[leetcode] Dynamic Programming

Backpack

Understand the Nine Lectures on Backpacks

01 Backpack , that is, items are limited.

for 物品
	for 容量（倒序）

• P1048 [NOIP2005 Popularization Group] Collecting Herbs [ Original Question | Solution]
• P1049 [NOIP2001 Popularization Group] Packing Problem [ Original Question | Solution]
• P1507 NASA's Food Plan [ Original Question | Solution]
• P1510 Jingwei Reclamation [ Original Question | Solution]

Complete backpack , i.e. unlimited items.

for 物品
	for 容量（正序）

Note that climbing stairs (LeetCode 70) requires an orderly sequence , but a general complete backpack does not need to be ordered, such as the classic coin collection: interview question 08.11. Coins . Note the difference between the two cases! The former recycles capacity first and recycles items, while the latter recycles items first and then recycles capacity.

• P1832 A+B Problem (re-upgrade) [ Original question | Solution]

• Change Exchange ( LeetCode 322 )

• Change Change II (LeetCode 518)

• Combined Sums IV (leetcode 377)

• Perfect Square Numbers (LeetCode 279)

• Word Splitting (leetcode 139)

Group backpacks . The items are divided into several groups, and the items in each group conflict with each other, and at most one is selected.

for 组号
	for 容量
		for 组内物品

• P1757 Babel's Group Backpack [ Original Question | Solution]

Multiple knapsacks , there are at most n[i] items available for the i-th item. It is a special case of grouping backpacks. It can be understood as follows: for the i-th item, only one of 0, 1, 2, 3, 4...n[i] can be selected.

for 物品种类
	for 容量
		for 该类物品数量

Requires binary optimization to 01 knapsack if timeout

• P2066 Machine Allocation [ Original Question | Solution]
• P1776 Treasure Screening [ Original Question | Solution]

mixed backpack

Some items are infinite (complete), and some items are finite (multiple). Process the complete knapsack first, and then convert multiple knapsacks into 01 knapsacks through binary optimization.

• P1833 Cherry Blossoms [ Original Title | Solution]

A backpack that satisfies a certain condition

• P1509 Search and search and search for GF [ Original question | Solution]

2D true false backpack

• P1877 [HAOI2012] Volume adjustment [ Original question | Solution]

Invest in stocks, multiple dp

• P1853 Maximum Benefit of Investment [ Original Question | Solution]

dynamic programming

First record the most recently encountered state dp.

• Robbery ( LeetCode 198 ) [ Original Problem Solution ]
• House robbery (upgrade topic, after selecting i, i-2, i-1, i+1, i+2 can not be selected, ask the maximum value that can be stolen) [original question solution]
• House robbery (upgrade question, you can steal 2 consecutive households, but you can't steal 3 consecutive households, ask the maximum value that can be stolen) [Original Problem Solution]
• House robbery (upgrade question, you can't steal consecutive residents, but there are k opportunities to steal consecutive residents, ask the maximum value that can be stolen) [Original Problem Solution]
• Robbery III ( LeetCode 337 ) [Original Problem Solution]
• Best Time to Buy and Sell Stocks III (LeetCode 123)
• Best Time to Buy and Sell Stocks IV (LeetCode 188)
• The best time to buy and sell stocks includes a freezing period (LeetCode 309) [ Original Problem Solution ]