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Code Implementation

Tallest Billboard Implementation

Below is the implementation of the tallest billboard:

solution.js

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/**
 * Find the tallest billboard installation.
 * Dynamic Programming with Difference State approach.
 *
 * @param {number[]} rods - Array of rod lengths
 * @return {number} - The largest possible height of the billboard
 */
function tallestBillboard(rods) {
  // Initialize dp map
  const dp = new Map();
  dp.set(0, 0);  // With no rods used, both supports have height 0
 
  for (const rod of rods) {
    // Create a copy of the current dp map
    const currentDp = new Map(dp);
 
    for (const [diff, height] of currentDp) {
      // Option 1: Add rod to the taller support
      if (diff >= 0) {
        dp.set(diff + rod, Math.max(dp.get(diff + rod) || 0, height));
      } else {
        if (diff + rod >= 0) {
          dp.set(diff + rod, Math.max(dp.get(diff + rod) || 0, height + rod + diff));
        } else {
          dp.set(diff + rod, Math.max(dp.get(diff + rod) || 0, height));
        }
      }
 
      // Option 2: Add rod to the shorter support
      if (diff >= 0) {
        if (diff - rod >= 0) {
          dp.set(diff - rod, Math.max(dp.get(diff - rod) || 0, height + rod));
        } else {
          dp.set(rod - diff, Math.max(dp.get(rod - diff) || 0, height + diff));
        }
      } else {
        dp.set(diff - rod, Math.max(dp.get(diff - rod) || 0, height));
      }
    }
  }
 
  return dp.get(0) || 0;  // Return the maximum height when both supports have the same height
}
 
/**
 * Find the tallest billboard installation.
 * Simplified Dynamic Programming approach.
 *
 * @param {number[]} rods - Array of rod lengths
 * @return {number} - The largest possible height of the billboard
 */
function tallestBillboardSimplified(rods) {
  // Initialize dp map
  const dp = new Map();
  dp.set(0, 0);  // With no rods used, both supports have height 0
 
  for (const rod of rods) {
    // Create a copy of the current dp map
    const currentDp = new Map(dp);
 
    for (const [diff, height] of currentDp) {
      // Option 1: Add rod to the first support
      dp.set(diff + rod, Math.max(dp.get(diff + rod) || 0, height + rod));
 
      // Option 2: Add rod to the second support
      dp.set(diff - rod, Math.max(dp.get(diff - rod) || 0, height));
    }
  }
 
  return dp.get(0) || 0;  // Return the maximum height when both supports have the same height
}
 
// Test cases
console.log(tallestBillboard([1, 2, 3, 6]));  // 6
console.log(tallestBillboard([1, 2, 3, 4, 5, 6]));  // 10
console.log(tallestBillboard([1, 2]));  // 0
 
console.log(tallestBillboardSimplified([1, 2, 3, 6]));  // 6
console.log(tallestBillboardSimplified([1, 2, 3, 4, 5, 6]));  // 10
console.log(tallestBillboardSimplified([1, 2]));  // 0

Step-by-Step Explanation

Let's break down the implementation:

Understand the Problem: First, understand that we need to find the maximum height of a billboard with two equal-height supports, using a collection of rods.
Define the State: Define the state dp[diff] as the maximum height of the shorter support when the difference between the heights of the two supports is diff.
Consider All Options: For each rod, consider three options: add it to the taller support, add it to the shorter support, or don't use it.
Handle Edge Cases: Handle edge cases such as when the difference becomes negative or when a support becomes taller than the other after adding a rod.
Return the Result: Return dp[0], which represents the maximum height when both supports have the same height.

Previous Next

String Problems

Palindrome Checker

Determine if a string reads the same forward and backward.

EasyString Manipulation

Message Encryption

Reverse a string to create a simple encryption system.

EasyString Manipulation

Word Puzzle Challenge

Check if two strings are anagrams of each other.

EasyString Manipulation

Learning Objective

Implement the tallest billboard solution in different programming languages.

Tallest Billboard Implementation

Below is the implementation of the tallest billboard in different programming languages. Select a language tab to view the corresponding code.

solution.js

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/**
 * Find the tallest billboard installation.
 * Dynamic Programming with Difference State approach.
 *
 * @param {number[]} rods - Array of rod lengths
 * @return {number} - The largest possible height of the billboard
 */
function tallestBillboard(rods) {
  // Initialize dp map
  const dp = new Map();
  dp.set(0, 0);  // With no rods used, both supports have height 0
 
  for (const rod of rods) {
    // Create a copy of the current dp map
    const currentDp = new Map(dp);
 
    for (const [diff, height] of currentDp) {
      // Option 1: Add rod to the taller support
      if (diff >= 0) {
        dp.set(diff + rod, Math.max(dp.get(diff + rod) || 0, height));
      } else {
        if (diff + rod >= 0) {
          dp.set(diff + rod, Math.max(dp.get(diff + rod) || 0, height + rod + diff));
        } else {
          dp.set(diff + rod, Math.max(dp.get(diff + rod) || 0, height));
        }
      }
 
      // Option 2: Add rod to the shorter support
      if (diff >= 0) {
        if (diff - rod >= 0) {
          dp.set(diff - rod, Math.max(dp.get(diff - rod) || 0, height + rod));
        } else {
          dp.set(rod - diff, Math.max(dp.get(rod - diff) || 0, height + diff));
        }
      } else {
        dp.set(diff - rod, Math.max(dp.get(diff - rod) || 0, height));
      }
    }
  }
 
  return dp.get(0) || 0;  // Return the maximum height when both supports have the same height
}
 
/**
 * Find the tallest billboard installation.
 * Simplified Dynamic Programming approach.
 *
 * @param {number[]} rods - Array of rod lengths
 * @return {number} - The largest possible height of the billboard
 */
function tallestBillboardSimplified(rods) {
  // Initialize dp map
  const dp = new Map();
  dp.set(0, 0);  // With no rods used, both supports have height 0
 
  for (const rod of rods) {
    // Create a copy of the current dp map
    const currentDp = new Map(dp);
 
    for (const [diff, height] of currentDp) {
      // Option 1: Add rod to the first support
      dp.set(diff + rod, Math.max(dp.get(diff + rod) || 0, height + rod));
 
      // Option 2: Add rod to the second support
      dp.set(diff - rod, Math.max(dp.get(diff - rod) || 0, height));
    }
  }
 
  return dp.get(0) || 0;  // Return the maximum height when both supports have the same height
}
 
// Test cases
console.log(tallestBillboard([1, 2, 3, 6]));  // 6
console.log(tallestBillboard([1, 2, 3, 4, 5, 6]));  // 10
console.log(tallestBillboard([1, 2]));  // 0
 
console.log(tallestBillboardSimplified([1, 2, 3, 6]));  // 6
console.log(tallestBillboardSimplified([1, 2, 3, 4, 5, 6]));  // 10
console.log(tallestBillboardSimplified([1, 2]));  // 0

Step-by-Step Explanation

1Understand the Problem

First, understand that we need to find the maximum height of a billboard with two equal-height supports, using a collection of rods.

2Define the State

Define the state dp[diff] as the maximum height of the shorter support when the difference between the heights of the two supports is diff.

3Consider All Options

For each rod, consider three options: add it to the taller support, add it to the shorter support, or don't use it.

4Handle Edge Cases

Handle edge cases such as when the difference becomes negative or when a support becomes taller than the other after adding a rod.

5Return the Result

Return dp[0], which represents the maximum height when both supports have the same height.

Language-Specific Notes

javascript

JavaScript's Map object is used to store the dynamic programming state.
The Map.get() method returns undefined if the key doesn't exist, so we use the || operator to provide a default value of 0.
Math.max() is used to find the maximum of two values.
The for...of loop is used to iterate through arrays and Map entries.
The new Map(dp) constructor is used to create a copy of a Map.

python

Python's dictionary is used to store the dynamic programming state.
The dict.get() method returns a default value if the key doesn't exist.
The max() function is used to find the maximum of two values.
The dict.copy() method is used to create a copy of a dictionary.
The dict.items() method is used to iterate through key-value pairs in a dictionary.

java

Java's HashMap is used to store the dynamic programming state.
The Map.getOrDefault() method returns a default value if the key doesn't exist.
Math.max() is used to find the maximum of two values.
The new HashMap<>(dp) constructor is used to create a copy of a HashMap.
The Map.Entry interface is used to iterate through key-value pairs in a HashMap.

cpp

C++'s unordered_map is used to store the dynamic programming state.
The std::max() function is used to find the maximum of two values.
The unordered_map copy constructor is used to create a copy of an unordered_map.
The auto keyword and range-based for loop are used to iterate through key-value pairs in an unordered_map.
In C++, accessing a non-existent key in an unordered_map creates it with a default value (0 for int).

Key Takeaways

The problem can be solved using dynamic programming with a state that represents the difference between the heights of the two supports.
Using a hash map to store the state allows us to handle a wide range of possible differences efficiently.
Considering all three options for each rod (add to first support, add to second support, don't use) ensures we find the optimal solution.
The simplified approach provides a cleaner implementation with the same time and space complexity.

Try It Yourself

Modify the code to implement an alternative approach and test it with the same examples.

Challenge:

Implement a function that solves the tallest billboard problem using a different approach than shown above.

Common Edge Cases

No Solution

Handle the case where it's impossible to create two supports of equal height (return 0).

rods = [1, 2]

Single Rod

Handle the case where there's only one rod (return 0, as we can't create two equal-height supports with a single rod).

rods = [5]

Equal Rods

Handle the case where all rods have the same length, making it easy to create equal-height supports.

rods = [3, 3, 3, 3]

Solution Approach All Problems

Problem Solution Code

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Tallest Billboard - Implementation

Code Implementation

Tallest Billboard Implementation

Below is the implementation of the tallest billboard:

solution.js

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/**
 * Find the tallest billboard installation.
 * Dynamic Programming with Difference State approach.
 *
 * @param {number[]} rods - Array of rod lengths
 * @return {number} - The largest possible height of the billboard
 */
function tallestBillboard(rods) {
  // Initialize dp map
  const dp = new Map();
  dp.set(0, 0);  // With no rods used, both supports have height 0
 
  for (const rod of rods) {
    // Create a copy of the current dp map
    const currentDp = new Map(dp);
 
    for (const [diff, height] of currentDp) {
      // Option 1: Add rod to the taller support
      if (diff >= 0) {
        dp.set(diff + rod, Math.max(dp.get(diff + rod) || 0, height));
      } else {
        if (diff + rod >= 0) {
          dp.set(diff + rod, Math.max(dp.get(diff + rod) || 0, height + rod + diff));
        } else {
          dp.set(diff + rod, Math.max(dp.get(diff + rod) || 0, height));
        }
      }
 
      // Option 2: Add rod to the shorter support
      if (diff >= 0) {
        if (diff - rod >= 0) {
          dp.set(diff - rod, Math.max(dp.get(diff - rod) || 0, height + rod));
        } else {
          dp.set(rod - diff, Math.max(dp.get(rod - diff) || 0, height + diff));
        }
      } else {
        dp.set(diff - rod, Math.max(dp.get(diff - rod) || 0, height));
      }
    }
  }
 
  return dp.get(0) || 0;  // Return the maximum height when both supports have the same height
}
 
/**
 * Find the tallest billboard installation.
 * Simplified Dynamic Programming approach.
 *
 * @param {number[]} rods - Array of rod lengths
 * @return {number} - The largest possible height of the billboard
 */
function tallestBillboardSimplified(rods) {
  // Initialize dp map
  const dp = new Map();
  dp.set(0, 0);  // With no rods used, both supports have height 0
 
  for (const rod of rods) {
    // Create a copy of the current dp map
    const currentDp = new Map(dp);
 
    for (const [diff, height] of currentDp) {
      // Option 1: Add rod to the first support
      dp.set(diff + rod, Math.max(dp.get(diff + rod) || 0, height + rod));
 
      // Option 2: Add rod to the second support
      dp.set(diff - rod, Math.max(dp.get(diff - rod) || 0, height));
    }
  }
 
  return dp.get(0) || 0;  // Return the maximum height when both supports have the same height
}
 
// Test cases
console.log(tallestBillboard([1, 2, 3, 6]));  // 6
console.log(tallestBillboard([1, 2, 3, 4, 5, 6]));  // 10
console.log(tallestBillboard([1, 2]));  // 0
 
console.log(tallestBillboardSimplified([1, 2, 3, 6]));  // 6
console.log(tallestBillboardSimplified([1, 2, 3, 4, 5, 6]));  // 10
console.log(tallestBillboardSimplified([1, 2]));  // 0

Step-by-Step Explanation

Let's break down the implementation:

Understand the Problem: First, understand that we need to find the maximum height of a billboard with two equal-height supports, using a collection of rods.
Define the State: Define the state dp[diff] as the maximum height of the shorter support when the difference between the heights of the two supports is diff.
Consider All Options: For each rod, consider three options: add it to the taller support, add it to the shorter support, or don't use it.
Handle Edge Cases: Handle edge cases such as when the difference becomes negative or when a support becomes taller than the other after adding a rod.
Return the Result: Return dp[0], which represents the maximum height when both supports have the same height.

Previous Next

String Problems

Palindrome Checker

Determine if a string reads the same forward and backward.

EasyString Manipulation

Message Encryption

Reverse a string to create a simple encryption system.

EasyString Manipulation

Word Puzzle Challenge

Check if two strings are anagrams of each other.

EasyString Manipulation

Learning Objective

Implement the tallest billboard solution in different programming languages.

Tallest Billboard Implementation

Below is the implementation of the tallest billboard in different programming languages. Select a language tab to view the corresponding code.

solution.js

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/**
 * Find the tallest billboard installation.
 * Dynamic Programming with Difference State approach.
 *
 * @param {number[]} rods - Array of rod lengths
 * @return {number} - The largest possible height of the billboard
 */
function tallestBillboard(rods) {
  // Initialize dp map
  const dp = new Map();
  dp.set(0, 0);  // With no rods used, both supports have height 0
 
  for (const rod of rods) {
    // Create a copy of the current dp map
    const currentDp = new Map(dp);
 
    for (const [diff, height] of currentDp) {
      // Option 1: Add rod to the taller support
      if (diff >= 0) {
        dp.set(diff + rod, Math.max(dp.get(diff + rod) || 0, height));
      } else {
        if (diff + rod >= 0) {
          dp.set(diff + rod, Math.max(dp.get(diff + rod) || 0, height + rod + diff));
        } else {
          dp.set(diff + rod, Math.max(dp.get(diff + rod) || 0, height));
        }
      }
 
      // Option 2: Add rod to the shorter support
      if (diff >= 0) {
        if (diff - rod >= 0) {
          dp.set(diff - rod, Math.max(dp.get(diff - rod) || 0, height + rod));
        } else {
          dp.set(rod - diff, Math.max(dp.get(rod - diff) || 0, height + diff));
        }
      } else {
        dp.set(diff - rod, Math.max(dp.get(diff - rod) || 0, height));
      }
    }
  }
 
  return dp.get(0) || 0;  // Return the maximum height when both supports have the same height
}
 
/**
 * Find the tallest billboard installation.
 * Simplified Dynamic Programming approach.
 *
 * @param {number[]} rods - Array of rod lengths
 * @return {number} - The largest possible height of the billboard
 */
function tallestBillboardSimplified(rods) {
  // Initialize dp map
  const dp = new Map();
  dp.set(0, 0);  // With no rods used, both supports have height 0
 
  for (const rod of rods) {
    // Create a copy of the current dp map
    const currentDp = new Map(dp);
 
    for (const [diff, height] of currentDp) {
      // Option 1: Add rod to the first support
      dp.set(diff + rod, Math.max(dp.get(diff + rod) || 0, height + rod));
 
      // Option 2: Add rod to the second support
      dp.set(diff - rod, Math.max(dp.get(diff - rod) || 0, height));
    }
  }
 
  return dp.get(0) || 0;  // Return the maximum height when both supports have the same height
}
 
// Test cases
console.log(tallestBillboard([1, 2, 3, 6]));  // 6
console.log(tallestBillboard([1, 2, 3, 4, 5, 6]));  // 10
console.log(tallestBillboard([1, 2]));  // 0
 
console.log(tallestBillboardSimplified([1, 2, 3, 6]));  // 6
console.log(tallestBillboardSimplified([1, 2, 3, 4, 5, 6]));  // 10
console.log(tallestBillboardSimplified([1, 2]));  // 0

Step-by-Step Explanation

1Understand the Problem

First, understand that we need to find the maximum height of a billboard with two equal-height supports, using a collection of rods.

2Define the State

Define the state dp[diff] as the maximum height of the shorter support when the difference between the heights of the two supports is diff.

3Consider All Options

For each rod, consider three options: add it to the taller support, add it to the shorter support, or don't use it.

4Handle Edge Cases

Handle edge cases such as when the difference becomes negative or when a support becomes taller than the other after adding a rod.

5Return the Result

Return dp[0], which represents the maximum height when both supports have the same height.

Language-Specific Notes

javascript

JavaScript's Map object is used to store the dynamic programming state.
The Map.get() method returns undefined if the key doesn't exist, so we use the || operator to provide a default value of 0.
Math.max() is used to find the maximum of two values.
The for...of loop is used to iterate through arrays and Map entries.
The new Map(dp) constructor is used to create a copy of a Map.

python

Python's dictionary is used to store the dynamic programming state.
The dict.get() method returns a default value if the key doesn't exist.
The max() function is used to find the maximum of two values.
The dict.copy() method is used to create a copy of a dictionary.
The dict.items() method is used to iterate through key-value pairs in a dictionary.

java

Java's HashMap is used to store the dynamic programming state.
The Map.getOrDefault() method returns a default value if the key doesn't exist.
Math.max() is used to find the maximum of two values.
The new HashMap<>(dp) constructor is used to create a copy of a HashMap.
The Map.Entry interface is used to iterate through key-value pairs in a HashMap.

cpp

C++'s unordered_map is used to store the dynamic programming state.
The std::max() function is used to find the maximum of two values.
The unordered_map copy constructor is used to create a copy of an unordered_map.
The auto keyword and range-based for loop are used to iterate through key-value pairs in an unordered_map.
In C++, accessing a non-existent key in an unordered_map creates it with a default value (0 for int).

Key Takeaways

The problem can be solved using dynamic programming with a state that represents the difference between the heights of the two supports.
Using a hash map to store the state allows us to handle a wide range of possible differences efficiently.
Considering all three options for each rod (add to first support, add to second support, don't use) ensures we find the optimal solution.
The simplified approach provides a cleaner implementation with the same time and space complexity.

Try It Yourself

Modify the code to implement an alternative approach and test it with the same examples.

Challenge:

Implement a function that solves the tallest billboard problem using a different approach than shown above.

Common Edge Cases

No Solution

Handle the case where it's impossible to create two supports of equal height (return 0).

rods = [1, 2]

Single Rod

Handle the case where there's only one rod (return 0, as we can't create two equal-height supports with a single rod).

rods = [5]

Equal Rods

Handle the case where all rods have the same length, making it easy to create equal-height supports.

rods = [3, 3, 3, 3]

Solution Approach All Problems

Code Implementation

Tallest Billboard Implementation

Step-by-Step Explanation

String ProblemsShow All

Palindrome Checker

Message Encryption

Word Puzzle Challenge

Learning Objective

Tallest Billboard Implementation

Step-by-Step Explanation

1Understand the Problem

2Define the State

3Consider All Options

4Handle Edge Cases

5Return the Result

Language-Specific Notes

javascript

python

java

cpp

Key Takeaways

Try It Yourself

Challenge:

Common Edge Cases

No Solution

Single Rod

Equal Rods

Tallest Billboard - Implementation

Code Implementation

Tallest Billboard Implementation

Step-by-Step Explanation

String ProblemsShow All

Palindrome Checker

Message Encryption

Word Puzzle Challenge

Learning Objective

Tallest Billboard Implementation

Step-by-Step Explanation

1Understand the Problem

2Define the State

3Consider All Options

4Handle Edge Cases

5Return the Result

Language-Specific Notes

javascript

python

java

cpp

Key Takeaways

Try It Yourself

Challenge:

Common Edge Cases

No Solution

Single Rod

Equal Rods

String Problems

String Problems