IPO

Problem Statement

LeetCode #502 - IPO

Solve this classic coding interview problem efficiently using multiple approaches.

What to notice first

• Understand the problem constraints and requirements.
• Consider multiple approaches with different trade-offs.
• Pattern mastery comes from knowing when to use each technique.

Examples

Input	Output	Explanation
[example1]	result1	Explanation goes here
[example2]	result2	Explanation goes here

Constraints

• Standard LeetCode constraints
• Refer to the official problem statement for exact details

Real-World Applications

Where this pattern appears

• Application 1 — describe where this is used
• Application 2 — describe where this is used
• Application 3 — describe where this is used

Complexity Comparison

Approach	Time	Space	Best When
Greedy (Max Heap)	O(n log n)	O(n)	Interview — clear greedy logic
Greedy (Sorted)	O(n log n)	O(n)	Alternative sorting approach
Dynamic Programming	O(n²)	O(n)	Learning or analysis

Which approach should you learn first?

• Pick Greedy (Max Heap) for the best interview answer — it is intuitive and efficient.
• Pick Greedy (Sorted) for a simpler greedy approach.
• Pick Dynamic Programming if you want to understand the problem structure.

Best Interview

Greedy (Max Heap)

O(n log n) time · O(n) space

Simpler Greedy

Greedy (Sorted)

O(n log n) time · O(n) space

Educational

Dynamic Programming

O(n²) time · O(n) space

Approach 1: Greedy with Max Heap (Recommended)

★ Recommended

Greedily select projects with highest profit that we can afford. Use a max heap to track available projects by profit.

⏱ Time O(n log n) Sorting + heap ops 💾 Space O(n) Heap storage

Solution Code

Python

ipo_greedy_max_heap.py

from typing import List


def ipo_greedy_max_heap(nums: List[int]) -> int:
    """
    Ipo - Greedy Max Heap approach.

    Time: O(n), Space: O(1) or O(n) depending on approach
    """
    pass


if __name__ == "__main__":
    # Test cases
    pass

C++

ipo_greedy_max_heap.cpp

#include <iostream>
#include <vector>
#include <unordered_map>
using namespace std;

class Solution {
public:
    int ipo_greedy_max_heap(vector<int>& nums) {
        // Ipo - Greedy Max Heap approach
        return 0;
    }
};

int main() {
    return 0;
}

Java

ipo_greedy_max_heap.java

import java.util.*;

class Solution {
    public int ipo_greedy_max_heap(int[] nums) {
        // Ipo - Greedy Max Heap approach
        return 0;
    }

    public static void main(String[] args) {
        // Test cases
    }
}

JavaScript

ipo_greedy_max_heap.js

/**
 * {@param {number[]} nums}
 * {@return {number}}
 */
var ipoGreedymaxheap = function(nums) {
    // Ipo - Greedy Max Heap approach
    return 0;
};

if (require.main === module) {
    // Test cases
}

Rust

ipo_greedy_max_heap.rs

pub fn ipo_greedy_max_heap(nums: Vec<i32>) -> i32 {
    // Ipo - Greedy Max Heap approach
    0
}

fn main() {
    // Test cases
}

Go

ipo_greedy_max_heap.go

package main

import "fmt"

func ipoGreedymaxheap(nums []int) int {
    // Ipo - Greedy Max Heap approach
    return 0
}

func main() {
    // Test cases
}

Approach 2: Greedy with Sorting

🎯 Interview Favourite

Sort projects by capital and select k projects with highest profits greedily.

⏱ Time O(n log n) Sorting 💾 Space O(n) Storage

Solution Code

Python

ipo_greedy_sorted.py

from typing import List


def ipo_greedy_sorted(nums: List[int]) -> int:
    """
    Ipo - Greedy Sorted approach.

    Time: O(n), Space: O(1) or O(n) depending on approach
    """
    pass


if __name__ == "__main__":
    # Test cases
    pass

C++

ipo_greedy_sorted.cpp

#include <iostream>
#include <vector>
#include <unordered_map>
using namespace std;

class Solution {
public:
    int ipo_greedy_sorted(vector<int>& nums) {
        // Ipo - Greedy Sorted approach
        return 0;
    }
};

int main() {
    return 0;
}

Java

ipo_greedy_sorted.java

import java.util.*;

class Solution {
    public int ipo_greedy_sorted(int[] nums) {
        // Ipo - Greedy Sorted approach
        return 0;
    }

    public static void main(String[] args) {
        // Test cases
    }
}

JavaScript

ipo_greedy_sorted.js

/**
 * {@param {number[]} nums}
 * {@return {number}}
 */
var ipoGreedysorted = function(nums) {
    // Ipo - Greedy Sorted approach
    return 0;
};

if (require.main === module) {
    // Test cases
}

Rust

ipo_greedy_sorted.rs

pub fn ipo_greedy_sorted(nums: Vec<i32>) -> i32 {
    // Ipo - Greedy Sorted approach
    0
}

fn main() {
    // Test cases
}

Go

ipo_greedy_sorted.go

package main

import "fmt"

func ipoGreedysorted(nums []int) int {
    // Ipo - Greedy Sorted approach
    return 0
}

func main() {
    // Test cases
}

Approach 3: Dynamic Programming

✓ Simple

Use DP to explore all possible combinations of projects and track maximum profit.

⏱ Time O(n²) All subsets 💾 Space O(n) DP table

Solution Code

Python

ipo_dp.py

from typing import List


def ipo_dp(nums: List[int]) -> int:
    """
    Ipo - Dp approach.

    Time: O(n), Space: O(1) or O(n) depending on approach
    """
    pass


if __name__ == "__main__":
    # Test cases
    pass

C++

ipo_dp.cpp

#include <iostream>
#include <vector>
#include <unordered_map>
using namespace std;

class Solution {
public:
    int ipo_dp(vector<int>& nums) {
        // Ipo - Dp approach
        return 0;
    }
};

int main() {
    return 0;
}

Java

ipo_dp.java

import java.util.*;

class Solution {
    public int ipo_dp(int[] nums) {
        // Ipo - Dp approach
        return 0;
    }

    public static void main(String[] args) {
        // Test cases
    }
}

JavaScript

ipo_dp.js

/**
 * {@param {number[]} nums}
 * {@return {number}}
 */
var ipoDp = function(nums) {
    // Ipo - Dp approach
    return 0;
};

if (require.main === module) {
    // Test cases
}

Rust

ipo_dp.rs

pub fn ipo_dp(nums: Vec<i32>) -> i32 {
    // Ipo - Dp approach
    0
}

fn main() {
    // Test cases
}

Go

ipo_dp.go

package main

import "fmt"

func ipoDp(nums []int) int {
    // Ipo - Dp approach
    return 0
}

func main() {
    // Test cases
}

Common mistakes

Watch for these pitfalls

• Mistake 1 — explain what to watch for
• Mistake 2 — explain what to watch for
• Mistake 3 — explain what to watch for

Related Problems

• Two Sum ↗ Easy #1
• Contains Duplicate ↗ Easy #217

Interview Tips

Key discussion points

• Trade-offs between different approaches
• Edge cases to consider
• Possible follow-up questions
• How to extend the solution