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==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'

Excalidraw Data

Text Elements

nums:[1,5,11,5] ^0XRv8K0d

状态定义dp[j]: 是否可以通过数组中的某些元素得到和为 j(和是否可达) ^Ap6X9uSI

初始状态dp[0] = true,因为总是可以通过不选元素实现 ^7M8aCW38

状态转移: ^bUvunsrV

1, 5, 11, 5 ^oa2iMXO7

nums: ^90Odqk6p

dp: ^r3AbKnfy

index: ^dKWmVQyF

0 ^y3bCkH47

1 ^Zbq18MkT

2 ^CcbYwACp

true ^XQzRiVNP

true ^kJvzciVm

4 ^Dg2sVKld

5 ^BWg3JVzx

7 ^ZMiv8ehC

8 ^RdfWp6zW

3 ^vSGFNEMC

6 ^5jSHWO8Q

11 ^U2jK170F

9 ^UhvEh5lo

10 ^d2D1wbbo

本题中比较反直觉的是dp的大小与nums的大小不一样 ^8AEnol94

false ^fXkmzYDi

true ^ZJm44k0l

false ^RfkjembW

false ^oea7cDGt

false ^hlivPUxa

false ^Od4lIVG8

true ^R9cTmfrD

false ^lE59MTo9

false ^bJnOca66

false ^xRvBb6Qj

对于数组中的每个数 num 和当前可能的目标和 j: • 如果不选当前数,dp[j] 的值保持不变。 • 如果选当前数,dp[j] 的值由 dp[j - num] 决定(即去掉当前数后,剩余和是否可达)。 ^LPGgLlTE

选当前数字的情况下: 如果之前能够通过某些数字组合得到 j-num 那么当前也能通过加上 num 达到 j ^ky7dw8d6

不选当前数字的情况下: 继承之前的状态 ^06OkV4hr

Embedded Files

3c1f390b1920658c7e6ec2feb9383d956a04e137: $$dp[j] = dp[j] || dp[j-num]$$

eb2d628e0dc8e1e35682f2ac8fda55bf33a103f9: [[Pasted Image 20250106171615_551.png]]

%%

Drawing

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