#1787. 【2017.3长乐省选集训Day8T2】朗格拉日计数

https://sjzezoj.com/submission/65357

S2OJ/1787/1787.cpp

@@ -0,0 +1,72 @@
+#include <iostream>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+const int N = 2e5 + 5;
+
+class BIT {
+  private:
+    int data[N];
+
+    static int lowbit(int x) {
+        return x & -x;
+    }
+
+  public:
+    void add(int x, int v) {
+        for (; x < N; x += lowbit(x)) {
+            data[x] += v;
+        }
+    }
+
+    int query(int x) {
+        int ans = 0;
+
+        for (; x; x -= lowbit(x)) {
+            ans += data[x];
+        }
+
+        return ans;
+    }
+};
+
+int n, a[N], pre_sm[N], suf_sm[N];
+long long ans;
+BIT bit_pre, bit_suf;
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    cin >> n;
+
+    for (int i = 1; i <= n; i++) {
+        cin >> a[i];
+    }
+
+    for (int i = 1; i <= n; i++) {
+        pre_sm[i] = bit_pre.query(a[i] - 1);
+        bit_pre.add(a[i], 1);
+    }
+
+    for (int i = n; i; i--) {
+        suf_sm[i] = bit_suf.query(a[i] - 1);
+        bit_suf.add(a[i], 1);
+    }
+
+    for (int i = 1; i <= n; i++) {
+        int pre_lg = i - pre_sm[i] - 1,
+            suf_lg = n - i - suf_sm[i];
+
+        ans += static_cast<long long>(pre_sm[i]) * suf_lg                                                            // 123
+             + static_cast<long long>(pre_lg) * (pre_lg - 1) / 2 - static_cast<long long>(pre_lg) * suf_sm[i]        // 231 = **1 - 321
+             + static_cast<long long>(suf_sm[i]) * (suf_sm[i] - 1) / 2 - static_cast<long long>(pre_lg) * suf_sm[i]  // 312 = 3** - 321
+            ;
+    }
+
+    cout << ans << endl;
+
+    return 0;
+}