BZOJ1911: [Apio2010]特别行动队(dp 斜率优化)
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2022-04-05 10:09:12
题意 "题目链接" Sol 裸的斜率优化,注意推导过程中的符号问题。 cpp include define Pair pair define MP(x, y) make_pair(x, y) define fi first define se second define int long long ......
题意
sol
裸的斜率优化,注意推导过程中的符号问题。
#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, inf = 6e18 + 10; const double eps = 1e-9; template <typename y> inline void chmin(y &a, y b){a = (a < b ? a : b);} template <typename y> inline void chmax(y &a, y b){a = (a > b ? a : b);} template <typename y> inline void debug(y a){cout << a << '\n';} template <typename y> inline ll sqr(y x){return 1ll * x * x;} int add(int x, int y) {if(x + y < 0) return x + y + mod; return x + y >= mod ? x + y - mod : x + y;} void add2(int &x, int y) {if(x + y < 0) x = x + y + mod; else x = (x + y >= mod ? x + y - mod : x + y);} int mul(int x, int y) {return 1ll * x * y % mod;} 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, s[maxn], a, b, c, f[maxn], q[maxn]; int f(int x) { return a * sqr(x) + b * x + c; } double y(int x) { return a * sqr(s[x]) - b * s[x] + f[x]; } double x(int x) { return s[x]; } double slope(int a, int b) { // debug((y(b) - y(a)) / (x(b) - x(a))); return double(y(b) - y(a)) / (x(b) - x(a)); } signed main() { n = read(); a = read(); b = read(); c = read(); for(int i = 1; i <= n; i++) s[i] = s[i - 1] + read(); q[1] = 0; for(int i = 1, h = 1, t = 1; i <= n; i++) { while(h < t && slope(q[h], q[h + 1]) > 2 * a * s[i]) h++; f[i] = f[q[h]] + f(s[i] - s[q[h]]); //printf("%d\n", q[h]); while(h < t && slope(q[t - 1], q[t]) < slope(q[t], i)) t--; q[++t] = i; } cout << f[n]; return 0; } /* 7 -1 160 -2000 14 82 61 85 41 10 34 */