Notes: Random Thoughts on Code
overview
Dynamic Programming is referred to as DP. Dynamic programming is to derive the current state from the previous state. Greedy has nothing to do with the previous state.
five steps
- Determine the meaning of the dp array and the subscript
- Determine the recursive formula
- How to initialize dp array
- Determine traversal order
- Example derivation dp array
Leek
basic question
1. Fibonacci numbers
2. Climb the stairs
3. Use the minimum cost to climb the stairs
4. Different paths
5. Different paths two
6. Integer split
7. Different Binary Search Trees
knapsack problem
8.0-1 Knapsack Theoretical Basis 1
Two-dimensional array
The best way to do dynamic programming is to give an example on paper to deduce the value of the corresponding dp array, and then write the code by hand!
The biggest difference between the 01 backpack and the complete backpack is that the complete backpack has unlimited items for each item. A full backpack can be transformed into a 01 backpack.
9.0-1 Knapsack Theoretical Basis II
One-dimensional array (rolling array)
10. Split equal sum subsets
If the values given by the title are all positive integers, then all non-zero subscripts can be initialized to 0. If the value given by the title is negative, then the non-zero subscripts must be initialized to negative infinity.
In this way, the dp array can obtain the maximum value during the recursion process, instead of being overwritten by the initial value .
dp[j] = max(dp[j], dp[j - nums[i]] + nums[i])11. The Weight of the Last Stone II
12. Goals and
The formula for finding combination problems is similar to this:
dp[j] += dp[j - nums[i]]13. Ones and Zeros
14. Theoretical basis of complete knapsack
Each item has an infinite number (that is, it can be put into the backpack multiple times). The only difference between the complete backpack and the 01 backpack problem is that each item has infinite pieces . In the complete knapsack, for a one-dimensional dp array, the nesting order of the two for loops does not matter!
15. Change Exchange II
If you want to find the number of combinations, the outer for loop traverses the items, and the inner for traverses the backpack .
If you want to find the number of permutations, the outer for loop traverses the backpack, and the inner loop traverses the items .
16. Combined sum four
17. Climb the stairs
18. Change Exchange
19. Perfect square numbers
20. Word splitting
21. Theoretical basis of multiple knapsacks
house robbery problem
22. Robbery
23. Robbery 2
The loop is closed, consider the case where the beginning is nums[0] and the end is nums[0].
24. Robbery
tree dp
stock question
25. The best time to buy and sell stocks
26. The best time to buy and sell stocks II
27. The best time to buy and sell stocks 3
28. The best time to buy and sell stocks IV
29. The best time to buy and sell stocks includes a freezing period
30. The best time to buy and sell stocks includes handling fees
subsequence problem
31. Longest increasing subsequence
dp classic problem
32. Longest Continuous Increasing Sequence
33. Longest repeating subarray
34. Longest Common Subsequence
35. Disjoint lines
36. Maximum Subsequence Sum
Classic topic: edit distance
37. Judgment subsequence
38. Different subsequences
If it is a continuous sequence, consider KMP
39. Delete operation of two strings
40. Edit Distance
41. Palindrome Skewers
42. Longest Palindromic Subsequence