CSES Robot Path Burn Chicken

// Knapsack DP is harder than FFT.
#include<bits/stdc++.h>
using namespace std;
typedef long long ll; typedef pair<int,int> pii; typedef pair<ll,ll> pll;
#define ff first
#define ss second
#define pb emplace_back
#define AI(x) begin(x),end(x)
template<class I>bool chmax(I&a,I b){return a<b?(a=b,true):false;}
template<class I>bool chmin(I&a,I b){return b<a?(a=b,true):false;}
#ifdef OWO
#define debug(args...) SDF(#args, args)
#define OIU(args...) ostream& operator<<(ostream&O,args)
#define LKJ(S,B,E,F) template<class...T>OIU(S<T...>s){O<<B;int c=0;for(auto i:s)O<<(c++?", ":"")<<F;return O<<E;}
LKJ(vector,'[',']',i)LKJ(deque,'[',']',i)LKJ(set,'{','}',i)LKJ(multiset,'{','}',i)LKJ(unordered_set,'{','}',i)LKJ(map,'{','}',i.ff<<':'<<i.ss)LKJ(unordered_map,'{','}',i.ff<<':'<<i.ss)
template<class...T>void SDF(const char* s,T...a){int c=sizeof...(T);if(!c){cerr<<"\033[1;32mvoid\033[0m\n";return;}(cerr<<"\033[1;32m("<<s<<") = (",...,(cerr<<a<<(--c?", ":")\033[0m\n")));}
template<class T,size_t N>OIU(array<T,N>a){return O<<vector<T>(AI(a));}template<class...T>OIU(pair<T...>p){return O<<'('<<p.ff<<','<<p.ss<<')';}template<class...T>OIU(tuple<T...>t){return O<<'(',apply([&O](T...s){int c=0;(...,(O<<(c++?", ":"")<<s));},t),O<<')';}
#else
#pragma GCC optimize("Ofast")
#define debug(...) ((void)0)
#endif

struct LISAN : vector<ll> {
    void done() { sort(AI()); erase(unique(AI()), end()); }
    int operator () (ll v) { return lower_bound(AI(), v) - begin(); }
};
struct BIT {
    int n; vector<int> val;
    BIT(int n = 0) : n(n), val(n+1, 0) {}
    void init(){ fill(AI(val), 0); };
    void modify(int p, int v){
        for(++p; p <= n; p += p & -p)
            val[p] += v;
    }
    int query(int p){
        int r = 0;
        for(++p; p > 0; p -= p&-p)
            r += val[p];
        return r;
    }
    int query(int l, int r){
        return query(r) - query(l-1);
    }
};
struct SOLVER {
    int dx, dy, tot;
    vector<vector<pii>> mods, ques, vers;
    BIT bit;
    SOLVER (int dx = 0, int dy = 0):
        dx(dx), dy(dy), mods(dy+1), ques(dy+1), vers(dx+1), bit(dx+1), tot(0) {}
    void init(){
        for(int i = 0; i <= dy; ++i) mods[i].clear();
        for(int i = 0; i <= dy; ++i) ques[i].clear();
        for(int i = 0; i <= dx; ++i) vers[i].clear();
        bit.init();
        tot = 0;
    }
    void add(int x1, int y1, int x2, int y2){
        ++tot;
        if(x1 == x2){
            if(y1 > y2) swap(y1, y2);
            mods[y1].pb(x1, 1);
            mods[y2+1].pb(x1, -1);
            vers[x1].pb(y1, y2);
        } else {
            if(x1 > x2) swap(x1, x2);
            ques[y1].pb(x1, x2);
        }
    }
    bool go(vector<pii> &v){
        if(v.size() <= 1) return false;
        sort(AI(v));
        int mx = -1;
        for(auto [l, r]: v){
            if(mx >= l) return true;
            mx = max(mx, r);
        }
        return false;
    }
    bool solve(){
        for(auto &i: ques) if(go(i)) return true;
        for(auto &i: vers) if(go(i)) return true;
        ll cnt = 0;
        for(int i = 0; i <= dy; ++i){
            for(auto [p, v]: mods[i])
                bit.modify(p, v);
            for(auto [l, r]: ques[i])
                cnt += bit.query(l, r);
            if(cnt >= tot) return true;
        }
        return false;
    }
};

typedef array<ll, 4> seg;
ll banana(seg a, seg b, LISAN &lx, LISAN &ly){
    if((a[0] == a[2]) and (b[0] == b[2])){
        if(a[0] != b[0]) return -1;
        return min(abs(ly[a[1]] - ly[b[1]]), abs(ly[a[1]] - ly[b[3]]));
    }
    if((a[1] == a[3]) and (b[1] == b[3])){
        if(a[1] != b[1]) return -1;
        return min(abs(lx[a[0]] - lx[b[0]]), abs(lx[a[0]] - lx[b[2]]));
    }
    if(a[0] == a[2]) return abs(ly[a[1]] - ly[b[1]]);
    return abs(lx[a[0]] - lx[b[0]]);
}

bool opposite(char a, char b){
    if(a > b) swap(a, b);
    return (a == 'D' and b == 'U')
        or (a == 'L' and b == 'R');
}

signed main(){
    ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
    int n; cin >> n;
    vector<ll> len;
    vector<pair<char, ll>> mv;
    int ret = n+1;
    for(int i = 0; i < n; ++i){
        char d; int x; cin >> d >> x;
        if(i > 0 and d == mv.back().ff){
            mv.back().ss += x;
            len.back() += x;
        } else {
            if(i > 0 and opposite(mv.back().ff, d))
                ret = min(i, ret);
            mv.pb(d, x);
            len.pb(x);
        }
    }
    n = len.size();

    vector<seg> segs;
    LISAN lx, ly; lx.pb(0), ly.pb(0);
    for(ll cx = 0, cy = 0, nx, ny, i = 0; i < n; ++i){
        auto [dir, x] = mv[i];
        if(dir == 'U') nx = cx, ny = cy + x;
        if(dir == 'D') nx = cx, ny = cy - x;
        if(dir == 'R') nx = cx + x, ny = cy;
        if(dir == 'L') nx = cx - x, ny = cy;
        segs.push_back({ cx, cy, nx, ny });
        if(cx != nx) lx.pb(nx);
        if(cy != ny) ly.pb(ny);
        cx = nx, cy = ny;
    }
    lx.done(); ly.done();
    for(auto &a: segs){
        a[0] = lx(a[0]); a[2] = lx(a[2]);
        a[1] = ly(a[1]); a[3] = ly(a[3]);
    }

    int l = 1, r = n, m;
    SOLVER solver(lx.size(), ly.size());
    while(l < r){
        m = (l+r) / 2;
        solver.init();
        for(int i = 0; i <= m; ++i)
            solver.add(segs[i][0], segs[i][1], segs[i][2], segs[i][3]);
        if(solver.solve()) r = m;
        else l = m+1;
        if(l >= ret) break;
    }

    ll sum = accumulate(begin(len), begin(len) + min(ret, l), 0ll);
    if(l == n or ret <= l){
        cout << sum << '\n';
        return 0;
    }
    debug(sum);
    ll ans = 1e18;
    for(int i = 0; i < l-1; ++i){
        ll d = banana(segs[l], segs[i], lx, ly);
        if(d != -1) ans = min(ans, d);
    }
    cout << sum + ans << '\n';
    return 0;
}