Problem Link :- GFG POTD
Problem statement
Given two arrays A[] and B[] of same length N. There are N types of sticks of lengths specified. Each stick of length A[i] is present in B[i] units (i=1 to N). You have to construct the squares and rectangles using these sticks. Each unit of a stick can be used as length or breadth of a rectangle or as a side of square. A single unit of a stick can be used only once.
Let S be the sum of lengths of all sticks that are used in constructing squares and rectangles. The task is to calulate the maximum possible value of S.
Let S be the sum of lengths of all sticks that are used in constructing squares and rectangles. The task is to calulate the maximum possible value of S.
Significance of problem
The "Maximum Possible Value" problem holds significance in its practical application to optimization challenges, particularly in resource allocation scenarios. In real-world contexts, this problem models the efficient utilization of resources represented by sticks of varying lengths. The task involves constructing squares and rectangles, where each stick unit contributes to the total sum.
The problem addresses the optimization of resource usage, reflecting scenarios where maximizing the utility of available resources is crucial. This is analogous to situations in manufacturing, construction, or project planning, where materials must be allocated efficiently to achieve the desired outcome.
Furthermore, the problem emphasizes the importance of strategic decision-making in utilizing resources. The code solution demonstrates a thoughtful approach by considering pairs of sticks for constructing rectangles, thereby maximizing the overall sum. The incorporation of conditions for odd pair counts showcases the adaptability required in real-world problem-solving, where constraints and conditions often influence decision-making.
Moreover, the problem encapsulates the concept of trade-offs in resource optimization. The decision to subtract twice the minimum stick length in certain cases highlights the need for balancing the desire to maximize the sum with the limitations imposed by the available resources.
In essence, mastering the "Maximum Possible Value" problem equips learners with insights into resource optimization strategies applicable across various domains. The problem's practical representation of efficiently utilizing sticks for constructing squares and rectangles provides a valuable foundation for tackling analogous challenges in real-world scenarios, where optimal resource allocation is paramount for achieving desired outcomes.
The problem addresses the optimization of resource usage, reflecting scenarios where maximizing the utility of available resources is crucial. This is analogous to situations in manufacturing, construction, or project planning, where materials must be allocated efficiently to achieve the desired outcome.
Furthermore, the problem emphasizes the importance of strategic decision-making in utilizing resources. The code solution demonstrates a thoughtful approach by considering pairs of sticks for constructing rectangles, thereby maximizing the overall sum. The incorporation of conditions for odd pair counts showcases the adaptability required in real-world problem-solving, where constraints and conditions often influence decision-making.
Moreover, the problem encapsulates the concept of trade-offs in resource optimization. The decision to subtract twice the minimum stick length in certain cases highlights the need for balancing the desire to maximize the sum with the limitations imposed by the available resources.
In essence, mastering the "Maximum Possible Value" problem equips learners with insights into resource optimization strategies applicable across various domains. The problem's practical representation of efficiently utilizing sticks for constructing squares and rectangles provides a valuable foundation for tackling analogous challenges in real-world scenarios, where optimal resource allocation is paramount for achieving desired outcomes.
Easiest Explanation
Imagine you have two arrays, A and B, and they both have the same number of elements, which we'll call N. Each element of A represents the length of a type of stick, and each element of B represents the number of units of that type of stick that you have.
Now, you want to construct as many squares and rectangles as possible using these sticks. You can use a single unit of a stick as either the length or the breadth of a rectangle, or as a side of a square. However, you can only use each unit of a stick once.
Your goal is to maximize the sum of the lengths of all the sticks that you use in constructing squares and rectangles. In other words, you want to use as many sticks as possible and use them as efficiently as possible to make the biggest shapes you can.
So, the question is asking you to find the maximum possible value of the sum of the lengths of all the sticks that you use to make squares and rectangles.But to find maximum possible values we will be using only rectangle
I hope that explanation helps! If you find any difficulty in solving, feel free to comment with your doubts.
Now, you want to construct as many squares and rectangles as possible using these sticks. You can use a single unit of a stick as either the length or the breadth of a rectangle, or as a side of a square. However, you can only use each unit of a stick once.
Your goal is to maximize the sum of the lengths of all the sticks that you use in constructing squares and rectangles. In other words, you want to use as many sticks as possible and use them as efficiently as possible to make the biggest shapes you can.
So, the question is asking you to find the maximum possible value of the sum of the lengths of all the sticks that you use to make squares and rectangles.But to find maximum possible values we will be using only rectangle
I hope that explanation helps! If you find any difficulty in solving, feel free to comment with your doubts.
class Solution { public: long long maxPossibleValue(int N,vector<int> A, vector<int> B) { long long ans=0; int mini = INT_MAX; long long cnt=0; for(int i=0;i<N;i++){ int pair = B[i]/2; ans+=(2*pair*A[i]); mini = min(mini,A[i]); cnt+=pair; } if(cnt%2!=0) return ans -= 2*mini; return ans; } };
Here's how the function works:
1. This code defines a class named Solution.
2. The Solution class contains a single function, "maxPossibleValue".
3. The "maxPossibleValue" function takes in three arguments: an integer "N" and two vectors "A" and "B", representing the number of stick types, the lengths of each stick type, and the number of units of each stick type, respectively. The function returns a long long integer.
4. In the "maxPossibleValue" function, we initialize three variables: "ans" (which will hold the maximum possible sum of lengths), "mini" (which will hold the length of the shortest stick type), and "cnt" (which will count the total number of sticks used).
5. We loop through all N stick types, and for each one, we calculate the number of pairs of sticks we can use to make squares or rectangles. We add twice the product of this number and the length of the stick type to "ans" (since each pair of sticks contributes twice the length of a single stick).
6. We update "mini" to be the minimum length of all the stick types we've seen so far.
7. We add the number of pairs of sticks we used to "cnt".
8. If "cnt" is odd (i.e., we used an odd number of sticks), we subtract twice "mini" from "ans" (since we can use two of the shortest sticks to form a single square or rectangle).
9. We return "ans", which is the maximum possible sum of lengths we can achieve using the given sticks to form squares and rectangles.
2. The Solution class contains a single function, "maxPossibleValue".
3. The "maxPossibleValue" function takes in three arguments: an integer "N" and two vectors "A" and "B", representing the number of stick types, the lengths of each stick type, and the number of units of each stick type, respectively. The function returns a long long integer.
4. In the "maxPossibleValue" function, we initialize three variables: "ans" (which will hold the maximum possible sum of lengths), "mini" (which will hold the length of the shortest stick type), and "cnt" (which will count the total number of sticks used).
5. We loop through all N stick types, and for each one, we calculate the number of pairs of sticks we can use to make squares or rectangles. We add twice the product of this number and the length of the stick type to "ans" (since each pair of sticks contributes twice the length of a single stick).
6. We update "mini" to be the minimum length of all the stick types we've seen so far.
7. We add the number of pairs of sticks we used to "cnt".
8. If "cnt" is odd (i.e., we used an odd number of sticks), we subtract twice "mini" from "ans" (since we can use two of the shortest sticks to form a single square or rectangle).
9. We return "ans", which is the maximum possible sum of lengths we can achieve using the given sticks to form squares and rectangles.
Learning Outcomes
Solving the "Maximum Possible Value" problem yields several valuable learning outcomes. Firstly, learners develop a deeper understanding of resource optimization strategies. The task of constructing squares and rectangles from sticks mirrors real-world scenarios where efficient resource allocation is essential for maximizing utility, such as in construction projects or manufacturing processes.
Secondly, learners enhance their proficiency in strategic decision-making. The code solution's approach to considering pairs of sticks for constructing rectangles illustrates the importance of thoughtful decision-making in utilizing resources effectively. This skill is transferable to various domains where optimizing resource usage is a key aspect of problem-solving.
Moreover, learners cultivate adaptability in handling constraints. The inclusion of conditions for odd pair counts in the code demonstrates the ability to navigate and accommodate specific scenarios, a crucial skill in real-world problem-solving where conditions and constraints influence decision-making.
Furthermore, the problem instills the concept of trade-offs. The decision to subtract twice the minimum stick length in certain cases highlights the need for balancing optimization goals with practical limitations imposed by the available resources.
Secondly, learners enhance their proficiency in strategic decision-making. The code solution's approach to considering pairs of sticks for constructing rectangles illustrates the importance of thoughtful decision-making in utilizing resources effectively. This skill is transferable to various domains where optimizing resource usage is a key aspect of problem-solving.
Moreover, learners cultivate adaptability in handling constraints. The inclusion of conditions for odd pair counts in the code demonstrates the ability to navigate and accommodate specific scenarios, a crucial skill in real-world problem-solving where conditions and constraints influence decision-making.
Furthermore, the problem instills the concept of trade-offs. The decision to subtract twice the minimum stick length in certain cases highlights the need for balancing optimization goals with practical limitations imposed by the available resources.
Conclusion
In conclusion, the "Maximum Possible Value" problem encapsulates essential principles in resource optimization, strategic decision-making, adaptability, and trade-offs. Its real-world applicability is evident in scenarios where efficient resource allocation is paramount, echoing challenges encountered in construction, manufacturing, and project planning. The code solution exemplifies a thoughtful approach to maximize the utility of stick units, providing learners with practical insights into tackling analogous challenges.
This problem fosters a holistic understanding of optimization strategies, emphasizing the importance of strategic decisions to maximize resource utilization. Moreover, the consideration of constraints and adaptability in handling specific scenarios reflects the dynamic nature of problem-solving in real-world contexts. The concept of trade-offs, highlighted by subtracting twice the minimum stick length in certain cases, underscores the need for a balanced approach between optimization goals and practical limitations.
In essence, mastering the "Maximum Possible Value" problem equips learners with a versatile skill set applicable across diverse domains, providing a foundational understanding of resource allocation challenges and reinforcing the broader concepts of optimization in computational problem-solving.
This problem fosters a holistic understanding of optimization strategies, emphasizing the importance of strategic decisions to maximize resource utilization. Moreover, the consideration of constraints and adaptability in handling specific scenarios reflects the dynamic nature of problem-solving in real-world contexts. The concept of trade-offs, highlighted by subtracting twice the minimum stick length in certain cases, underscores the need for a balanced approach between optimization goals and practical limitations.
In essence, mastering the "Maximum Possible Value" problem equips learners with a versatile skill set applicable across diverse domains, providing a foundational understanding of resource allocation challenges and reinforcing the broader concepts of optimization in computational problem-solving.
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