code(java) : Solved que-1 of day-4 (Monocarp and Bracket Sequence)

Problems/Data-structures/Day-04/sol/dwivediprashant/Solution1.java

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+/*
+Problem Summary:
+- Given a partially known regular bracket sequence.
+- Odd positions are missing ('_'), even positions are fixed.
+- Restore missing brackets to form a valid RBS with minimum total cost.
+- Cost = sum of distances between matched bracket pairs.
+
+Key Ideas:
+- Valid RBS requires balance never goes negative.
+- To minimize cost, close brackets as early as possible.
+- Only open a bracket when forced.
+
+Greedy Strategy:
+- Traverse left to right.
+- Maintain current balance and a stack of '(' positions.
+- At '_' positions:
+  • If balance == 0 → must place '('
+  • Else → place ')'
+- At fixed positions:
+  • Follow given '(' or ')'
+
+Cost Calculation:
+- On encountering ')', pop matching '(' from stack.
+- Add (currentIndex - openIndex) to total cost.
+
+Complexity:
+- Time: O(n) per test case
+- Space: O(n)
+
+Problem submission link:----------------------------------------------------------------------------------
+https://codeforces.com/contest/1997/submission/355801157
+*/
+
+import java.io.*;
+import java.util.*;
+
+public class Solution1 {
+    public static void main(String[] args) throws Exception {
+        FastScanner fs = new FastScanner(System.in);
+        StringBuilder out = new StringBuilder();
+
+        int t = fs.nextInt();
+        while (t-- > 0) {
+            int n = fs.nextInt();
+            char[] s = fs.next().toCharArray();
+
+            int balance = 0;
+            long cost = 0;
+            Deque<Integer> stack = new ArrayDeque<>();
+
+            for (int i = 0; i < n; i++) {
+                if ((i & 1) == 0) {
+                    if (balance == 0) {
+                        stack.push(i);
+                        balance++;
+                    } else {
+                        balance--;
+                        int openPos = stack.pop();
+                        cost += i - openPos;
+                    }
+                } else {
+                    if (s[i] == '(') {
+                        stack.push(i);
+                        balance++;
+                    } else {
+                        balance--;
+                        int openPos = stack.pop();
+                        cost += i - openPos;
+                    }
+                }
+            }
+
+            out.append(cost).append('\n');
+        }
+
+        System.out.print(out);
+    }
+
+    static class FastScanner {
+        private final byte[] buffer = new byte[1 << 16];
+        private int ptr = 0, len = 0;
+        private final InputStream in;
+
+        FastScanner(InputStream in) {
+            this.in = in;
+        }
+
+        private int read() throws IOException {
+            if (ptr >= len) {
+                len = in.read(buffer);
+                ptr = 0;
+                if (len <= 0) return -1;
+            }
+            return buffer[ptr++];
+        }
+
+        int nextInt() throws IOException {
+            int c;
+            do {
+                c = read();
+            } while (c <= ' ');
+            boolean neg = false;
+            if (c == '-') {
+                neg = true;
+                c = read();
+            }
+            int val = 0;
+            while (c > ' ') {
+                val = val * 10 + (c - '0');
+                c = read();
+            }
+            return neg ? -val : val;
+        }
+
+        String next() throws IOException {
+            int c;
+            do {
+                c = read();
+            } while (c <= ' ');
+            StringBuilder sb = new StringBuilder();
+            while (c > ' ') {
+                sb.append((char) c);
+                c = read();
+            }
+            return sb.toString();
+        }
+    }
+}