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Link to the respondentem quaestionem:188. Optimum tempus emere et vendere nervo IV - LeetCode

Niuke nexus thematis respondentis:Optimum tempus emere et vendere nervo (4)_Niuke Topic_Niuke.com (nowcoder.com)

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1. Duis thema

1、Status representation

Ut clarius distinguamusemptumetvendere, repone cumHave stocksetnulla stirpeDuae civitates.

• f[i][j]: Nequaquam. ego In fine diei factum j transaction, currently inHave stocksMaximum commodum rei publicae.
• g[i][j]: Nequaquam. ego In fine diei factum j transaction, currently innulla stirpeMaximum commodum rei publicae.

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2. Transitus rei publicae aequationis

for* f*[i][j]sunt etiam duae condiciones in quibus ego Post dies completus j Res, in manu ad hoc tempusHave stocksstatus:

• exist i-1 in caelo, in manibusHave stockset negotiatus est j SECUNDUS. Pridie i-mo die nihil.Reditus in hoc tempore est f[i - 1][j]。
• exist i-1 in caelo, in manibusnon stockset negotiatus est j SECUNDUS.In primisego Cum sol cecidit, uncias emi tessera.Sicego In fine diei ligna funt.Reditus in hoc tempore estg[i - 1][j] - prices[i]。

In his duobus casibus quid opus est?maximum valoremita status aequationis ipsius f transitus est;

f[i][j] = max(f[i - 1][j], g[i - 1][j] - prices[i]

for* g*[i][j], duas sequentes condiciones in quibus possumus ego Post dies completus j Res, in manu ad hoc tempusnon stocksstatus:

• exist i-1 In die diei lignum in manibus meis non habui et eas dedi. j SECUNDUS.I-th die nihil .Reditus in hoc tempore estg[i - 1][j]。
• exist i-1 Die aurorae nervum habui in manibus meis, et dedi ea. j - 1 SECUNDUS.In primisego Cum serenum est, put Truncus venditus.Sicego In fine diei, negotiamur j SECUNDUS.Reditus in hoc tempore est f[i - 1][j - 1] + pretia[i]。

In his duobus casibus quid opus est?maximum valorem,ergo g* Aequatio status transitus est:

g[i][j] = max(g[i - 1][j], f[i - 1][j - 1] + prices[i])

Negotiatio inter eos talis est:

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3. Initialization

• cum in 0 diebus non solum inemit semelstatus, reditus in hoc tempore est -Prices[0] ,quodhoc f[0][0] = - prices[0] 。
• ut accipere max Cum, aliqui nullae civitatesNulla impedimentummunus, omnes nos initialize sicut -INF(ususINT_MIN Per calculi processus eruntredundantiamPericulum hic INF Accipe dimidium 0x3f3f3f3f satis, parvum).

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4、Ordo impletionis in forma

Imple in utroque ordine a summo ad imum, ordinem quemque a sinistro ad dextrum, et imple utrasque tabulas simul.

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5、reditus valorem

Redit valorem maximum in re publica venditionis, sed quotiens negotiatus est nescimus, unde redit g* Maxima vis in ultimo ordine tabulae.

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6、ipsum

Numerus negotiorum noster dimidium totius numeri dierum non excedens, primum ergo possumus k Cum ea agamus et magnitudinem problematum optimize:k = min(k, n / 2)。

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2. Codicis

//力扣
//【动态规划-二维dp-2个状态】
class Solution {
    //f[i][j]:第i天结束后，完成了j次交易，此时处于“买入”状态下的最大利润
    //g[i][j]:第i天结束后，完成了j次交易，此时处于“卖出”状态下的最大利润
private:
    const int INF=0x3f3f3f3f;
public:
    int maxProfit(int k, vector<int>& prices) {
        int n=prices.size();
        k=min(k, n/2); //优化:处理最多交易次数
        vector<vector<int>> f(n, vector<int>(k+1, -INF));
        vector<vector<int>> g(n, vector<int>(k+1, -INF));
        f[0][0]=-prices[0], g[0][0]=0;
        for(int i=1; i<n; i++)
        {
            for(int j=0; j<=k; j++)
            {
                f[i][j]=max(f[i-1][j], g[i-1][j]-prices[i]);
                g[i][j]=g[i-1][j];
                if(j>=1) g[i][j]=max(g[i][j], f[i-1][j-1]+prices[i]);
            }
        }
        int res=0;
        for(int j=0; j<=k; j++)
            res=max(res, g[n-1][j]);
        return res;
    }
};
 
//【动态规划-二维dp-2k+1个状态】
class Solution {
    //dp[i][0] -- 没有操作
    //下面j为奇数：买入；j为偶数：卖出 (j的范围：1~2k-1)
    //dp[i][j] -- 第1~k次买入
    //dp[i][j+1] -- 第1~k次卖出
public:
    int maxProfit(int k, vector<int>& prices) {
        int n=prices.size();
        vector<vector<int>> dp(n, vector<int>(2*k+1));
        for(int j=1; j<2*k; j+=2)
            dp[0][j]=-prices[0];
        for(int i=1; i<n; i++)
        {
            for(int j=0; j<2*k; j+=2)
            {
                dp[i][j+1]=max(dp[i-1][j+1], dp[i-1][j]-prices[i]);
                dp[i][j+2]=max(dp[i-1][j+2], dp[i-1][j+1]+prices[i]);
            }
        }
        return dp[n-1][2*k];
    }
};

//牛客
#include <iostream>
#include <cstring>
using namespace std;
 
const int INF=0x3f3f3f3f;
const int N=1010, M=110;
int prices[N];
int f[N][M], g[N][M];
//f[i][j]:第i天结束后，完成了j次交易，此时处于“买入”状态下的最大利润
//g[i][j]:第i天结束后，完成了j次交易，此时处于“卖出”状态下的最大利润
 
int main()
{
    int n, k;
    cin >> n >> k;
    for(int i=0; i<n; i++)
        cin >> prices[i];
    memset(f, -INF, sizeof(f));
    memset(g, -INF, sizeof(g));
    int res=0;
    f[0][0]=-prices[0], g[0][0]=0;
    for(int i=1; i<n; i++)
    {
        for(int j=0; j<=k; j++)
        {
            f[i][j]=max(f[i-1][j], g[i-1][j]-prices[i]);
            g[i][j]=g[i-1][j];
            if(j>0) g[i][j]=max(g[i][j], f[i-1][j-1]+prices[i]);
            res=max(res, g[i][j]);
        }
    }
    cout << res << endl;
    return 0;
}
 
//值得学习的代码
#include <iostream>
using namespace std;
 
const int N = 1010, M = 110;
 
int n, k, p[N];
int f[N][M], g[N][M];
 
int main()
{
    cin >> n >> k;
    for(int i = 0; i < n; i++) cin >> p[i];
 
    k = min(k, n / 2);
    for(int j = 0; j <= k; j++) f[0][j] = g[0][j] = -0x3f3f3f3f;
    f[0][0] = -p[0], g[0][0] = 0;
 
    for(int i = 1; i < n; i++)
    {
        for(int j = 0; j <= k; j++)
        {
            f[i][j] = max(f[i - 1][j], g[i - 1][j] - p[i]);
            g[i][j] = g[i - 1][j];
            if(j >= 1) g[i][j] = max(g[i][j], f[i - 1][j - 1] + p[i]);
        }
    }
 
    int ret = 0;
    for(int j = 0; j <= k; j++) ret = max(ret, g[n - 1][j]);
 
    cout << ret << endl;
 
    return 0;
}

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3. Meditatio et emendationem

Series quaestionum quasi nervum emptionis et venditionis accuratam familiaritatem cum punctorum cognitionis requirit.