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๐Ÿ”ฐAuthentic Coding Solutions(with Outputs)
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def ss(arr):
    total_sum = sum(arr)
    n = len(arr)
    a = set()
    a.add(0)
    for num in arr:
        b = set()
        for s in a:
            b.add(s + num)
        a.update(b)
    return 0 in a
N = int(input())
arr = list(map(int, input().split()))
result = ss(arr)
print("true" if result else "false")


Negate subsequence
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#include<bits/stdc++.h>
using namespace std;
int solve(int N, int M, vector<int>& P, vector<int>& W) {
    int wateredCount = 0;
    int i = 0;
    for (int j = 0; j < M && i < N; ++j) {
        int water = W[j];
       
        if (i < N - 1) {
            if (water >= P[i] + P[i + 1]) {
                wateredCount += 2;
                P[i] = 0;
                P[i + 1] = 0;
                i += 2;
            } else if (water >= P[i]) {
                wateredCount++;
                P[i] = 0;
                i++;
            } else if (water >= P[i + 1]) {
                wateredCount++;
                P[i + 1] = 0;
                i += 2;
            } else {
                i++;
            }
        } else {
            if (water >= P[i]) {
                wateredCount++;
                P[i] = 0;
            }
            break;
        }
    }
    return wateredCount;
}

int main() {
    int N, M;
    cin >> N >> M;
    vector<int> P(N);
    vector<int> W(M);
   
    for (int i = 0; i < N; ++i) {
        cin >> P[i];
    }
   
    for (int i = 0; i < M; ++i) {
        cin >> W[i];
    }

    int result = solve(N, M, P, W);
    cout << result << endl;
    return 0;
}


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Wishing all students a joyful and prosperous Diwali! As you prepare for your upcoming challenges, may the festival of lights inspire you with renewed energy and determination. Embrace the spirit of the season and let it illuminate your path to success. Remember, hard work and perseverance will guide you through any obstacles. Stay focused, believe in your abilities, and celebrate each step of your journey. You've got this!
int findmaximumPackages(vector<int>&arr)
{
    int n = arr.size();
    int mx = *max_element(arr.begin(), arr.end());
    mx = mx * 2;
    int res = 0;
    map<int, int>mp;
    for (auto it : arr) {
        mp[it]++;
    }
    for (int i = 1; i <= mx; i++) {
        int sm = 0;
        for (int j = 1; j <= (i - 1) / 2; j++) {
            sm += min(mp[j], mp[i - j]);
        }
        if (i % 2 == 0) {
            sm += (mp[i / 2] / 2);
        }
        res = max(res, mp[i] + sm);
    }
    return res;
}

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