Difference Array

algos/range_queries/DifferenceArray/soln/Sujal/solution1.cpp

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+//submission link - https://cses.fi/problemset/result/15793543/
+
+
+/*
+Problem:
+You are given an array of n integers.
+You need to process q queries of two types:
+1) Add value u to all elements in range [a, b]
+2) Print the value at position k
+
+Queries are mixed and can come in any order.
+
+Approach:
+We use a Fenwick Tree (Binary Indexed Tree).
+
+Idea:
+- We convert range update into two point updates:
+    add u at index a
+    subtract u at index b+1
+- Fenwick Tree stores these updates.
+- For query type 2, we take prefix sum up to k
+  and add it to the original value at index k.
+
+This works because prefix sum gives
+the total update applied to that position.
+
+Time Complexity:
+- Each update: O(log n)
+- Each query: O(log n)
+- Total: O((n + q) log n)
+
+Space Complexity:
+- O(n)
+*/
+
+#include<bits/stdc++.h>
+using namespace std;
+
+struct Fenwick{
+    int n;
+    vector<long long> bit;
+
+    Fenwick(int n):n(n),bit(n+1,0){}
+
+    void add(int i,long long v){
+        for(;i<=n;i+=i&-i)
+            bit[i]+=v;
+    }
+
+    long long sum(int i){
+        long long s=0;
+        for(;i>0;i-=i&-i)
+            s+=bit[i];
+        return s;
+    }
+};
+
+int main(){
+    ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    int n,q;
+    cin>>n>>q;
+
+    vector<long long>x(n+1);
+    for(int i=1;i<=n;i++)
+        cin>>x[i];
+
+    Fenwick fw(n+1);
+
+    while(q--){
+        int type;
+        cin>>type;
+
+        if(type==1){
+            int a,b;
+            long long u;
+            cin>>a>>b>>u;
+            fw.add(a,u);
+            fw.add(b+1,-u);
+        }else{
+            int k;
+            cin>>k;
+            cout<<x[k]+fw.sum(k)<<"\n";
+        }
+    }
+}