# C++ program to find longest possible time not greater than T to solve all problems

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Suppose we have an array A with N elements. Have another number T. Consider Amal is trying to participate in a programming contest. It lasts for T minutes and present N problems. He has A[i] time to solve ith problem. He will choose zero or more problems to solve from the N problems, so that it takes no longer T minutes in total to solve them. We have to find the longest possible time it will take to solve his choice of problems.

So, if the input is like T = 17; A = [2, 3, 5, 7, 11], then the output will be 17, because if he chooses the first four problems, it takes him 2 + 3 + 5 + 7 = 17 minutes in total to solve them, which is the longest possible time not exceeding T minutes.

## Steps

To solve this, we will follow these steps −

n := size of A
Define an array b of size (n / 2) and c of size (n - n/2)
for initialize i := 0, when i < n / 2, update (increase i by 1), do:
b[i] := A[i]
for initialize i := n / 2, when i < n, update (increase i by 1), do:
c[i - n / 2] = A[i]
Define an array B, C
for bit in range 0 to 2^(n/2), increase bit after each iteration, do
p := 0
for initialize i := 0, when i < n / 2, update (increase i by 1), do:
if bit AND 2^i is non zero, then
p := p + b[i]
insert p at the end of B
for bit in range 0 to 2^(n - n/2), increase bit after each iteration
p := 0
for initialize i := 0, when i < n - n / 2, update (increase i by 1), do:
if bit AND 2^i is non-zero, then
p := p + c[i]
insert p at the end of C
mx := 0
sort the array C
for initialize i := 0, when i < size of B, update (increase i by 1), do:
if t - B[i] < 0, then:
Ignore following part, skip to the next iteration
itr = next larger element of (t - B[i]) in C
(decrease itr by 1)
mx := maximum of mx and (itr + B[i])
return mx

## Example

Let us see the following implementation to get better understanding −

#include <bits/stdc++.h>
using namespace std;

int solve(int t, vector<int> A){
int n = A.size();
vector<int> b(n / 2), c(n - n / 2);
for (int i = 0; i < n / 2; i++)
b[i] = A[i];
for (int i = n / 2; i < n; i++)
c[i - n / 2] = A[i];
vector<int> B, C;
for (int bit = 0; bit < (1 << (n / 2)); bit++){
int p = 0;
for (int i = 0; i < n / 2; i++){
if (bit & (1 << i))
p += b[i];
}
B.push_back(p);
}
for (int bit = 0; bit < (1 << (n - n / 2)); bit++){
int p = 0;
for (int i = 0; i < n - n / 2; i++){
if (bit & (1 << i))
p += c[i];
}
C.push_back(p);
}
int mx = 0;
sort(C.begin(), C.end());
for (int i = 0; i < B.size(); i++){
if (t - B[i] < 0)
continue;
auto itr = upper_bound(C.begin(), C.end(), t - B[i]);
itr--;
mx = max(mx, *itr + B[i]);
}
return mx;
}
int main(){
int T = 17;
vector<int> A = { 2, 3, 5, 7, 11 };
cout << solve(T, A) << endl;
}

## Input

17, { 2, 3, 5, 7, 11 }

## Output

17