116 lines
2 KiB
C++
116 lines
2 KiB
C++
#include <bits/stdc++.h> // {{{
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// https://codeforces.com/blog/entry/96344
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#pragma GCC optimize("O2,unroll-loops")
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#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
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using namespace std;
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using i32 = int32_t;
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using u32 = uint32_t;
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using i64 = int64_t;
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using u64 = uint64_t;
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using f64 = double;
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using f128 = long double;
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#if __cplusplus >= 202002L
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template <typename T>
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constexpr T MIN = std::numeric_limits<T>::min();
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template <typename T>
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constexpr T MAX = std::numeric_limits<T>::max();
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template <typename T>
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[[nodiscard]] static T sc(auto&& x) {
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return static_cast<T>(x);
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}
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template <typename T>
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[[nodiscard]] static T sz(auto&& x) {
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return static_cast<T>(x.size());
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}
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#endif
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static void NO() {
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std::cout << "NO\n";
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}
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static void YES() {
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std::cout << "YES\n";
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}
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template <typename T>
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using vec = std::vector<T>;
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#define all(x) (x).begin(), (x).end()
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#define rall(x) (x).rbegin(), (x).rend()
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#define ff first
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#define ss second
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#ifdef LOCAL
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#define db(...) std::print(__VA_ARGS__)
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#define dbln(...) std::println(__VA_ARGS__)
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#else
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#define db(...)
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#define dbln(...)
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#endif
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// }}}
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void solve() {
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u32 n;
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cin >> n;
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string s;
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cin >> s;
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/*
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f(x) -> max # 0/1s in x
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count f(s[l: r]) for all l <= r
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formulate it
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f(s[l:r])
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f(s[0:0]) + f(s[0:1]) + f(s[0:2]) + f(s[0:3]) + f(s[0:4]) + ...
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f(s[1:1]) + f(s[1:2]) + f(s[1:3]) + f(s[1:4]) + ...
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one idea: sum f(s[l:r]) = sum min(prefix[0][l][r], prefix[1][l][r]) +
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|prefix[0][l][r] - prefix[1][l[r]]| = sum + sum
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first term:
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= (i + 1) * (n - i), take min
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min doesn't work, since varies
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must leverage: max(x, y) = (x + y + |x-y|)/2 = sum x + y
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for all i:
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cnts[s[i] == 0] += (i + 1) * (n - i)
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div. by 2 after
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second term: |x-y| in an aggregate way
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ret (first + second) / 2
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*/
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}
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int main() { // {{{
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cin.tie(nullptr)->sync_with_stdio(false);
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cin.exceptions(cin.failbit);
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u32 tc = 1;
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cin >> tc;
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for (u32 t = 0; t < tc; ++t) {
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solve();
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}
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return 0;
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}
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// }}}
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