dp趣题 | 易学教程

[CEOI2017]Chase

#include<iostream>
#include<cstring>
#include<cstdio>
#include<algorithm>
#include<queue>
#include<set>
#include<vector>
#include<cmath>
using namespace std;
typedef long long ll;
const int maxn = 1e5 + 7;
int n,m;
int p[maxn];
ll sum[maxn];
int l,last[maxn],other[maxn<<1],pre[maxn<<1];
ll ans,up[maxn][101],down[maxn][101];
vector<int> e[maxn];
void add(int x,int y){
    l ++;
    pre[l] = last[x];
    last[x] = l;
    other[l] = y;
}
void dfs(int x,int fa){
    for(int i = 1;i <= m ;i ++){
        up[x][i] = sum[x];
        down[x][i] = sum[x] - p[fa];
    }
    for(int i = 0;i < e[x].size();i ++){
        int v = e[x][i];
        if(v == fa)continue;
        dfs(v,x);
        for(int j = 1;j < m;j ++)
        ans = max(ans,up[x][j] + down[v][m - j]);
        for(int j = 1;j <= m;j ++){
            up[x][j] = max(up[x][j],max(up[v][j],up[v][j-1] + sum[x] - p[v]));
            down[x][j] = max(down[x][j],max(down[v][j],down[v][j-1] + sum[x] - p[fa]));
        }
    }
    reverse(e[x].begin(),e[x].end());
    for(int i = 1;i <= m ;i ++){
        up[x][i] = sum[x];
        down[x][i] = sum[x] - p[fa];
    }
    for(int i = 0;i < e[x].size();i ++){
        int v = e[x][i];
        if(v == fa)continue;
        for(int j = 1;j < m;j ++)
        ans = max(ans,up[x][j] + down[v][m - j]);
        for(int j = 1;j <= m;j ++){
            up[x][j] = max(up[x][j],max(up[v][j],up[v][j-1] + sum[x] - p[v]));
            down[x][j] = max(down[x][j],max(down[v][j],down[v][j-1] + sum[x] - p[fa]));
        }
    }
    ans = max(ans,max(up[x][m],down[x][m]));
}
int main()
{
    scanf("%d%d",&n,&m);
    for(int i = 1;i <= n ;i ++){
        scanf("%d",&p[i]);
    }
    for(int i = 1;i < n ;i ++){
        int a,b;
        scanf("%d%d",&a,&b);
        e[a].push_back(b);
        e[b].push_back(a);
        sum[a] += p[b];
        sum[b] += p[a];
    }
    dfs(1,0);
    cout<<ans<<endl;
    return 0;
}

SP703 SERVICE - Mobile Service

#include<iostream>
#include<cstring>
#include<cstdio>
#include<algorithm>
#include<queue>
#include<set>
#include<vector>
#include<cmath>
using namespace std;
typedef long long ll;
int t;
int n,m;
int dp[1010][201][210];
int p[1010];
int a[201][201];
int main()
{
    scanf("%d",&t);
    while(t --){
        scanf("%d%d",&m,&n);
        memset(dp,0x3f,sizeof dp);
        for(int i = 1;i <= m;i ++){
            for(int j = 1;j <= m;j ++){
                scanf("%d",&a[i][j]);
            }
        }
        for(int i = 1;i <= n ;i ++){
            scanf("%d",&p[i]);
        }
        dp[0][1][2] = 0;p[0] = 3;
        for(int i = 0;i < n ;i ++){
            for(int j = 1;j <= m;j ++){
                for(int k = 1;k <= m;k ++){
                    int d = p[i];
                    if(j == k || j == d || k == d)continue;
                    if(j != p[i+1] && k != p[i+1])
                    dp[i+1][j][k] = min(dp[i+1][j][k],dp[i][j][k] + a[d][p[i+1]]);
                    if(k != p[i+1] && d != p[i+1])
                    dp[i+1][d][k] = min(dp[i+1][d][k],dp[i][j][k] + a[j][p[i+1]]);
                    if(j != p[i+1] && d != p[i+1])
                    dp[i+1][j][d] = min(dp[i+1][j][d],dp[i][j][k] + a[k][p[i+1]]);
                }
            }
        }
        int ans = 1e9 + 7;
        for(int i = 1;i <= m;i ++)
        for(int j = 1;j <= m;j ++)
        if(i != j)ans = min(dp[n][i][j],ans);
        printf("%d\n",ans);
    }
    return 0;
}

[HNOI2010]合唱队

#include<iostream>
#include<cstring>
#include<cstdio>
#include<algorithm>
#include<queue>
#include<set>
#include<vector>
#include<cmath>
using namespace std;
typedef long long ll;
const int maxn = 1001;
const int mo = 19650827;
int n;
int a[maxn],dp[maxn][maxn][2];
int main()
{
    scanf("%d",&n);
    for(int i = 1;i <= n ;i ++){
        scanf("%d",a + i);
    }
    for(int i = 1;i <= n ;i ++)
    dp[i][i][0] = 1;
    for(int l = 2;l <= n;l ++){
        for(int i = 1;i <= n - l + 1;i ++){
            int j = i + l - 1;
            if(a[i] < a[i+1])(dp[i][j][0] += dp[i+1][j][0])%mo;
            if(a[i] < a[j])(dp[i][j][0] += dp[i+1][j][1])%mo;
            if(a[j] > a[j-1])(dp[i][j][1] += dp[i][j-1][1])%mo;
            if(a[j] > a[i])(dp[i][j][1] += dp[i][j-1][0])%mo;
            dp[i][j][0] %= mo;dp[i][j][1] %= mo;
        }
    }
    printf("%d",(dp[1][n][0] + dp[1][n][1])%mo);
    return 0;
}

货物分组

#include<iostream>
#include<cstring>
#include<cstdio>
#include<algorithm>
#include<queue>
#include<set>
#include<vector>
#include<cmath>
using namespace std;
typedef long long ll;
const int maxn = 5001;
int n,m;
ll sum[maxn];
int a[maxn],ans = 1e9 + 7;
ll dp[maxn];
int main()
{
    scanf("%d%d",&n,&m);
    for(int i = 1;i <= n;i ++){
        scanf("%d",&a[i]);
        sum[i] = sum[i - 1] + a[i];
    }
    memset(dp,0x3f,sizeof dp);
    dp[0] = 0;
    for(int i = 1;i <= n;i ++){
        int mx = 0,mn = 1e9 + 7;
        for(int j = i;j >= 1;j --){
            if(sum[i] - sum[j-1] > m)break;
            mx = max(mx,a[j]);
            mn = min(mn,a[j]);
            dp[i] = min(dp[i],dp[j-1] + mx - mn + sum[n] - sum[j-1]);
        }
    }
    cout<<dp[n]<<endl;
    return 0;
}

来源：https://www.cnblogs.com/wtz2333/p/12233123.html

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