noi.ac #289. 电梯(单调队列)
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2023-01-02 18:31:29
题意 "题目链接" Sol 傻叉的我以为给出的$t$是单调递增的,然后$100\rightarrow0$ 首先可以按$t$排序,那么转移方程为 $f[i] = min_{j=0}^{i 1}(max(t[i], f[j]) + 2 max_{k=j+1}^i x[k])$ 不难发现,若$i defi ......
题意
sol
傻叉的我以为给出的\(t\)是单调递增的,然后\(100\rightarrow0\)
首先可以按\(t\)排序,那么转移方程为
\(f[i] = min_{j=0}^{i-1}(max(t[i], f[j]) + 2 * max_{k=j+1}^i x[k])\)
不难发现,若\(i < j\)且\(x[i] < x[j]\),那么从\(i\)转移过来一定是不优的,一定是从\(i\)之前的某个位置转移过来。(f单增)
然后直接单调队列搞一搞就行了,
#include<bits/stdc++.h> #define pair pair<int, int> #define fi first #define se second #define ll long long #define getchar() (p1 == p2 && (p2 = (p1 = buf) + fread(buf, 1, 1<<22, stdin), p1 == p2) ? eof : *p1++) char buf[(1 << 22)], *p1 = buf, *p2 = buf; using namespace std; const int maxn = 1e6 + 10; 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;} 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, q[maxn], val[maxn], top; ll f[maxn]; pair a[maxn]; signed main() { n = read(); for(int i = 1; i <= n; i++) a[i].fi = read(), a[i].se = read(); sort(a + 1, a + n + 1); for(int i = 1; i <= n; i++) { while(top && a[i].se > a[top].se) top--; a[++top] = a[i]; } memset(f, 0x7f, sizeof(f)); n = top; f[0] = 0; int l = 1, r = 0, las = 0; for(int i = 1; i <= n; i++) { while(l <= r && a[i].fi >= f[q[l]]) las = q[l++]; if(las < i) chmin(f[i], a[i].fi + 2ll * a[las + 1].se); if(l <= r) chmin(f[i], val[l]); int cur = f[i] + 2ll * a[i + 1].se; while(l <= r && cur <= val[r]) r--; q[++r] = i; val[r] = cur; } cout << f[n]; return 0; }
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