Codeforces C. Minimum Grid Path (Round 106 Rated for Div.2) (模拟枚举/前缀(和&最小值))

传送门

题意:需要你从从原点(0,0)出发走到平面第一象限中的终点(n,n),你只能向右或向上行走整数步,且过程中最多变换n-1次方向。现在告诉你n段路程分别的平均成本,试找到走到终点的最小消耗。

思路:

既然最多变换n-1次方向,即我们可以利用完n段线段的成本。

于是我们枚举最后一段时在第i次结束(走到终点),注意:这以为这之前 i-1 段路程都是交替变换方向的。

对于奇数位置,走到总距离和必须刚好等于n,于是我们找到该奇数位置 i 以及之前的所有奇数位置的最小值,让其走最多的步数,其余的位置都只走一步。偶数位置同理。不断更新答案取得最小值即可。

代码实现:

#include<bits/stdc++.h>
#define endl '\n'
#define null NULL
#define ll long long
#define int long long
#define pii pair<int, int>
#define lowbit(x) (x &(-x))
#define ls(x) x<<1
#define rs(x) (x<<1+1)
#define me(ar) memset(ar, 0, sizeof ar)
#define mem(ar,num) memset(ar, num, sizeof ar)
#define rp(i, n) for(int i = 0, i < n; i ++)
#define rep(i, a, n) for(int i = a; i <= n; i ++)
#define pre(i, n, a) for(int i = n; i >= a; i --)
#define IOS ios::sync_with_stdio(0); cin.tie(0);cout.tie(0);
const int way[4][2] = {
   
   {1, 0}, {-1, 0}, {0, 1}, {0, -1}};
using namespace std;
const int  inf = 0x3f3f3f3f3f3f3f3f;
const double PI = acos(-1.0);
const double eps = 1e-6;
const ll   mod = 1e9+7;
const int  N = 2e5 + 5;

inline void read(int &x){
    char t=getchar();
    while(!isdigit(t)) t=getchar();
    for(x=t^48,t=getchar();isdigit(t);t=getchar()) x=x*10+(t^48);
}

int t, n, c[N];
int ma[N], mb[N], pra[N], prb[N];

signed main()
{
    IOS;

    cin >> t;
    while(t --){
        cin >> n;
        me(ma); me(mb);
        me(pra); me(prb);
        for(int i = 1; i <= n; i ++){
            cin >> c[i];
            if(i&1){
                if(i==1) ma[i] = pra[i] = c[i];
                else ma[i] = min(ma[i-2], c[i]), pra[i] = pra[i-2]+c[i];
            }
            else{
                if(i==2) mb[i] = prb[i] = c[i];
                else mb[i] = min(mb[i-2], c[i]), prb[i] = prb[i-2]+c[i];
            }
        }
        int ans = inf;
        for(int i = 2; i <= n; i ++){
            int tmp = 0, k = i/2;
            if(i&1){
                tmp += prb[i-1]+(n-k)*mb[i-1];
                tmp += pra[i]+(n-k-1)*ma[i];
            }
            else{
                tmp += prb[i]+(n-k)*mb[i];
                tmp += pra[i-1]+(n-k)*ma[i-1];
            }
            ans = min(ans, tmp);
//            cout << "i: " << i << " tmp: " << tmp << endl;
        }
        cout << ans << endl;
    }

    return 0;
}

Java练习:期间忘记tmp定义成long型 wa4,再又就是所有数组定义成long型的话如果都是1e5+10大小的话就会 t3,呜呜呜绝了

import java.util.Scanner;
import java.util.*;

public class Main {

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int t = in.nextInt();
        while(t>0) {
            t --;
            int n = in.nextInt();
            long [] c = new long[n+10];
            long [] ma = new long[n+10];
            long [] mb = new long[n+10];
            long [] pra = new long[n+10];
            long [] prb = new long[n+10];
            for(int i = 1; i <= n; i ++){
                c[i] = in.nextLong();
                if(i%2!=0){
                    if(i==1) ma[i] = pra[i] = c[i];
                    else {
                        ma[i] = Math.min(ma[i-2], c[i]);
                        pra[i] = pra[i-2]+c[i];
                    }
                }
                else{
                    if(i==2) mb[i] = prb[i] = c[i];
                    else{
                        mb[i] = Math.min(mb[i-2], c[i]);
                        prb[i] = prb[i-2]+c[i];
                    }
                }
            }
            long ans = 1L<<60;
            for(int i = 2; i <= n; i ++){
                long tmp = 0, k = i/2;
                if(i%2!=0){
                    tmp += prb[i-1]+(n-k)*mb[i-1];
                    tmp += pra[i]+(n-k-1)*ma[i];
                }
                else{
                    tmp += prb[i]+(n-k)*mb[i];
                    tmp += pra[i-1]+(n-k)*ma[i-1];
                }
                ans = Math.min(ans, tmp);
            }
            System.out.println(ans);
        }
        in.close();
    }
}

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转载自blog.csdn.net/Satur9/article/details/115003661