1847:A — The Man who became a God
- Author — PoPularPlusPlus
#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define ull unsigned long long
#define pb(e) push_back(e)
#define sv(a) sort(a.begin(),a.end())
#define sa(a,n) sort(a,a+n)
#define mp(a,b) make_pair(a,b)
#define all(x) x.begin(),x.end()
void solve(){
int n , k;
cin >> n >> k;
ll arr[n];
for(int i = 0; i < n; i++)cin >> arr[i];
vector<ll> v;
ll sum = 0;
for(int i = 1; i < n; i++){
v.pb(abs(arr[i] - arr[i-1]));
sum += v.back();
}
sort(all(v));
for(int groups = 1; groups < k; groups++){
sum -= v.back();
v.pop_back();
}
cout << sum << '\n';
}
int main(){
ios_base::sync_with_stdio(false);
cin.tie(NULL);
int t;cin >> t;while(t--)
solve();
return 0;
}
- Author — PoPularPlusPlus
#include <iostream>
#include <vector>
using namespace std;
#define ll long long
#define ull unsigned long long
#define pb(e) push_back(e)
#define sv(a) sort(a.begin(),a.end())
#define sa(a,n) sort(a,a+n)
#define mp(a,b) make_pair(a,b)
#define all(x) x.begin(),x.end()
void solve(){
int n;
cin >> n;
int arr[n];
for(int i = 0; i < n; i++)cin >> arr[i];
int cur = arr[0];
int part = 1;
for(int i = 0; i < n; i++){
cur &= arr[i];
if(cur == 0){
if(i == n-1)break;
part++;
cur = arr[i + 1];
}
}
if(cur != 0)part--;
part = max(part,1);
cout << part << '\n';
}
int main(){
ios_base::sync_with_stdio(false);
cin.tie(NULL);
int t;cin >> t;while(t--)
solve();
return 0;
}
1847:C- Vampiric Powers, anyone?
- Author — PoPularPlusPlus
At the end of the array, you can only achieve xor of any subarray of the original array.
Lets denote $$$f(u,v) =$$$ xor of all $$$a_i$$$ such that $$$min(u,v) \leq i < max(u,v)$$$. In the first operation you add $$$f(n,i)$$$. I.e. $$$[u_1,v_1)=[n,i)$$$. It can be proven that $$$f(u_k,v_k) = f(v_{k-1},v_k)$$$ in the $$$k$$$-th operation which is a range.
Suppose we have taken $$$k$$$ ranges that already satisfy this property. Now, I add a new $$$k+1$$$-th range. So, first I need to take the $$$k$$$-th range $$$f(u_k,v_k)$$$. Now I'm xoring it with the range $$$f(u_{k - 1}, v_{k - 1})$$$. As [ $$$u_k, v_k$$$) and [ $$$u_{k - 1}, v_{k - 1}$$$) share an endpoint, the result for these ranges will be a range.
For two ranges $$$f(x,y)$$$ and $$$f(y,z)$$$, if the two ranges do not intersect, the result will be the sum of the two ranges $$$f(x,z)$$$. If the two ranges intersect, then the intersections will be cancelled out, and the result will be the difference $$$f(x,z)$$$.
Now, we maintain a boolean array $$$b$$$ where $$$b_i$$$ is $$$1$$$ if there is some $$$j$$$ such that $$$a_1 \oplus a_2 \oplus \cdots \oplus a_j = i$$$. Initially, $$$b$$$ is all $$$0$$$. We loop $$$j$$$ from $$$1$$$ to $$$n$$$ and check for each $$$k$$$ if $$$b_k=1$$$. If it is, then there is some position $$$p < j$$$ such that $$$a_1 \oplus a_2 \oplus \cdots \oplus a_p = k$$$. If we take xor of range from $$$(p,j]$$$, then it will be $$$k \oplus a_1 \oplus a_2 \oplus \cdots \oplus a_j$$$ (as $$$a_1 \oplus a_2 \oplus \cdots \oplus a_p$$$ gets cancelled). This $$$a_1 \oplus a_2 \oplus \cdots \oplus a_j$$$ can be stored as we loop ahead. We are looping all possible prefix xors and not all prefix positions because $$$n$$$ is large.
Time Complexity — $$$O(n \cdot 2^8)$$$.
- Author — PoPularPlusPlus
- Author — StArChAn
- Idea — astoria
- Prepared by — PoPularPlusPlus