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2291. Maximum Profit From Trading Stocks 👍

Approach 1: 2D DP

  • Time: $O(n\cdot\texttt{budget})$
  • Space: $O(n\cdot\texttt{budget})$
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class Solution {
 public:
  int maximumProfit(vector<int>& present, vector<int>& future, int budget) {
    const int n = present.size();
    // dp[i][j] := max profit of buying present[0..i) with j budget
    vector<vector<int>> dp(n + 1, vector<int>(budget + 1));

    for (int i = 1; i <= n; ++i) {
      const int profit = future[i - 1] - present[i - 1];
      for (int j = 0; j <= budget; ++j)
        if (j < present[i - 1])
          dp[i][j] = dp[i - 1][j];
        else
          dp[i][j] = max(dp[i - 1][j], profit + dp[i - 1][j - present[i - 1]]);
    }

    return dp[n][budget];
  }
};

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class Solution {
  public int maximumProfit(int[] present, int[] future, int budget) {
    final int n = present.length;
    // dp[i][j] := max profit of buying present[0..i) with j budget
    int[][] dp = new int[n + 1][budget + 1];

    for (int i = 1; i <= n; ++i) {
      final int profit = future[i - 1] - present[i - 1];
      for (int j = 0; j <= budget; ++j)
        if (j < present[i - 1])
          dp[i][j] = dp[i - 1][j];
        else
          dp[i][j] = Math.max(dp[i - 1][j], profit + dp[i - 1][j - present[i - 1]]);
    }

    return dp[n][budget];
  }
}

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class Solution:
  def maximumProfit(self, present: List[int], future: List[int], budget: int) -> int:
    n = len(present)
    # dp[i][j] := max profit of buying present[0..i) with j budget
    dp = [[0] * (budget + 1) for _ in range(n + 1)]

    for i in range(1, n + 1):
      profit = future[i - 1] - present[i - 1]
      for j in range(budget + 1):
        if j < present[i - 1]:
          dp[i][j] = dp[i - 1][j]
        else:
          dp[i][j] = max(dp[i - 1][j], profit + dp[i - 1][j - present[i - 1]])

    return dp[n][budget]

Approach 2: 1D DP

  • Time: $O(n\cdot\texttt{budget})$
  • Space: $O(\texttt{budget})$
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class Solution {
 public:
  int maximumProfit(vector<int>& present, vector<int>& future, int budget) {
    const int n = present.size();
    // dp[i] := max profit of buying present so far with i budget
    vector<int> dp(budget + 1);

    for (int i = 0; i < n; ++i)
      for (int j = budget; j >= present[i]; --j)
        dp[j] = max(dp[j], future[i] - present[i] + dp[j - present[i]]);

    return dp[budget];
  }
};

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class Solution {
  public int maximumProfit(int[] present, int[] future, int budget) {
    final int n = present.length;
    // dp[i] := max profit of buying present so far with i budget
    int[] dp = new int[budget + 1];

    for (int i = 0; i < n; ++i)
      for (int j = budget; j >= present[i]; --j)
        dp[j] = Math.max(dp[j], future[i] - present[i] + dp[j - present[i]]);

    return dp[budget];
  }
}

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class Solution:
  def maximumProfit(self, present: List[int], future: List[int], budget: int) -> int:
    n = len(present)
    # dp[i] := max profit of buying present so far with i budget
    dp = [0] * (budget + 1)

    for p, f in zip(present, future):
      for j in range(budget, p - 1, -1):
        dp[j] = max(dp[j], f - p + dp[j - p])

    return dp[budget]