870. Advantage Shuffle
Medium
TopicsCompanies
You are given two integer arrays nums1 and nums2 both of the same length. The advantage of nums1 with respect to nums2 is the number of indices i for which nums1[i] > nums2[i].
Return any permutation of nums1 that maximizes its advantage with respect to nums2.
 
Example 1:
Input: nums1 = [2,7,11,15], nums2 = [1,10,4,11]
Output: [2,11,7,15]


Example 2:
Input: nums1 = [12,24,8,32], nums2 = [13,25,32,11]
Output: [24,32,8,12]


 
Constraints:
1 <= nums1.length <= 105
nums2.length == nums1.length
0 <= nums1[i], nums2[i] <= 109

Bahii 3ana problem ismo “Advantage Shuffle” oky : 
—> Fe problem h4a 3ana two lists “nums1” and “nums2” el zouz 3andhom  nefess el toull … 
—> oky bsh t7eb “the advantage” of list x relatively 3le y lzem , el indices “i” ykonn 
—> nums1[i] > nums2[i] for kol indice “i” oky 

Bahii el problem honi y7ebik tl3 any permutation fe “nums1” t5alik “maximize” it advantage % 3le nums2 

Q- awl seoul chnowa el input & output format ? 

—> input : nums1:List[int] , nums2:List[int] 
—> output : permuted_nums1:List[int] 


Q- oky first question did i can also shuffle num2 yes or non ? 

Non 
Q- oky 




In this example : nums1=[2,7,11,15] , nums2=[1,10,4,11] 


In this example (without any shuffling) 

That advantage rank of nums1 % 3le nums2 is 3 kefh ? 

nums1[0]>nums2[0] —> +1
Nums1[2] >nums2[2] —>+1
Nums1[3] > nums3[3] —>+1

Q- ame z3ma ha4ii e7sen “configuration” of nums1 possible ? bsh we maximize the advantage rank? 

Q- ntswer lee ? tnjm t3tena configuration 5er ? 
Ken we souffle nums1[1]<->nums1[2] we get 

A rank = 4 >3 oky donc njmo nl9wa 5er 

Q- twa ha4a logic 5aterik entik 3andikk “eyes” and percetront 5aletik fe example sghir kema hka 
Treason about a better configuration oky : ame z3ma njmo “generalize” a better a more format and systematic abrouch , be m3na h4a njmo n5l9o algorithm bien verfier bsh ysolvy this problem ? 


Q- n7wloo mele ? ntswer fema paradigm mt3 problem solving “ynjm” y9rabna el solution ideal enou enik entii ? twell fe kol mara tmaximizy the solution local (tw b3ed n3mlo definition leha) 3le ame enik tl9a solution global bien confirmer oky ? 

Q- trh kefhhh ? oky 

Q- awl 7aje 5alina n7wloo we define the local optimum solution  in this problem ? 

—> bahi honi the local optimum howa el enik tal9a “i” where nums1[i] >nums2[i] 
Fel position ha4ii 

Q- donc kefh? Njmo we granted this local optimum condition ? 

→ i think we have two step (precompute step and on fly solution oky ) 

The precompute step this first sort the input list “nums1” in a non-decreasing order oky 


→ the second step : is to use on fly pointer updation to update the value of nums1[i] if we get 
nums1[i]<nums[j] 

Note the actual logic of how we efficiently update the value need more investigation oky 
→ but for now we stop 
Q- we have done a lot  of work and thinking process so far ? 
Q- this why i need some guidance 
Q- first to know if am i in the right direction yes or non 
Q- second to help me reduce the search space and reduce my energie to focus on the most important chanallges oky
Q- do not guive actual solution with code , just more abstract ideas and hints 
Q- be my mentor here oky 

Let me help guide your thinking process for the Advantage Shuffle problem. You've already done some good analysis!

Let's break down what we know and provide some direction:

1. Your initial analysis is correct:
- We can only shuffle nums1
- We need to maximize the count of positions where nums1[i] > nums2[i]
- Local optimization is about finding good matchups

2. Your intuition about sorting nums1 is a great start! Here's why:
- When we have sorted nums1, we have more control over which value we want to use against each nums2[i]
- This gives us the flexibility to make optimal "matchups"

Here's a key insight to consider:
Think of this as a matching game. For each position in nums2, we want to:
- Either beat it with the smallest possible number from nums1 that's larger (why waste a bigger number if a smaller one can win?)
- Or if we can't beat it, what should we do with our current number?

Some guiding questions to help you develop the algorithm:
1. If we sort nums1, how can we efficiently find the smallest number that beats a given nums2[i]?
2. What should we do with numbers from nums1 that can't beat any number in nums2?
3. How can we keep track of which numbers from nums1 we've already used?

You're definitely on the right track with sorting nums1. The next step is to think about:
- How to efficiently match numbers from sorted nums1 to nums2
- What to do with "leftover" numbers that can't win any comparison

Would you like to think about any of these aspects in more detail?

Remember: The goal is to be greedy but smart about which numbers we use to beat each position in nums2.


Q- oky twa lzemna nchof el logic mt3 mapping eli ynjm ykon honii ? oky 

Q- awll 7aje jet le mo5ii enou nts3mloo two pointers (i and j) 

i just iterate from left to right in the sorted_nums1 (from the smallest one to the biggest ) 

We j zeda men left to right leken honii el m3nch el logic keml est natively men left to right 
Wle fema more sophisticated technique 


Q- 5alina we proof the correctness of the last method using this example 

nums1 = [12,24,8,32], nums2 = [13,25,32,11]

Bahii nums1.sort() t3tina [8,12,24,32] & nums2=[13,25,32,11] 

Hanii ntswer el naive logic mch s7i7 barsha 

Ntswer lzmna data structure t5alina nextract el max value mt3 nums2 kol mara (m3 index mt3ha ) and we compare it with the min value of nums2 

Ken akbar integer fe nums2 asghir men ‘asghir” elemnt fe nums2 
→ donc directl the sorted list is the best configuration to get the max rank oky 


Q- we have done a lot  of work and thinking process so far ? 
Q- this why i need some guidance 
Q- first to know if am i in the right direction yes or non 
Q- second to help me reduce the search space and reduce my energie to focus on the most important chanallges oky
Q- do not guive actual solution with code , just more abstract ideas and hints 
Q- be my mentor here oky