洛谷P4360 [CEOI2004]鋸木廠選址(dp 斜率優化)
阿新 • • 發佈:2018-12-31
題意
Sol
列舉第二個球放的位置,用字首和推一波之後發現可以斜率優化
// luogu-judger-enable-o2 #include<bits/stdc++.h> #define Pair pair<int, int> #define MP(x, y) make_pair(x, y) #define fi first #define se second #define int long long #define LL long long #define Fin(x) {freopen(#x".in","r",stdin);} #define Fout(x) {freopen(#x".out","w",stdout);} using namespace std; const int MAXN = 1e6 + 10, mod = 1e9 + 7; LL INF = 2e18 + 10; const double eps = 1e-9; template <typename A, typename B> inline bool chmin(A &a, B b){if(a > b) {a = b; return 1;} return 0;} template <typename A, typename B> inline bool chmax(A &a, B b){if(a < b) {a = b; return 1;} return 0;} template <typename A, typename B> inline LL add(A x, B y) {if(x + y < 0) return x + y + mod; return x + y >= mod ? x + y - mod : x + y;} template <typename A, typename B> inline void add2(A &x, B y) {if(x + y < 0) x = x + y + mod; else x = (x + y >= mod ? x + y - mod : x + y);} template <typename A, typename B> inline LL mul(A x, B y) {return 1ll * x * y % mod;} template <typename A, typename B> inline void mul2(A &x, B y) {x = (1ll * x * y % mod + mod) % mod;} template <typename A> inline void debug(A a){cout << a << '\n';} template <typename A> inline LL sqr(A x){return 1ll * x * x;} inline int read() { char c = getchar(); int x = 0, f = 1; while(c < '0' || c > '9') {if(c == '-') f = -1; c = getchar();} while(c >= '0' && c <= '9') x = x * 10 + c - '0', c = getchar(); return x * f; } int N, w[MAXN], d[MAXN], s[MAXN], sw[MAXN], g[MAXN], f[MAXN], q[MAXN]; int calc(int l, int r) { if(l > r) return 0; return s[r] - s[l - 1] - d[l - 1] * (sw[r] - sw[l - 1]); } double Y(int x) { return g[x]; } double X(int x) { return d[x]; } double slope(int a, int b) { return double(Y(b) - Y(a)) / (X(b) - X(a)); } signed main() { N = read(); for(int i = 1; i <= N; i++) w[i] = read(), d[i] = read(); reverse(w + 1, w + N + 1); reverse(d + 1, d + N + 1); for(int i = 1; i <= N; i++) d[i] += d[i - 1], s[i] = s[i - 1] + w[i] * d[i], sw[i] = w[i] + sw[i - 1]; LL ans = INF; for(int i = 1; i <= N; i++) g[i] = calc(1, i - 1)- s[i] + d[i] * sw[i]; q[1] = 0; for(int i = 1, h = 1, t = 1; i <= N; i++) { f[i] = INF; while(h < t && slope(q[h], q[h + 1]) < sw[i - 1]) h++; f[i] = g[q[h]] - d[q[h]] * sw[i - 1]; while(h < t && slope(q[t - 1], q[t]) > slope(q[t], i)) t--; q[++t] = i; //for(int j = i - 1; j >= 1; j--) chmin(f[i], g[j] - d[j] * sw[i - 1]); f[i] += s[i - 1]; } for(int i = 1; i <= N; i++) f[i] += calc(i + 1, N), chmin(ans, f[i]); cout << ans; return 0; } /* */