121/P1121.cpp

@@ -0,0 +1,80 @@
+#include <iostream>
+#include <algorithm>
+#include <limits>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+const int N = 2e5 + 5;
+
+int n, a[N];
+bool flag = true;
+long long sum, s_max[N], s_min[N], f_max[N], f_min[N], g_max[N], g_min[N], ans;
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    cin >> n;
+
+    for (int i = 1; i <= n; i++) {
+        cin >> a[i];
+
+        sum += a[i];
+        flag &= a[i] < 0;
+    }
+
+    if (flag) {
+        std::sort(a + 1, a + 1 + n);
+
+        cout << a[n] + a[n - 1] << endl;
+
+        exit(0);
+    }
+
+    ans = std::numeric_limits<int>::min();
+    std::fill_n(s_max, N, std::numeric_limits<int>::min());
+    std::fill_n(s_min, N, std::numeric_limits<int>::max());
+    std::fill_n(f_max, N, std::numeric_limits<int>::min());
+    std::fill_n(f_min, N, std::numeric_limits<int>::max());
+    std::fill_n(g_max, N, std::numeric_limits<int>::min());
+    std::fill_n(g_min, N, std::numeric_limits<int>::max());
+
+    for (int i = 1; i <= n; i++) {
+        s_max[i] = std::max(s_max[i - 1] + a[i], static_cast<long long>(a[i]));
+        s_min[i] = std::min(s_min[i - 1] + a[i], static_cast<long long>(a[i]));
+
+        f_max[i] = std::max(f_max[i - 1], s_max[i]);
+        f_min[i] = std::min(f_min[i - 1], s_min[i]);
+    }
+
+    std::fill_n(s_max, N, std::numeric_limits<int>::min());
+    std::fill_n(s_min, N, std::numeric_limits<int>::max());
+
+    for (int i = n; i; i--) {
+        s_max[i] = std::max(s_max[i + 1] + a[i], static_cast<long long>(a[i]));
+        s_min[i] = std::min(s_min[i + 1] + a[i], static_cast<long long>(a[i]));
+
+        g_max[i] = std::max(g_max[i + 1], s_min[i]);
+        g_min[i] = std::min(g_min[i + 1], s_min[i]);
+    }
+
+    std::cerr << ans << endl;
+
+    // 不跨环
+    for (int i = 1; i < n; i++) {
+        ans = std::max(ans, f_max[i] + g_max[i + 1]);
+    }
+
+    std::cerr << ans << endl;
+
+    // 跨环
+    for (int i = 1; i < n; i++) {
+        ans = std::max(ans, sum - (f_min[i] + g_min[i + 1]));
+    }
+
+    cout << ans << endl;
+
+    return 0;
+}