Codeforces 1221D

题意

对于n个栅栏,对于每个(i),有高度(a[i]),对于任意(2<=i<=n),有(a[i] ot=a[i-1]),则称该组栅栏为好栅栏,每个栅栏可花费(b[i])提升(1)个高度(可无限提升)。给一组栅栏,问最少花费多少可以将这组栅栏变为好栅栏。

分析

对于第(i)个栅栏,他要保证不与第(i-1)(i+1)个栅栏相同,最多提升(2),如果提升(2)与第(i-1)(i+1)相同,则可选择提升(0)(1),同理如果此时与另一侧栅栏相同,则可提升(0)(1)使该栅栏与两侧栅栏不同。题意给出其实提醒了(DP)(说(a[i] ot= a[i-1]))。我们设置(DP[i][j])表示对于第(i)个栅栏,提升(j)后,使得前(i)个栅栏为好栅栏,(0<=j<=2)
((1))对于(a[i]=a[i-1])的情况
如果第(i)个栅栏提升(0),则第(i-1)个栅栏需提升(1)或者(2),那么有

[dp[i][0] = min(dp[i - 1][1], dp[i - 1][2] ]

如果第(i)个栅栏提升(1),则第(i-1)个栅栏需提升(0)或者(2),那么有

[dp[i][1] = min(dp[i - 1][0], dp[i - 1][2]) + b[i] ]

如果第(i)个栅栏提升(2),则第(i-1)个栅栏需提升(0)或者(1),那么有

[dp[i][2] = min(dp[i - 1][0], dp[i - 1][1]) + b[i] * 2 ]

((2))对于(a[i]=a[i-1]+1)的情况
如果第(i)个栅栏提升(0),则第(i-1)个栅栏需提升(0)或者(2),那么有

[dp[i][0] = min(dp[i - 1][0], dp[i - 1][2]) ]

如果第(i)个栅栏提升(1),则第(i-1)个栅栏需提升(0)或者(1),那么有

[dp[i][1] = min(dp[i - 1][0], dp[i - 1][1]) + b[i] ]

如果第(i)个栅栏提升(2),则第(i-1)个栅栏需提升(0)或者(1)或者(2),那么有

[dp[i][2] = min(dp[i - 1][0], min(dp[i - 1][1],dp[i-1][2])) + b[i] * 2 ]

((3))对于(a[i]=a[i-1]+2)的情况
如果第(i)个栅栏提升(0),则第(i-1)个栅栏需提升(0)或者(1),那么有

[dp[i][0] = min(dp[i - 1][0], dp[i - 1][1]) ]

如果第(i)个栅栏提升(1),则第(i-1)个栅栏需提升(0)或者(1)或者(2),那么有

[dp[i][1] = min(dp[i - 1][0], min(dp[i - 1][1], dp[i - 1][2])) + b[i] ]

如果第(i)个栅栏提升(2),则第(i-1)个栅栏需提升(0)或者(1)或者(2),那么有

[dp[i][2] = min(dp[i - 1][0], min(dp[i - 1][1], dp[i - 1][2])) + b[i] * 2 ]

((4))对于(a[i]=a[i-1]-1)的情况
如果第(i)个栅栏提升(0),则第(i-1)个栅栏需提升(0)或者(1)或者(2),那么有

[dp[i][0] = min(dp[i - 1][0], min(dp[i - 1][1], dp[i - 1][2])) ]

如果第(i)个栅栏提升(1),则第(i-1)个栅栏需提升(1)或者(2),那么有

[dp[i][1] = min(dp[i - 1][1], dp[i - 1][2]) + b[i] ]

如果第(i)个栅栏提升(2),则第(i-1)个栅栏需提升(0)或者(2),那么有

[dp[i][2] = min(dp[i - 1][0], dp[i - 1][2]) + b[i] * 2 ]

((5))对于(a[i]=a[i-1]-2)的情况
如果第(i)个栅栏提升(0),则第(i-1)个栅栏需提升(0)或者(1)或者(2),那么有

[dp[i][0] = min(dp[i - 1][0], min(dp[i - 1][1], dp[i - 1][2])) ]

如果第(i)个栅栏提升(1),则第(i-1)个栅栏需提升(0)或者(1)或者(2),那么有

[dp[i][1] = min(dp[i - 1][0], min(dp[i - 1][1], dp[i - 1][2])) + b[i] ]

如果第(i)个栅栏提升(2),则第(i-1)个栅栏需提升(1)或者(2),那么有

[dp[i][2] = min(dp[i - 1][1], dp[i - 1][2]) + b[i] * 2 ]

((6)其他情况 第)i$个栅栏提升(0,1,2),第(i-1)个栅栏可提升(0)或者(1)或者(2),有

[dp[i][0] = min(dp[i - 1][0], min(dp[i - 1][1], dp[i - 1][2])) ]

[dp[i][1] = min(dp[i - 1][0], min(dp[i - 1][1], dp[i - 1][2])) + b[i] ]

[dp[i][2] = min(dp[i - 1][0], min(dp[i - 1][1], dp[i - 1][2])) + b[i] * 2 ]

最后输出(min(dp[n][0], min(dp[n][1], dp[n][2])))即可

#pragma GCC optimize(3, "Ofast", "inline")

#include <bits/stdc++.h>

#define start ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
#define ll long long
#define int ll
#define ls st<<1
#define rs st<<1|1
#define pii pair<int,int>
using namespace std;
const int maxn = (ll) 3e5 + 5;
const int mod = 1000000007;
const int inf = 0x3f3f3f3f;
int dp[maxn][3];
int a[maxn], b[maxn];

signed main() {
    start;
    int q;
    cin >> q;
    while (q--) {
        int n;
        cin >> n;
        for (int i = 1; i <= n; ++i) {
            cin >> a[i] >> b[i];
            dp[i][0] = dp[i][1] = (ll) (1e18) + 5;//千万不能用memset
        }
        /*初始化*/
        dp[1][0] = 0;
        dp[1][1] = b[1];
        dp[1][2] = b[1] * 2;
        for (int i = 2; i <= n; ++i) {
            if (a[i] == a[i - 1]) {
                dp[i][0] = min(dp[i - 1][1], dp[i - 1][2]);
                dp[i][1] = min(dp[i - 1][0], dp[i - 1][2]) + b[i];
                dp[i][2] = min(dp[i - 1][0], dp[i - 1][1]) + b[i] * 2;
            } else if (a[i] == a[i - 1] + 1) {
                dp[i][0] = min(dp[i - 1][0], dp[i - 1][2]);
                dp[i][1] = min(dp[i - 1][0], dp[i - 1][1]) + b[i];
                dp[i][2] = min(dp[i - 1][0], min(dp[i - 1][1],dp[i-1][2])) + b[i] * 2;
            } else if (a[i] == a[i - 1] + 2) {
                dp[i][0] = min(dp[i - 1][0], dp[i - 1][1]);
                dp[i][1] = min(dp[i - 1][0], min(dp[i - 1][1], dp[i - 1][2])) + b[i];
                dp[i][2] = min(dp[i - 1][0], min(dp[i - 1][1], dp[i - 1][2])) + b[i] * 2;
            } else if (a[i] == a[i - 1] - 1) {
                dp[i][0] = min(dp[i - 1][0], min(dp[i - 1][1], dp[i - 1][2]));
                dp[i][1] = min(dp[i - 1][1], dp[i - 1][2]) + b[i];
                dp[i][2] = min(dp[i - 1][0], dp[i - 1][2]) + b[i] * 2;
            } else if (a[i] == a[i - 1] - 2) {
                dp[i][0] = min(dp[i - 1][0], min(dp[i - 1][1], dp[i - 1][2]));
                dp[i][1] = min(dp[i - 1][0], min(dp[i - 1][1], dp[i - 1][2])) + b[i];
                dp[i][2] = min(dp[i - 1][1], dp[i - 1][2]) + b[i] * 2;
            } else {
                dp[i][0] = min(dp[i - 1][0], min(dp[i - 1][1], dp[i - 1][2]));
                dp[i][1] = min(dp[i - 1][0], min(dp[i - 1][1], dp[i - 1][2])) + b[i];
                dp[i][2] = min(dp[i - 1][0], min(dp[i - 1][1], dp[i - 1][2])) + b[i] * 2;
            }
        }
        cout << min(dp[n][0], min(dp[n][1], dp[n][2])) << '
';
    }
    return 0;
}

(这题我竟然和一个吉尔吉斯斯坦的小姐姐代码撞了,被判重然后unrated,哭了)

原文地址:https://www.cnblogs.com/F-Mu/p/11561159.html