SE103 - Week 10, Session 2

Transcript

1. Week 10: Dynamic Programming + Backtracking

2. - Backtracing: Efficient searching with constraints - Dynamic Programming: Recursively

   build most optimal solution Backtracking vs DP

3. Given an array of integers nums and a positive integer

   k, find whether it's possible to divide this array into k non-empty subsets whose sums are all equal. Input: nums = [4, 3, 2, 3, 5, 2, 1], k = 4
 Output: True 
 (5), (1, 4), (2,3), (2,3) have equal sums Partition to K Equal Sum Subsets

4. Given an array of integers nums and a positive integer

   k, find whether it's possible to divide this array into k non-empty subsets whose sums are all equal. Input: nums = [4, 3, 2, 3, 5, 2, 1], k = 4
 Output: True 
 (5), (1, 4), (2,3), (2,3) have equal sums Input: nums = [1], k = 3 
 Output: ?? Partition to K Equal Sum Subsets

5. Given an array of integers nums and a positive integer

   k, find whether it's possible to divide this array into k non-empty subsets whose sums are all equal. Input: nums = [4, 3, 2, 3, 5, 2, 1], k = 4
 Output: True 
 (5), (1, 4), (2,3), (2,3) have equal sums Input: nums = [1], k = 3 
 Output: false Partition to K Equal Sum Subsets

6. Given an array of integers nums and a positive integer

   k, find whether it's possible to divide this array into k non-empty subsets whose sums are all equal. Input: nums = [4, 3, 2, 3, 5, 2, 1], k = 4
 Output: True 
 (5), (1, 4), (2,3), (2,3) have equal sums Input: nums = [1], k = 3 
 Output: false Input: nums = [1, 1, 1], k = 3
 Output: ?? Partition to K Equal Sum Subsets

7. Given an array of integers nums and a positive integer

   k, find whether it's possible to divide this array into k non-empty subsets whose sums are all equal. Input: nums = [4, 3, 2, 3, 5, 2, 1], k = 4
 Output: True 
 (5), (1, 4), (2,3), (2,3) have equal sums Input: nums = [1], k = 3 
 Output: false Input: nums = [1, 1, 1], k = 3
 Output: true Partition to K Equal Sum Subsets

8. Given an array of integers nums and a positive integer

   k, find whether it's possible to divide this array into k non-empty subsets whose sums are all equal. Input: nums = [4, 3, 2, 3, 5, 2, 1], k = 4
 Output: True 
 (5), (1, 4), (2,3), (2,3) have equal sums Input: nums = [1], k = 3 
 Output: false Input: nums = [1, 1, 1], k = 3
 Output: true Input: nums = [1, 2, 3], k = 2
 Output: ?? Partition to K Equal Sum Subsets

9. Given an array of integers nums and a positive integer

   k, find whether it's possible to divide this array into k non-empty subsets whose sums are all equal. Input: nums = [4, 3, 2, 3, 5, 2, 1], k = 4
 Output: True 
 (5), (1, 4), (2,3), (2,3) have equal sums Input: nums = [1], k = 3 
 Output: false Input: nums = [1, 1, 1], k = 3
 Output: true Input: nums = [1, 2, 3], k = 2
 Output: true Partition to K Equal Sum Subsets

10. Given an array of integers nums and a positive integer

    k, find whether it's possible to divide this array into k non-empty subsets whose sums are all equal. Let’s think about some base cases to get us started:
 
 
 Partition to K Equal Sum Subsets

11. Given an array of integers nums and a positive integer

    k, find whether it's possible to divide this array into k non-empty subsets whose sums are all equal. Let’s think about some base cases to get us started:
 nums = [1, 2] , k = 1 -> returns true
 
 
 Partition to K Equal Sum Subsets

12. Given an array of integers nums and a positive integer

    k, find whether it's possible to divide this array into k non-empty subsets whose sums are all equal. Let’s think about some base cases to get us started:
 nums = [1, 2] , k = 1 -> returns true
 If k = 1, we’re done!
 
 
 
 Partition to K Equal Sum Subsets

13. Given an array of integers nums and a positive integer

    k, find whether it's possible to divide this array into k non-empty subsets whose sums are all equal. Let’s think about some base cases to get us started:
 nums = [1, 2] , k = 1 -> returns true
 If k = 1, we’re done!
 
 nums = [1, 2], k = 2 -> returns false
 
 
 
 
 Partition to K Equal Sum Subsets

14. Given an array of integers nums and a positive integer

    k, find whether it's possible to divide this array into k non-empty subsets whose sums are all equal. Let’s think about some base cases to get us started:
 nums = [1, 2] , k = 1 -> returns true
 If k = 1, we’re done!
 
 nums = [1, 2], k = 2 -> returns false
 If sum(nums) % k != 0 , we can return false
 
 
 
 Partition to K Equal Sum Subsets

15. Given an array of integers nums and a positive integer

    k, find whether it's possible to divide this array into k non-empty subsets whose sums are all equal. Let’s think about some base cases to get us started:
 nums = [1, 2] , k = 1 -> returns true
 If k = 1, we’re done!
 
 nums = [1, 2], k = 2 -> returns false
 If sum(nums) % k != 0 , we can return false
 
 nums = [1, 2, 3], k = 2 -> returns true
 
 
 Partition to K Equal Sum Subsets

16. Given an array of integers nums and a positive integer

    k, find whether it's possible to divide this array into k non-empty subsets whose sums are all equal. Let’s think about some base cases to get us started:
 nums = [1, 2] , k = 1 -> returns true
 If k = 1, we’re done!
 
 nums = [1, 2], k = 2 -> returns false
 If sum(nums) % k != 0 , we can return false
 
 nums = [1, 2, 3], k = 2 -> returns true
 Each bucket needs sum(nums) / k => 3
 
 Partition to K Equal Sum Subsets

17. Backtracking template: 1. Search - what are we searching /

    solving for? 2. GetCandidates - get all the possible potential solutions (local solutions) 3. IsSolution - is this candidate a solution? 4. Backtrack - Undo any state that was caused with local guesses Partition to K Equal Sum Subsets

18. create k-groups
 
 search:
 for number in nums:
 if k

    group’s sum doesn’t exceed target
 - add it to k group
 - recursively search with one less number
 
 if every number is in a group, search was successful
 Partition to K Equal Sum Subsets

19. nums = [1, 2, 3, 4] , k = 2

    Partition to K Equal Sum Subsets

20. nums = [1, 2, 3, 4] , k = 2

    Partition to K Equal Sum Subsets

21. nums = [1, 2, 3, 4] , k = 2

    sum = ?? sum = ?? Partition to K Equal Sum Subsets

22. nums = [1, 2, 3, 4] , k = 2

    sum = 5 sum = 5 Partition to K Equal Sum Subsets

23. nums = [1, 2, 3, 4] , k = 2

    sum = 5 sum = 5 Partition to K Equal Sum Subsets

24. nums = [1, 2, 3, 4] , k = 2

    Partition to K Equal Sum Subsets sum = 5 sum = 5 1 1

25. nums = [1, 2, 3, 4] , k = 2

    Partition to K Equal Sum Subsets sum = 5 sum = 5 1 1 1 1 recurse

26. nums = [1, 2, 3, 4] , k = 2

    Partition to K Equal Sum Subsets sum = 5 sum = 5 1 1 1 1 recurse recurse 3 2 2 2 2 2 2 3

27. Dynamic Programming:
 Partition to K Equal Sum Subsets

28. Dynamic Programming:
 
 use ‘mask’ to determine the current state.

    
 -> tells us which numbers have been used already. It also allows us to set the ith bit, unset the ith bit, check if ith bit is set in one step Partition to K Equal Sum Subsets

29. Dynamic Programming:
 
 use ‘mask’ to determine the current state.

    
 -> tells us which numbers have been used already. It also allows us to set the ith bit, unset the ith bit, check if ith bit is set in one step For example: nums[] = [2, 1, 4, 3, 5, 6, 2], mask = (1100101), which means that { 2, 1, 5, 2 } have been used in this state Partition to K Equal Sum Subsets

30. 2 problems 30 minutes for each problem Pick the person

    that has their birthday coming up next! Mock Interviews

31. Practice more Permutations, Combinations, DP -> take HackerRank Look more

    into Partition to K equal subsets with DP if you’re super advanced. Otherwise, simple backtracking approach with recursion would be fine 99.99% of the time. Review Week! Coming Up

32. Dynamic Programming:
 
 - target = sum/k - only start

    a new subset when we have a subset who’s sum = target - don’t allow any state where sum > target Partition to K Equal Sum Subsets

33. Dynamic Programming:
 
 use ‘mask’ to determine the current state.

    
 -> tells us which numbers have been used already. It also allows us to set the ith bit, unset the ith bit, check if ith bit in one step For example: nums[] = [2, 1, 4, 3, 5, 6, 2], mask = (1100101), which means that { 2, 1, 5, 2 } have been used in this state 
 Partition to K Equal Sum Subsets

34. Dynamic Programming:
 
 use ‘mask’ to determine the current state.

    
 -> tells us which numbers have been used already. It also allows us to set the ith bit, unset the ith bit, check if ith bit in one step For example: nums[] = [2, 1, 4, 3, 5, 6, 2], mask = (1100101), which means that { 2, 1, 5, 2 } have been used in this state Let’s say our target = 8,
 dp[1100101] = (2 + 1 + 5 + 2) % 8 = 2
 -> We need to find an unused number to satisfy the next state
 Partition to K Equal Sum Subsets

35. Mistakes I made early in my career

36. Mistakes I made early in my career - Asking too

    many questions without trying to look for the answers first

37. Mistakes I made early in my career - Asking too

    many questions without trying to look for the answers first - Not asking for the projects / tasks I want. Not telling my manager what I want

38. Mistakes I made early in my career - Asking too

    many questions without trying to look for the answers first - Not asking for the projects / tasks I want. Not telling my manager what I want - Overpromising

39. Mistakes I made early in my career - Asking too

    many questions without trying to look for the answers first - Not asking for the projects / tasks I want. Not telling my manager what I want - Overpromising - Trying to change too much within the first 3 months

40. Mistakes I made early in my career - Asking too

    many questions without trying to look for the answers first - Not asking for the projects / tasks I want. Not telling my manager what I want - Overpromising - Trying to change too much within the first 3 months - Not getting iterative feedback

41. Mistakes I made early in my career - Asking too

    many questions without trying to look for the answers first - Not asking for the projects / tasks I want. Not telling my manager what I want - Overpromising - Trying to change too much within the first 3 months - Not getting iterative feedback - Not learning from my own interview mistakes

42. Mistakes I made early in my career - Asking too

    many questions without trying to look for the answers first - Not asking for the projects / tasks I want. Not telling my manager what I want - Overpromising - Trying to change too much within the first 3 months - Not getting iterative feedback - Not learning from my own interview mistakes - Trying to learn all the cool new techlogies and frameworks