[Fix #109] Added Solution for Easy Difference Array Problem (CSES 1651)

algos/range_queries/DifferenceArray/soln/Krishna200608/Solution1.cpp

@@ -0,0 +1,99 @@
+/**
+ * Problem: Range Update Queries (CSES 1651)
+ * Link: https://cses.fi/problemset/task/1651/
+ * Difficulty: Easy
+ *
+ * -------------------------
+ * Short Problem Statement
+ * -------------------------
+ * You are given an array of N integers and Q queries of two types:
+ * 1. Add a value `u` to all elements in the range [a, b].
+ * 2. Query the current value at a specific position `k`.
+ *
+ * -------------------------
+ * Approach (Difference Array + Fenwick Tree)
+ * -------------------------
+ * A plain Difference Array supports range updates in O(1),
+ * but retrieving a single element requires computing a prefix sum,
+ * resulting in O(N) per query — too slow for large Q.
+ *
+ * To handle both operations efficiently:
+ *
+ * 1. Difference Array Concept:
+ *    - A range update [L, R] by +X can be represented as:
+ *        diff[L]     += X
+ *        diff[R + 1] -= X
+ *
+ * 2. Fenwick Tree (Binary Indexed Tree):
+ *    - We store the difference array updates inside a Fenwick Tree.
+ *    - This allows both updates and prefix-sum queries in O(log N).
+ *
+ * 3. Point Value Retrieval:
+ *    - The final value at index `k` is:
+ *        initial_array[k] + prefix_sum(diff, k)
+ *
+ * -------------------------
+ * Time & Space Complexity
+ * -------------------------
+ * Time Complexity:  O((N + Q) log N)
+ * Space Complexity: O(N)
+ */
+
+#include <bits/stdc++.h>
+using namespace std;
+
+const int MAXN = 200005;
+long long bit[MAXN];
+int n, q;
+
+// Fenwick Tree update (1-based indexing)
+void update(int idx, long long val) {
+    for (; idx <= n; idx += idx & -idx) {
+        bit[idx] += val;
+    }
+}
+
+// Fenwick Tree prefix sum query
+long long query(int idx) {
+    long long sum = 0;
+    for (; idx > 0; idx -= idx & -idx) {
+        sum += bit[idx];
+    }
+    return sum;
+}
+
+void solve() {
+    cin >> n >> q;
+
+    vector<long long> initial_arr(n + 1);
+    for (int i = 1; i <= n; i++) {
+        cin >> initial_arr[i];
+    }
+
+    while (q--) {
+        int type;
+        cin >> type;
+
+        if (type == 1) {
+            // Range update: add u to [a, b]
+            int a, b;
+            long long u;
+            cin >> a >> b >> u;
+            update(a, u);
+            update(b + 1, -u);
+        } else {
+            // Point query: get value at k
+            int k;
+            cin >> k;
+            cout << initial_arr[k] + query(k) << '\n';
+        }
+    }
+}
+
+int main() {
+    ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    solve();
+    return 0;
+}