甯歌闈㈣瘯棰樻€濇兂鏂规硶鏁寸悊(杞?

Posted 2020-11-30

鏍囩锛?a href='http://www.mamicode.com/so/1/%e5%8e%bb%e9%99%a4' title='鍘婚櫎'>鍘婚櫎   杩涘埗   baidu   鍋氫簡   鏇存柊   閫昏緫   鎯呭喌   

鏈€杩戜竴鐩村湪鎵惧伐锛屽崥瀹㈤兘娌℃€庝箞鏇存柊浜嗭紝瑙夊緱涔熻鎬荤粨鍜屾€濊€冧簺涓滆タ浜嗭紝浜庢槸渚挎湁浜嗚繖绡囨枃绔犮€傝皥鍒?闈㈣瘯棰?/a>锛屽叾瀹炲畠鏈夊緢澶氱锛屾湁鍋忔妧鏈殑锛堣吘璁紝娣樺疂闂緱澶氾級锛涙湁鍋忕畻娉曪紝閫昏緫鍜屾暟瀛︾殑锛堝井杞紝璋锋瓕锛岀櫨搴︼紝闃块噷浜戠瓑闂緱澶氾級銆傛垜鍠滄鍚庤€咃紝鏈€杩戜篃鍋氫簡寰堝杩欐柟闈㈢殑棰樼洰锛屽洿瑙備簡寰堝鍏虫敞绠楁硶鍜岄潰璇曢鐨勫崥瀹紝姣斿锛坖uly绔ラ瀷锛夈€傚浜庡緢澶氱簿濡欑殑棰樼洰锛屽父甯稿湪鎯宠繖浜涘嚭棰樼殑绔ラ瀷鏄€庝箞鎯冲埌鐨勶紝鍥犱负杩欎簺棰樼洰纭疄鑳藉寰堟繁鍏ョ殑鑰冨療鍑轰竴涓潰璇曡€呯殑閫昏緫锛岀畻娉曞拰鎬濈淮鍔熷簳銆傛湰鏂囩珷涓昏鏄€荤粨鑷繁鍦ㄥ仛杩欎簺闈㈣瘯棰樺拰浜嗚В鐩稿簲瑙ｆ硶鐨勮繃绋嬩腑鎬濊€冪殑涓€浜涗笢瑗匡紝鎰熻杩欎簺涓滆タ鍦ㄥ緢澶氶鐩腑閮藉嚭鐜拌繃锛岄潪甯稿€煎緱鎶借薄鍑烘潵涓撻棬鐞嗚В銆?

銆€銆€涓€ 鍙屾寚閽堥亶鍘?/strong>

銆€銆€鎵€璋撳弻鎸囬拡锛屾槸鍒╃敤涓や釜鎸囬拡瀵逛竴涓湁搴忔暟缁勮繘琛岄亶鍘嗭紝鏌ユ壘鍑虹鍚堣姹傜殑鏁版嵁闆嗗悎銆傜浉淇″ぇ瀹堕兘鎺ヨЕ鍒颁簡杩欑鎬濈淮妯″紡鐨勮В棰樻柟娉曪紝鍙槸娌℃湁娉ㄦ剰鍒扮舰浜嗐€備笅闈妇鍑犱釜渚嬪瓙鍚с€?/span>

銆€銆€渚?锛氱粰瀹氫竴涓暟缁刟[n]锛屾眰鏁扮粍涓槸鍚﹀瓨鍦ㄤ袱涓暟鐨勫拰绛変簬缁欏畾鍊約um骞惰緭鍑猴紵

銆€銆€杩欎釜闂寰堝父瑙侊紝鎴戝綋骞村湪闈㈣瘯寰蒋瀹炰範鐢熺殑鏃跺€欏氨琚棶鍒颁簡姝ら锛岃В鍐虫柟娉曟湁寰堝绉嶏紝杩欓噷鎴戝氨涓嶈禈杩帮紝鎴戣鐨勬槸鐢ㄥ弻鎸囬拡閬嶅巻娉曠殑銆傞鍏堟暟缁勪笉涓€瀹氭湁搴忥紝瀵规暟缁勬帓搴忔槸蹇呴』鐨勩€傞偅涔堜究鏉ュ埌浜嗚繖鏍蜂竴涓満鏅細瀵规湁搴忔暟缁勫浣曢亶鍘嗘潵姹傚緱绗﹀悎瑕佹眰鐨勬暟鎹泦鍚堬紵鍙屾寚閽堢殑瑙ｅ喅鏂规硶濡備笅锛氬畾涔変袱涓寚閽堬紙i 鍜?j锛夛紝鍒嗗埆鎸囧悜鏁扮粍澶村拰灏撅紝閭ｄ箞浼氬嚭鐜板涓嬩笁绉嶆儏鍐碉細

1. 濡傛灉a[i]+a[j] == sum锛岄偅涔堝緢鏄剧劧锛屽彧瑕佽緭鍑鸿繖涓や釜鏁帮紝骞舵妸鎸囬拡i+1鍜宩-1鎸囧悜涓嬩竴涓暟鍗冲彲銆傦紙杩欓噷涓嶈緭鍑洪噸澶嶇殑缁勫悎锛?/span>
2. 濡傛灉a[i]+a[j] > sum锛岃鏄庡綋鍓嶉亶鍘嗙殑鏁板€煎亸澶э紝鎵€浠ュ彲浠ユ妸j-1浠ュ噺灏忓拰鐨勫€硷紝鍦ㄧ户缁瘮杈冦€?/span>
3. 濡傛灉a[i]+a[j] < sum锛岃鏄庡綋鍓嶉亶鍘嗙殑鏁板€煎亸灏忥紝鍚屾牱涓轰簡鍔犲ぇ鍜屽彲浠ユ妸i+1銆?/span>

鎬荤殑鏃堕棿澶嶆潅搴﹀彇鍐充簬鎺掑簭鍗砄(nlogn)銆?/span>

渚?锛氳繖棰樻潵鑷紪绋嬩箣缇?.21鍙€冨姞娉曠殑闈㈣瘯棰橈紝鍘熼澶ц嚧鎰忔€濇槸鍐欎竴涓▼搴忥紝瀵逛簬涓€涓?2浣嶆暣鏁帮紝杈撳嚭瀹冩墍鏈夊彲鑳界殑杩炵画鑷劧鏁颁箣鍜岀殑绠楀紡锛岃姹傛槸杩欎簺杩炵画鑷劧鏁颁箣鍜岃绛変簬鍘熸暟銆備緥濡? = 2+1; 9 = 4+5锛? = 2+3+4绛夈€?/span>

杩欓鏈変袱绉嶈В娉曪紝 鍏朵腑涓€绉嶄究鏄弻鎸囬拡娉曪紝杩樻湁涓€绉嶆瘮杈冨阀濡欙紝鏄垜鍚屽鍦ㄩ潰璇曢樋閲屼簯璁＄畻鐨勬椂鍊欐兂鍒扮殑锛屽埄鐢ㄤ簡鏁板鏂规硶锛岀畝鍗曟潵璇存槸姹傚嚭涓€涓叕寮忔潵銆傝繖閲屽彧璇村弻鎸囬拡鐨勮В娉曘€?/span>

杩欓噷闇€瑕佷竴涓浆鍖栵紝鎶婃眰n涓墍鏈夊彲鑳界殑杩炵画鑷劧鏁颁箣鍜屽綊绾︿负鍦ㄦ暟缁剓1,2,3,...,n}涓壘鎵€鏈夎繛缁瓙搴忓垪鍜岀瓑浜巒鐨勯棶棰樸€傝繖閲屽悓鏍蜂篃鏄繖鏍蜂竴涓満鏅細瀵规湁搴忔暟缁勫浣曢亶鍘嗘潵姹傚緱绗﹀悎瑕佹眰鐨勬暟鎹泦鍚堬紵杩欐椂鐨勫弻鎸囬拡鍙互涓嶆槸涓€澶翠竴灏句簡锛岃€屾槸涓や釜閮芥寚鍚戝ご閮紝杩欐牱鍙互浠ラ珮鏁堢殑椤哄簭閬嶅巻鎴戜滑瑕佹壘鐨勬墍鏈夐泦鍚堛€傚垵濮嬭i=j=1锛岃繖閲屽悓鏍蜂細鍑虹幇涓夌鎯呭喌锛?/span>

1. sum[i,j] == sum锛?鐩存帴杈撳嚭i鍒癹鐨勫€硷紝骞舵妸i+1,j+1,鍥犱负鍙槸i+1鑲畾鏄笉绛夌殑锛屽洜涓哄拰灏忎簡锛屽悓鏍穓+1鍙細浣垮拰鍙樺ぇ锛屾墍浠ヤ袱涓兘瑕佸線鍓嶅姞锛堟敞鎰忚繖閲屾寚閽堜笉鐢ㄨ€冭檻鍑忓皬锛屽洜涓鸿繖鍦ㄤ互鍓嶅氨鑰冭檻杩囦簡锛?/span>
2. sum[i,j] < sum锛岃鏄庡亸灏忥紝閭ｄ箞鎻愰珮j鏉ヤ娇寰楀拰鍙樺ぇ鎵嶆湁鍙兘鐩哥瓑
3. sum[i,j] > sum锛岃鏄庡亸澶э紝閭ｄ箞鎻愰珮i鏉ヤ娇寰楀拰鍙樺皬鎵嶆湁鍙兘鐩哥瓑

杩欐牱锛屼唬鐮佸氨鍑烘潵浜嗭細

//璁＄畻杩炵画鍜屼负n鐨勬墍鏈夊瓙搴忓垪
void GetAnswer(int n)
{
	int i=1;
	int j=1;

	while(i<=n/2 && j <= n)
	{
		
		int sum = (j+i)*(j-i+1)/2;

		if(sum == n)
		{
			for(int k=i; k <= j; k++)
				cout<<k<<" ";
			cout<<endl;
			j++;
			i++;
		}
		else if(sum < n)
		{//sum[i..j]<n,鍙兘鎻愰珮j浠ュ澶um
			j++;
		}
		else//sum[i..j]>n,鍙兘鎻愰珮i浠ュ噺灏弒um
			i++;
	}
}

杩欓噷鐨勬€濇兂鏈川涓婁笌涓婇潰渚嬮1鏄浉鍚岀殑锛岃繖涔熸槸鎴戞娊璞″嚭杩欑鎬濈淮妯″瀷鐨勫師鍥狅紝褰撻亣鍒版湁搴忔暟缁勬垨鑰呭綊绾﹀埌鏈夊簭鏁扮粍鏃讹紝鍒╃敤鍙屾寚閽堥亶鍘嗙殑鏂规硶鏄眰寰楁垜浠渶瑕佺殑鏁版嵁闆嗗悎鐨勪竴绉嶇浉瀵规瘮杈冮珮鏁堢殑鏂规硶銆?/span>

浜?鎺掗櫎浠ュ噺灏戣В绌洪棿澶у皬

鐩镐俊杩欑鏂规硶澶у閮藉惉杩囷紝浣嗘槸瀹為檯浣跨敤鐨勬椂鍊欏嵈鏃跺父蹇樹簡鍘昏€冭檻杩欑鎬濈淮妯″紡锛屾垜杩欓噷涓剧殑閮芥槸寰堝阀濡欑殑渚嬪瓙锛屼篃鏄垜閬囧埌鐨勶紝鎰熻缁濆鍊煎緱鎶婅繖绉嶆€濊€冩柟娉曟€荤粨鍑烘潵銆?/span>

 渚? 姝ょ瑙ｆ硶寰堝€煎緱涓€璇寸殑棰樼洰鏉ヨ嚜缂栫▼涔嬬編2.3 瀵绘壘鍙戝笘姘寸帇锛屽ぇ鑷存剰鎬濇槸锛?/span>

 鏌愯鍧涙湁涓€涓€滄按鐜嬧€濓紝缁忓父鍙戝笘锛屾嵁璇磋鈥滄按鐜嬧€濆彂甯栨暟鐩秴杩囦簡甯栧瓙鎬绘暟鐨勪竴鍗婏紝閭ｄ箞濡備綍鍦╥d鍙戝笘鍒楄〃涓揩閫熺殑鏌ユ壘鍒拌繖涓€鈥滄按鐜嬧€濓紵

杩欓亾棰橀潪甯稿ソ鐨勪綋鐜颁簡鎺掗櫎娉曠殑闈炲嚒鏁堟灉锛屽鏋滅洿鎺ュ幓姹傝繖涓按鐜嬶紝鏂规硶涔熶笉灏戯紝渚嬪鎸夊彂甯栨暟鎺掑簭锛屼絾鏄繖鑷冲皯鏄疧(nlogn)鏃堕棿澶嶆潅搴︼紝瀹為檯涓婃渶濂界殑绠楁硶鍗存槸灏藉彲鑳界殑鍘诲噺灏戣В绌洪棿锛屾妸涓嶅彲鑳界殑鍘婚櫎鎺夛紝鐣欎笅鐨勮嚜鐒舵槸瑕佹眰鐨勭殑瑙ｃ€傚浜庤繖閬撻锛屽氨鏄瘡娆″幓闄や袱涓笉鍚宨d鐨勫彂甯栵紝鐢变簬榛樿姘寸帇鍙戝笘瓒呰繃涓€鍗婏紝閭ｄ箞鍘婚櫎浠讳綍涓や釜涓嶅悓id鍚庝粛鐒舵槸瓒呰繃涓€鍗婄殑锛寃hy锛熷彲浠ヨ繖鏍锋兂锛屽紑濮嬫弧瓒崇殑鍏紡鏄?x>y/2,閭ｄ箞鍑忓幓涓や釜涓嶅悓id鍚庯紝鏈€鍧忔儏鍐碉紝杩欎袱涓笉鍚宨d涓湁涓€涓槸姘寸帇鐨刬d锛屽垯(x-1)/(y-2) > (y/2-1)/(y-2) > 1/2锛屽嵆浠嶇劧鏄ぇ浜庝簩鍒嗕箣涓€鐨勶紝 鎵€浠ュ彲浠ヤ笉鏂殑杩欐牱鍋氱洿鍒版渶缁堝墿涓嬫按鐜媔d涓烘銆傜紪绋嬩箣缇庝笂缁欏嚭浜嗕竴涓潪甯哥簿濡欑殑绋嬪簭锛岃繖閲屼笉璧樿堪銆?/span>