code(java) : solved que 2 of day 9 on codeforces

Author: dwivediprashant

Problems/Data-structures/Day-09/sol/prashant_dwivedi/Solution2.java

@@ -0,0 +1,138 @@
+// 1. Problem Statement -------------------------------------------------
+/*
+Given an array of n distinct integers.
+Define the weakness as the number of triplets (i, j, k) such that:
+i < j < k and a[i] > a[j] > a[k].
+
+You need to count all such decreasing triplets.
+Constraints are large, so brute force is not allowed.
+*/
+
+// 2. Approach -----------------------------------------------------------
+/*
+Fix j as the middle element.
+For each j:
+- Count how many elements greater than a[j] exist on its left
+- Count how many elements smaller than a[j] exist on its right
+
+Each combination forms a valid triplet.
+Fenwick Tree (Binary Indexed Tree) is used to compute counts efficiently.
+Coordinate compression is applied because values are large.
+*/
+
+// 3. Complexity ---------------------------------------------------------
+/*
+Time Complexity: O(n log n)
+Space Complexity: O(n)
+*/
+
+// 4. Problem Submission Link --------------------------------------------
+/*
+https://codeforces.com/contest/61/submission/356384283
+*/
+
+import java.io.*;
+import java.util.*;
+
+public class Solution2 {
+
+    static class Fenwick {
+        int n;
+        long[] bit;
+
+        Fenwick(int n) {
+            this.n = n;
+            bit = new long[n + 1];
+        }
+
+        void update(int i, long v) {
+            while (i <= n) {
+                bit[i] += v;
+                i += i & -i;
+            }
+        }
+
+        long query(int i) {
+            long s = 0;
+            while (i > 0) {
+                s += bit[i];
+                i -= i & -i;
+            }
+            return s;
+        }
+
+        long range(int l, int r) {
+            return query(r) - query(l - 1);
+        }
+    }
+
+    public static void main(String[] args) throws Exception {
+        FastScanner fs = new FastScanner(System.in);
+
+        int n = fs.nextInt();
+        int[] a = new int[n];
+        for (int i = 0; i < n; i++) a[i] = fs.nextInt();
+
+        int[] b = a.clone();
+        Arrays.sort(b);
+        Map<Integer, Integer> map = new HashMap<>(n);
+        int id = 1;
+        for (int x : b) if (!map.containsKey(x)) map.put(x, id++);
+
+        int[] c = new int[n];
+        for (int i = 0; i < n; i++) c[i] = map.get(a[i]);
+
+        long[] L = new long[n];
+        long[] R = new long[n];
+
+        Fenwick fw = new Fenwick(n);
+        for (int i = 0; i < n; i++) {
+            L[i] = fw.range(c[i] + 1, n);
+            fw.update(c[i], 1);
+        }
+
+        fw = new Fenwick(n);
+        for (int i = n - 1; i >= 0; i--) {
+            R[i] = fw.query(c[i] - 1);
+            fw.update(c[i], 1);
+        }
+
+        long ans = 0;
+        for (int i = 0; i < n; i++) ans += L[i] * R[i];
+
+        System.out.println(ans);
+    }
+
+    static class FastScanner {
+        private final byte[] buf = new byte[1 << 16];
+        private int idx = 0, size = 0;
+        private final InputStream in;
+
+        FastScanner(InputStream in) {
+            this.in = in;
+        }
+
+        int read() throws IOException {
+            if (idx >= size) {
+                size = in.read(buf);
+                idx = 0;
+                if (size <= 0) return -1;
+            }
+            return buf[idx++];
+        }
+
+        int nextInt() throws IOException {
+            int c, s = 1, x = 0;
+            do c = read(); while (c <= ' ');
+            if (c == '-') {
+                s = -1;
+                c = read();
+            }
+            while (c > ' ') {
+                x = x * 10 + (c - '0');
+                c = read();
+            }
+            return x * s;
+        }
+    }
+}