# 鍔ㄦ€佽鍒掞紙浜岋級涔嬫墦瀹跺姭鑸?/span>
鐩镐俊缁忚繃涓婁竴鏈熷潖铔嬪摜璇︾粏鐨勮瑙ｏ紝灏忎紮浼翠滑瀵逛竴鑸殑鍔ㄦ€佽鍒掑凡缁忔湁浜嗗垵姝ョ殑璁よ瘑锛岃寰楁垜鍒氭帴瑙﹀姩鎬佽鍒掔殑鏃跺€欙紝涓€鐩撮兘闂嚜宸变竴涓棶棰橈紝涓轰粈涔堣繖绫荤畻娉曞彨鍔ㄦ€佽鍒掑憿锛熸湁浠€涔堝惈涔?鐩镐俊鐖辨€濊€冪殑灏忎紮浼翠滑涔熸湁杩欎釜鐤戦棶锛屾垜鐨勭瓟妗堟槸璁╅€掑綊鏈夎蹇嗭紝鏍规嵁浠ュ線鐨勮蹇嗗姩鎬佽鍒掍笅涓€姝ャ€傚鏋滀綘鏈夋洿濂界殑瑙ｉ噴锛岃寰楀悗鍙拌仈绯诲潖铔嬪摜鍝︺€傚鏋滀綘涔熷枩娆㈠潖铔嬪摜鐨勫唴瀹癸紝璁板緱鍏虫敞鍔狆煈嶅摝銆?/span>
棰樼洰鍐呭
鍘熼鑾峰彇閾炬帴锛?/span>https://leetcode-cn.com/problems/house-robber-iii/
鏄笉鏄劅瑙夌幇鍦ㄥ皬鍋风殑鏅哄晢閮借繖涔堢殑楂橈紝杩樻槸涓€涓绠楁満涓撳锛堟槸浣犲悧锛熷搱鍝堬級銆?/span>
灏忓伔锛氬挶浠繖鑱屼笟涓嶆槸璋佹兂褰撳氨鑳藉綋鐨勶紝鍜变滑鏄笓涓氱殑銆?/span>
棰樿В鎬濇兂
杩欐槸鎴戣窇鍑烘潵鐨勬晥鏋滐細鏈熷緟灏忎紮浼寸殑瓒呰秺鍝︼紙鏈夌偣椋樹簡锛夈€?/span>
鎬濇兂杩樻槸鐢ㄧ殑鍓嶉潰鎵撳鍔垗涓€鍜屼簩鐨勬€濇兂锛堝姩鎬佽鍒掞級
鍙槸鎶婅緟鍔╂暟缁勶紝鎹㈡垚浜嗘爲鑺傜偣涓殑val鍙橀噺锛岀敋鑷宠繍琛屽唴瀛樺彲浠ラ€氳繃杩唬鍚庡簭閬嶅巻鐨勬€濇兂杩樿兘鍑忓皯閮ㄥ垎鐨勬秷鑰椼€?/span>
鏈€鍚庣殑鏃堕棿澶嶆潅搴︿负 O(n)锛岀┖闂村鏉傚害涓篛(1)锛岃繖鍎垮叾瀹炲彲浠ヤ笉鏀瑰彉val鍙橀噺鐨勫€硷紝鏈変綑鍔涚殑灏忎紮浼村彲浠ユ€濊€冧竴涓嬨€?/span>
棰樿В涓昏鐨勬€濇兂杩樻槸鍔ㄦ€佽鍒掔殑閫夊拰涓嶉€?/span>锛?/span>
濡傛灉閫変簡i鑺傜偣锛岄偅涔坕鐨勫瓙鑺傜偣灏变笉鑳介€夛紝鏈€澶氳繕鑳介€塱瀛愯妭鐐圭殑瀛愯妭鐐瑰強瀹冧滑鐨勫瀛愩€傞偅涔堝氨鍙互鍦ㄩ€変簡i鐨勬儏鍐典笅鐨勬渶澶у€煎拰娌℃湁閫塱鐨勬儏鍐典笅鐨勬渶澶у€艰繘琛屾瘮杈冿紝璋佸ぇ锛屽氨璇存槑杩欎釜鏍戠殑鏈€澶у伔鍙栫殑money涓哄灏戙€?/span>
杞Щ鏂圭▼锛堝亣璁惧乏鑺傜偣锛屽彸缁撶偣鍙婁粬浠殑瀛╁瓙閮藉瓨鍦級涓猴細
dp[i]=max(f(i)+dp[i->l->l]+dp[i->l->r]+dp[i->r->l]+dp[i->r->r],dp[i->l]+dp[i->r])
绗﹀彿瀹氫箟瑙ｉ噴锛?/span>
1锔忊儯dp[i]琛ㄧず浠涓烘牴缁撶偣鐨勫瓙鏍戠殑鏈€澶у伔鍙栫殑money銆?/span>
2锔忊儯dip[i->l->l] 濡傛灉i鐨勫乏鑺傜偣鐨勫乏鑺傜偣瀛樺湪锛岄偅涔堜互i宸﹁妭鐐圭殑宸﹁妭鐐逛负鏍圭殑瀛愭爲鎵€鑳藉伔鍙栫殑鏈€澶у€硷紝鍚岀悊鍏朵粬绗﹀彿绫讳技銆?/span>
3锔忊儯f(i) 琛ㄧずi鑺傜偣涓殑val鍙橀噺鐨勫ぇ灏忋€?/span>
鍥犱负鍔ㄦ€佽鍒掕閫夋嫨璁＄畻鐨勬柟鍚戯紝濡傛灉浠庢牴寰€涓嬮潰璁＄畻锛岄偅涔堜細瀛樺湪寰堝lamp sub-problem锛岃繖姝ｆ槸鍔ㄦ€佽鍒掓墍瑕佽В鍐崇殑闂锛?/span>鎵€浠ユ垜浠氨瑕佹€濊€冨浣曚粠鏍瑰線涓婄畻锛岄偅涔堝湪鏍戠殑閬嶅巻涓紝鍚庡簭閬嶅巻鎭板ソ鍙互婊¤冻鍦ㄧ畻鏍圭殑鏃跺€欙紝瀛愭爲宸茬粡绠楀ソ浜嗐€?/span>
鍏蜂綋瀹炵幇浠ｇ爜:
/**
* Definition for a binary tree node.
* public class TreeNode {
* int val;
* TreeNode left;
* TreeNode right;
* TreeNode(int x) { val = x; }
* }
*/
class Solution {
public int rob(TreeNode root) {
//鍒ゆ柇鏄惁涓簄ull
if(root!=null)
{
if (root.left!=null) {
rob(root.left);
}
if (root.right!=null){
rob(root.right);
}
//鐒跺悗璁＄畻璇ョ粨鐐圭殑鏈€澶у€硷紝鍓嶆彁鏄笂闈㈢殑宸﹀彸缁撶偣宸茬粡璁＄畻
coculate(root);
return root.val;
}else {
return 0;
}
}
public void coculate(TreeNode node){
//瀹氫箟涓や釜鍙橀噺
int choice=0; //閫塶ode
int nochoice=0; //涓嶉€塶ode
//鐗瑰垽
if (node==null)
return;
else
choice=node.val;
//璁＄畻node鐨勫乏瀛愭爲
if (node.left!=null){
nochoice+=node.left.val;
if (node.left.left!=null){
choice+=node.left.left.val;
}
if (node.left.right!=null){
choice+=node.left.right.val;
}
}
//璁＄畻node鐨勫彸瀛愭爲
if (node.right!=null){
nochoice+=node.right.val;
if (node.right.left!=null){
choice+=node.right.left.val;
}
if (node.right.right!=null){
choice+=node.right.right.val;
}
}
//杩斿洖閫変笉閫塶ode鐨勫悇鑷儏鍐典笅鏈€澶х殑money
node.val=choice>nochoice?choice:nochoice;
}
}
鎬荤粨
缁忚繃杩欎竴鏈熷唴瀹圭殑鍒嗕韩锛岀浉淇″皬浼欎即浠凡缁忓鍔ㄦ€佽鍒掓湁浜嗕竴涓瘮杈冪洿瑙傜殑鎰熷彈浜嗐€傛棤璁烘槸闈㈣瘯杩樻槸鑰冪爺鑰冨彇濂界殑瀛︽牎锛岀浉淇＄畻娉曠殑鐔熺〝鑳借浣犱滑鏇村姞鍑哄僵鍑轰紬銆傛湡寰呬綘浠殑杩涙銆?/span>
姘歌繙鍋氱埍瀛︿範鐨勫皬鐧姐€傛垜鏄潖铔嬪摜锛屽挶浠笅鏈熷啀浼氥€?/span>
以上是关于鍔ㄦ€佽鍒掞紙浜岋級涔嬫墦瀹跺姭鑸?/h1>