From b7c875d1577f23327b37dcaa16292594c548cf57 Mon Sep 17 00:00:00 2001
From: Hizenberg469 <growlingraptor@gmail.com>
Date: Wed, 6 Aug 2025 19:35:25 +0300
Subject: [PATCH] Meet in the Middle

---
 Meet-in-middle/meetInMiddle.cpp | 108 ++++++++++++++++++++++++++++++++
 1 file changed, 108 insertions(+)
 create mode 100644 Meet-in-middle/meetInMiddle.cpp

diff --git a/Meet-in-middle/meetInMiddle.cpp b/Meet-in-middle/meetInMiddle.cpp
new file mode 100644
index 0000000..afd19cf
--- /dev/null
+++ b/Meet-in-middle/meetInMiddle.cpp
@@ -0,0 +1,108 @@
+/*
+    Topic: Meet in the Middle
+    Question link: https://www.spoj.com/problems/SUBSUMS/
+*/
+
+#include <iostream>
+#include <vector>
+#include <cmath>
+#include <algorithm>
+
+#define ll long long int
+
+using namespace std;
+
+vector<ll> subsetSums;
+vector<ll> firstHalf;
+vector<ll> secondHalf;
+
+void printVector(vector<ll> &v){
+
+    int sz = (int)v.size();
+    for( int i = 0 ; i < sz ; i++ )
+        cout << v[i] << ' ';
+
+    cout << '\n';
+}
+
+void recursiveApproach(int curIdx, ll currSum, int N, vector<int> &S){
+
+    //Base case...
+    if( curIdx == N ){
+        subsetSums.push_back(currSum);
+        return;
+    }
+
+    recursiveApproach(curIdx + 1, currSum + S[curIdx], N, S);
+    recursiveApproach(curIdx + 1, currSum, N, S);
+
+}
+
+void bitmaskApproach(int startIdx, int N, vector<int> &S){
+
+    ll currSum = 0;
+    for(int mask = 0 ; mask < pow(2, N) ; ++mask ){
+        currSum = 0;
+        for(int i = 0 ; i < N ; ++i){
+            if( mask & (1<<i) ){
+                currSum += S[i + startIdx];
+            }
+        }
+
+        subsetSums.push_back(currSum);
+    }
+}
+
+void generateAllSubsetSum(vector<int> &S){
+
+    // // Using Recursive Approach...
+    // subsetSums.clear();
+    // recursiveApproach(0, 0LL, (int)S.size()/2, S);
+    // firstHalf = subsetSums; // deep copy
+
+    // subsetSums.clear();
+    // recursiveApproach((int)S.size()/2, 0LL, (int)S.size(), S);
+    // secondHalf = subsetSums; // deep copy
+
+    // Using Bitmask Approach...
+    subsetSums.clear();
+    bitmaskApproach(0, (int)S.size()/2, S);
+    firstHalf = subsetSums; // deep copy
+
+    subsetSums.clear();
+    bitmaskApproach((int)S.size()/2, (int)S.size() - S.size()/2, S);
+    secondHalf = subsetSums; // deep copy
+
+} 
+
+int main(){
+
+    int N, A, B;
+    ll noOfSubset = 0LL;
+    
+    cin >> N >> A >> B;
+    
+    vector<int> S(N);
+
+    for(int i = 0 ; i < N ; i++ )
+        cin >> S[i];
+
+    
+    generateAllSubsetSum(S);
+
+    // printVector(firstHalf);
+    // printVector(secondHalf);
+
+    sort(secondHalf.begin(), secondHalf.end());
+
+    int sz = (int)firstHalf.size();
+    int a = 0;
+    for(int i = 0 ; i < sz ; ++i){
+        noOfSubset += upper_bound(secondHalf.begin(), secondHalf.end(), B - firstHalf[i])
+                    -
+                    lower_bound(secondHalf.begin(), secondHalf.end(), A - firstHalf[i]);
+    }
+
+    cout << noOfSubset << '\n';
+    return 0;
+}
\ No newline at end of file