CodeForces

题意:构造一个由a组成的串,如果插入或删除一个a,花费时间x,如果使当前串长度加倍,花费时间y,问要构造一个长度为n的串,最少花费多长时间。

分析:dp[i]---构造长度为i的串需要花费的最短时间。

1、构造长度为1的串,只能插入,dp[1] = x。

2、当前串的长度i为偶数,可以

(1)长度为i/2的串加倍:dp[i / 2] + y

(2)长度为i-1的串插入一个a:dp[i - 1] + x

3、当前串的长度i为奇数,可以

(1)长度为i/2的串加倍,再加上一个a:dp[i / 2] + y + x

(2)长度为i/2+1的串加倍,再删除一个a:dp[i / 2 + 1] + y + x

(3)长度为i-1的串插入一个a:dp[i - 1] + x

#include<cstdio>
#include<cstring>
#include<cstdlib>
#include<cctype>
#include<cmath>
#include<iostream>
#include<sstream>
#include<iterator>
#include<algorithm>
#include<string>
#include<vector>
#include<set>
#include<map>
#include<stack>
#include<deque>
#include<queue>
#include<list>
#define lowbit(x) (x & (-x))
const double eps = 1e-8;
inline int dcmp(double a, double b){
    if(fabs(a - b) < eps) return 0;
    return a > b ? 1 : -1;
}
typedef long long LL;
typedef unsigned long long ULL;
const int INT_INF = 0x3f3f3f3f;
const int INT_M_INF = 0x7f7f7f7f;
const LL LL_INF = 0x3f3f3f3f3f3f3f3f;
const LL LL_M_INF = 0x7f7f7f7f7f7f7f7f;
const int dr[] = {0, 0, -1, 1, -1, -1, 1, 1};
const int dc[] = {-1, 1, 0, 0, -1, 1, -1, 1};
const int MOD = 1e9 + 7;
const double pi = acos(-1.0);
const int MAXN = 1e7 + 10;
const int MAXT = 10000 + 10;
using namespace std;
LL dp[MAXN];
int main(){
    LL n, x, y;
    scanf("%lld%lld%lld", &n, &x, &y);
    memset(dp, LL_INF, sizeof dp);
    dp[1] = x;
    for(LL i = 2; i <= n; ++i){
        if(i % 2 == 0){
            dp[i] = min(dp[i / 2] + y, dp[i - 1] + x);
        }
        else{
            dp[i] = min(dp[i / 2] + x + y, dp[i - 1] + x);
            dp[i] = min(dp[i], dp[i / 2 + 1] + y + x);
        }
    }
    printf("%lld
", dp[n]);
    return 0;
}

  

原文地址:https://www.cnblogs.com/tyty-Somnuspoppy/p/7140973.html