Add Day-01 Mathematics prefix sum solution

Author: ronakgoyal1

Problems/Mathematics/Day-01/sol/RonakGoyal/Solution1.cpp

@@ -0,0 +1,68 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+/*
+Problem Statement:
+Given an array of integers and multiple range queries, find the sum
+of elements in a given range for each query.
+
+Approach (Using Prefix Sums):
+We construct a prefix sum array where prefix[i] stores the sum of
+elements from index 0 to i. For any range [l, r], the sum can be
+calculated in O(1) time using:
+prefix[r] - prefix[l - 1].
+
+Time Complexity:
+O(n + q)
+
+Space Complexity:
+O(n)
+
+Example:
+Input:
+5
+1 2 3 4 5
+1
+1 3
+
+Output:
+9
+
+*/
+
+int main() {
+    int n;
+    cin >> n;
+
+    vector<int> arr(n), prefix(n);
+
+    // Building prefix sum array
+    for (int i = 0; i < n; i++) {
+        cin >> arr[i];
+        if (i == 0) {
+            prefix[i] = arr[i];
+        } else {
+            prefix[i] = prefix[i - 1] + arr[i];
+        }
+    }
+
+    int q;
+    cin >> q;
+
+    // Answering queries
+    while (q--) {
+        int l, r;
+        cin >> l >> r;
+
+        int sum;
+        if (l == 0) {
+            sum = prefix[r];
+        } else {
+            sum = prefix[r] - prefix[l - 1];
+        }
+
+        cout << sum << endl;
+    }
+
+    return 0;
+}