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§¥§Ý§ñ §á§â§à§ã§ä§à§ä§í §á§â§Ö§Õ§á§à§Ý§à§Ø§Ú§Þ, §é§ä§à §Ó§ã§Ö §Ó§ç§à§Õ§ß§í§Ö §é§Ú§ã§Ý§Ñ §â§Ñ§Ó§ß§í 0, 1 §Ú§Ý§Ú 2. §¿§ä§à §ß§Ö §Ú§Ù§Þ§Ö§ß§Ú§ä §â§Ö§Ù§å§Ý§î§ä§Ñ§ä, §á§à§ã§Ü§à§Ý§î§Ü§å §ß§å§Ø§Ö§ß §ä§à§Ý§î§Ü§à §Þ§à§Õ§å§Ý§î, §â§Ñ§Ó§ß§í§Û 3.
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§¥§Ý§ñ §ä§à§Ô§à, §é§ä§à§Ò§í §à§Ò§ì§Ö§Õ§Ú§ß§Ú§ä§î §Ó §ã§Ö§ä§î?n?§Ñ§ß§ä§Ö§ß§ß, §â§Ñ§Ù§Ò§â§à§ã§Ñ§ß§ß§í§ç §á§à §ã§ä§â§Ñ§ß§Ö, §Ü§à§ä§à§â§å§ð §Þ§à§Ø§ß§à §á§â§Ö§Õ§ã§ä§Ñ§Ó§Ú§ä§î §Ó §Ó§Ú§Õ§Ö 2D-§á§Ý§à§ã§Ü§à§ã§ä§Ú, §ß§Ö§à§Ò§ç§à§Õ§Ú§Þ§à §å§ã§ä§Ñ§ß§à§Ó§Ú§ä§î §â§Ñ§Õ§Ú§å§ã §á§Ö§â§Ö§Õ§Ñ§é§Ú §Ü§Ñ§Ø§Õ§à§Û §Ñ§ß§ä§Ö§ß§ß§í §â§Ñ§Ó§ß§í§Þ §à§Õ§ß§à§Þ§å §Ú §ä§à§Þ§å §Ø§Ö §ß§Ö§à§ä§â§Ú§è§Ñ§ä§Ö§Ý§î§ß§à§Þ§å §Ó§Ö§ë§Ö§ã§ä§Ó§Ö§ß§ß§à§Þ§å §é§Ú§ã§Ý§å?r. §¥§Ñ§Ý§î§ß§à§ã§ä§î §Õ§Ö§Û§ã§ä§Ó§Ú§ñ §Ñ§ß§ä§Ö§ß§ß§í §à§á§â§Ö§Õ§Ö§Ý§ñ§Ö§ä§ã§ñ §Ü§Ñ§Ü §Þ§ß§à§Ø§Ö§ã§ä§Ó§à §Ó§ã§Ö§ç §ä§à§é§Ö§Ü, §â§Ñ§ã§ã§ä§à§ñ§ß§Ú§Ö §Õ§à §Ü§à§ä§à§â§í§ç §Õ§à §Ñ§ß§ä§Ö§ß§ß§í §ß§Ö §á§â§Ö§Ó§í§ê§Ñ§Ö§ä?r. §¦§ã§Ý§Ú §â§Ñ§Õ§Ú§å§ã§í §Õ§Ó§å§ç §Ñ§ß§ä§Ö§ß§ß §Ú§Þ§Ö§ð§ä §à§Ò§ë§å§ð §ä§à§é§Ü§å, §ï§ä§Ú §Ñ§ß§ä§Ö§ß§ß§í §Þ§à§Ô§å§ä §ß§Ñ§á§â§ñ§Þ§å§ð §ã§Ó§ñ§Ù§í§Ó§Ñ§ä§î§ã§ñ. §¬§â§à§Þ§Ö §ä§à§Ô§à, §Ö§ã§Ý§Ú §Ñ§ß§ä§Ö§ß§ß§í A §Ú B §Þ§à§Ô§å§ä §à§Ò§Þ§Ö§ß§Ú§Ó§Ñ§ä§î§ã§ñ §Õ§Ñ§ß§ß§í§Þ§Ú, §Ñ §ä§Ñ§Ü§Ø§Ö §Ñ§ß§ä§Ö§ß§ß§í B §Ú C, §ä§à §Ñ§ß§ä§Ö§ß§ß§í A §Ú C §ä§Ñ§Ü§Ø§Ö §Þ§à§Ô§å§ä §à§Ò§Þ§Ö§ß§Ú§Ó§Ñ§ä§î§ã§ñ §Õ§Ñ§ß§ß§í§Þ§Ú §é§Ö§â§Ö§Ù §Ñ§ß§ä§Ö§ß§ß§å B.
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§°§á§ä§Ú§Þ§Ñ§Ý§î§ß§à§Ö r, §ä§à §Ö§ã§ä§î §Þ§Ú§ß§Ú§Þ§Ñ§Ý§î§ß§à§Ö r, §á§â§Ú §Ü§à§ä§à§â§à§Þ §ã§Ó§ñ§Ù§Ñ§ß §á§à§ã§ä§â§à§Ö§ß§ß§í§Û §Ô§â§Ñ§æ, §Þ§à§Ø§Ö§ä §Ò§í§ä§î §ß§Ñ§Û§Õ§Ö§ß§à §ã §á§à§Þ§à§ë§î§ð §Ò§Ú§ß§Ñ§â§ß§à§Ô§à §á§à§Ú§ã§Ü§Ñ. §¥§Ý§ñ §Ó§Ö§â§ç§ß§Ö§Û §Ô§â§Ñ§ß§Ú§è§í §Þ§í §Þ§à§Ø§Ö§Þ §á§à§ã§ä§Ñ§Ó§Ú§ä§î, §ß§Ñ§á§â§Ú§Þ§Ö§â, 109. §³§Ý§à§Ø§ß§à§ã§ä§î O (n2 log2?109)
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N?§é§Ö§Ý§à§Ó§Ö§Ü §ã§ä§à§ñ§ä §Ó §à§é§Ö§â§Ö§Õ§Ú. §§ð§Õ§ñ§Þ §ã§ä§Ñ§ß§à§Ó§Ú§ä§ã§ñ §ã§Ü§å§é§ß§à, §á§à§ï§ä§à§Þ§å §à§ß§Ú §á§à§Ó§à§â§Ñ§é§Ú§Ó§Ñ§ð§ä§ã§ñ §Ú §å§ã§ä§Ñ§ß§Ñ§Ó§Ý§Ú§Ó§Ñ§ð§ä §Ù§â§Ú§ä§Ö§Ý§î§ß§í§Û §Ü§à§ß§ä§Ñ§Ü§ä. §¥§Ó§Ñ §é§Ö§Ý§à§Ó§Ö§Ü§Ñ A §Ú B, §ã§ä§à§ñ§ë§Ú§Ö §Ó §à§é§Ö§â§Ö§Õ§Ú, §Þ§à§Ô§å§ä §Ó§Ú§Õ§Ö§ä§î §Õ§â§å§Ô §Õ§â§å§Ô§Ñ, §Ö§ã§Ý§Ú §à§ß§Ú §ã§ä§à§ñ§ä §â§ñ§Õ§à§Þ §Õ§â§å§Ô §ã §Õ§â§å§Ô§à§Þ §Ú§Ý§Ú §Ö§ã§Ý§Ú §Þ§Ö§Ø§Õ§å §ß§Ú§Þ§Ú §ß§Ö§ä §Ý§ð§Õ§Ö§Û §ã§ä§â§à§Ô§à §Ó§í§ê§Ö (>), §é§Ö§Þ §é§Ö§Ý§à§Ó§Ö§Ü A §Ú§Ý§Ú §é§Ö§Ý§à§Ó§Ö§Ü B. §¯§Ñ§á§Ú§ê§Ú§ä§Ö §á§â§à§Ô§â§Ñ§Þ§Þ§å, §à§á§â§Ö§Õ§Ö§Ý§ñ§ð§ë§å§ð §Ü§à§Ý§Ú§é§Ö§ã§ä§Ó§à §á§Ñ§â §Ý§ð§Õ§Ö§Û, §Ü§à§ä§à§â§í§Ö §å§ã§ä§Ñ§ß§Ñ§Ó§Ý§Ú§Ó§Ñ§ð§ä §Ù§â§Ú§ä§Ö§Ý§î§ß§í§Û §Ü§à§ß§ä§Ñ§Ü§ä.?
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§¯§Ö§ã§Þ§à§ä§â§ñ §ß§Ñ §ä§à, §é§ä§à §â§Ö§ê§Ö§ß§Ú§Ö §Ú§Þ§Ö§Ö§ä §Õ§Ó§Ñ §Ó§Ý§à§Ø§Ö§ß§ß§í§ç §è§Ú§Ü§Ý§Ñ, §à§Ò§ë§Ñ§ñ §ã§Ý§à§Ø§ß§à§ã§ä§î §â§Ñ§Ó§ß§Ñ O(N), §á§à§ä§à§Þ§å §é§ä§à §Ü§Ñ§Ø§Õ§í§Û §é§Ö§Ý§à§Ó§Ö§Ü §Ó§ç§à§Õ§Ú§ä §Ó §ã§ä§Ö§Ü §Ú §Ó§í§ç§à§Õ§Ú§ä §Ú§Ù §ß§Ö§Ô§à §â§à§Ó§ß§à §à§Õ§Ú§ß §â§Ñ§Ù, §Ñ §Ü§Ñ§Ø§Õ§Ñ§ñ §Ú§ä§Ö§â§Ñ§è§Ú§ñ §Ó§ß§å§ä§â§Ö§ß§ß§Ö§Ô§à §è§Ú§Ü§Ý§Ñ §Ú§Ù§Ó§Ý§Ö§Ü§Ñ§Ö§ä §Ú§Ù §ã§ä§Ö§Ü§Ñ §à§Õ§Ú§ß §ï§Ý§Ö§Þ§Ö§ß§ä.
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§¢§â§à§ã§Ñ§ñ §æ§Ú§Ô§å§â§å, §Ú§Ô§â§à§Ü §Þ§à§Ø§Ö§ä §Ó§â§Ñ§ë§Ñ§ä§î §Ö§Ö §ß§Ñ 90, 180 §Ú§Ý§Ú 270 §Ô§â§Ñ§Õ§å§ã§à§Ó §Ú §á§Ö§â§Ö§Þ§Ö§ë§Ñ§ä§î §Ö§Ö §Ó§Ý§Ö§Ó§à §Ú§Ý§Ú §Ó§á§â§Ñ§Ó§à, §á§à§Ü§Ñ §æ§Ú§Ô§å§â§Ñ §á§à§Ý§ß§à§ã§ä§î§ð §à§ã§ä§Ñ§Ö§ä§ã§ñ §ß§Ñ §á§à§Ý§Ö. §©§Ñ§ä§Ö§Þ §æ§Ú§Ô§å§â§Ñ §á§Ñ§Õ§Ñ§Ö§ä §Õ§à §ä§Ö§ç §á§à§â, §á§à§Ü§Ñ §ß§Ö §à§ã§ä§Ñ§ß§à§Ó§Ú§ä§ã§ñ §ß§Ñ §Õ§ß§Ö §á§à§Ý§ñ §Ú§Ý§Ú §ß§Ñ §å§Ø§Ö §Ù§Ñ§ß§ñ§ä§í§ç §Ü§Ý§Ö§ä§Ü§Ñ§ç. §£ §ß§Ñ§ê§Ö§Þ §Ó§Ñ§â§Ú§Ñ§ß§ä§Ö §ä§Ö§ä§â§Ú§ã§Ñ §æ§Ú§Ô§å§â§Ñ §Õ§à§Ý§Ø§ß§Ñ §å§á§Ñ§ã§ä§î §ä§Ñ§Ü, §é§ä§à§Ò§í §Ó§ã§Ö §é§Ñ§ã§ä§Ú §æ§Ú§Ô§å§â§í §à§Ü§Ñ§Ù§Ñ§Ý§Ú§ã§î §Ó§ß§Ú§Ù§å §á§à§Ý§ñ §Ú§Ý§Ú §ß§Ñ §å§Ø§Ö §Ù§Ñ§ß§ñ§ä§í§ç §Ü§Ý§Ö§ä§Ü§Ñ§ç. §¥§â§å§Ô§Ú§Þ§Ú §ã§Ý§à§Ó§Ñ§Þ§Ú, §á§à§ã§Ý§Ö §ä§à§Ô§à, §Ü§Ñ§Ü §æ§Ú§Ô§å§â§Ñ §å§á§Ñ§Ý§Ñ, §ß§Ö §Þ§à§Ø§Ö§ä §Ò§í§ä§î §ã§Ó§à§Ò§à§Õ§ß§à§Û §Ü§Ý§Ö§ä§Ü§Ú, §ä§Ñ§Ü§à§Û, §é§ä§à §Ü§Ñ§Ü§Ñ§ñ-§ä§à §Ü§Ý§Ö§ä§Ü§Ñ §ß§Ñ§Õ §ß§Ö§Û §Ù§Ñ§ß§ñ§ä§Ñ.
§¯§Ñ§á§â§Ú§Þ§Ö§â, §á§å§ã§ä§î §á§à§Ý§Ö §Ú§Þ§Ö§Ö§ä §ê§Ú§â§Ú§ß§å §Ó §ê§Ö§ã§ä§î §ã§ä§à§Ý§Ò§è§à§Ó §ã §ß§Ñ§é§Ñ§Ý§î§ß§í§Þ§Ú §Ó§í§ã§à§ä§Ñ§Þ§Ú (§Ü§à§Ý§Ú§é§Ö§ã§ä§Ó§à §å§Ø§Ö §Ù§Ñ§ß§ñ§ä§í§ç §Ü§Ó§Ñ§Õ§â§Ñ§ä§à§Ó §Ó §Ü§Ñ§Ø§Õ§à§Þ §ã§ä§à§Ý§Ò§è§Ö) 2, 1, 1, 1,?0,??1. §©§Ñ§ä§Ö§Þ §æ§Ú§Ô§å§â§å §ß§à§Þ§Ö§â 5 §Þ§à§Ø§ß§à §ã§Ò§â§à§ã§Ú§ä§î §ß§Ñ §á§à§Ý§Ö §á§ñ§ä§î§ð §â§Ñ§Ù§Ý§Ú§é§ß§í§Þ§Ú §ã§á§à§ã§à§Ò§Ñ§Þ§Ú. :
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§£§Ñ§Þ §Õ§Ñ§ß§í §ß§Ñ§é§Ñ§Ý§î§ß§í§Ö §Ó§í§ã§à§ä§í §Ó§ã§Ö§ç §ã§ä§à§Ý§Ò§è§à§Ó §Ú §æ§Ú§Ô§å§â§Ñ, §Ü§à§ä§à§â§å§ð §ß§å§Ø§ß§à §Ó§Ò§â§à§ã§Ú§ä§î §Ó §á§à§Ý§Ö.
§¯§Ñ§á§Ú§ê§Ú§ä§Ö §á§â§à§Ô§â§Ñ§Þ§Þ§å, §Ü§à§ä§à§â§Ñ§ñ §Ó§í§é§Ú§ã§Ý§ñ§Ö§ä §Ü§à§Ý§Ú§é§Ö§ã§ä§Ó§à §â§Ñ§Ù§Ý§Ú§é§ß§í§ç §ã§á§à§ã§à§Ò§à§Ó §ã§Õ§Ö§Ý§Ñ§ä§î §ï§ä§à, §ä. §Ö. §Ü§à§Ý§Ú§é§Ö§ã§ä§Ó§à §â§Ñ§Ù§Ý§Ú§é§ß§í§ç §Ü§à§ß§æ§Ú§Ô§å§â§Ñ§è§Ú§Û §á§à§Ý§ñ, §Ü§à§ä§à§â§í§Ö §Þ§à§Ø§ß§à §á§à§Ý§å§é§Ú§ä§î, §ã§Ò§â§Ñ§ã§í§Ó§Ñ§ñ §æ§Ú§Ô§å§â§å.
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§Ó§Ó§à§Õ |
§Ó§í§Ó§à§Õ |
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6 5 2 1 1 1 0 1 ? |
5? |
?§²§Ö§ê§Ö§ß§Ú§Ö:
§±§â§Ö§Õ§ã§ä§Ñ§Ó§î§ä§Ö, §é§ä§à §æ§Ú§Ô§å§â§Ñ §ß§Ñ§ç§à§Õ§Ú§ä§ã§ñ §Ó§ß§Ú§Ù§å §á§å§ã§ä§à§Ô§à §á§à§Ý§ñ. §©§Ñ§ä§Ö§Þ §æ§Ú§Ô§å§â§å §Þ§à§Ø§ß§à §Ù§Ñ§Ü§à§Õ§Ú§â§à§Ó§Ñ§ä§î §Ü§Ñ§Ü §á§à§ã§Ý§Ö§Õ§à§Ó§Ñ§ä§Ö§Ý§î§ß§à§ã§ä§î §é§Ú§ã§Ö§Ý, §Ö§ã§Ý§Ú §Þ§í §Ù§Ñ§á§Ú§ê§Ö§Þ §ã§Ñ§Þ§å§ð §ß§Ú§Ø§ß§ð§ð §Ù§Ñ§ß§ñ§ä§å§ð §ã§ä§â§à§Ü§å §Õ§Ý§ñ §Ü§Ñ§Ø§Õ§à§Ô§à §ã§ä§à§Ý§Ò§è§Ñ, §Ü§à§ä§à§â§í§Û §Ù§Ñ§ß§Ú§Þ§Ñ§Ö§ä §æ§Ú§Ô§å§â§Ñ.
§¯§Ñ§á§â§Ú§Þ§Ö§â, §æ§Ú§Ô§å§â§Ñ §ß§à§Þ§Ö§â 5 §Ù§Ñ §é§Ö§ä§í§â§Ö §à§Ò§à§â§à§ä§Ñ §Õ§Ñ§Ö§ä §ã§Ý§Ö§Õ§å§ð§ë§Ú§Ö §é§Ö§ä§í§â§Ö §á§à§ã§Ý§Ö§Õ§à§Ó§Ñ§ä§Ö§Ý§î§ß§à§ã§ä§Ú: {1, 1, 1}, {1, 2}, {2, 1, 2} §Ú {2, 1}.
§±§à§ã§Ý§Ö§Õ§à§Ó§Ñ§ä§Ö§Ý§î§ß§à§ã§ä§î A §ã§à§à§ä§Ó§Ö§ä§ã§ä§Ó§å§Ö§ä §á§à§ã§Ý§Ö§Õ§à§Ó§Ñ§ä§Ö§Ý§î§ß§à§ã§ä§Ú B, §Ö§ã§Ý§Ú §Õ§à§Ò§Ñ§Ó§Ý§Ö§ß§Ú§Ö §ß§Ö§Ü§à§ä§à§â§à§Û §Ü§à§ß§ã§ä§Ñ§ß§ä§í §Ü§à §Ó§ã§Ö§Þ §ï§Ý§Ö§Þ§Ö§ß§ä§Ñ§Þ A §Õ§Ñ§Ö§ä §á§à§ã§Ý§Ö§Õ§à§Ó§Ñ§ä§Ö§Ý§î§ß§à§ã§ä§î B.
§¯§Ñ§á§â§Ú§Þ§Ö§â, §á§à§ã§Ý§Ö§Õ§à§Ó§Ñ§ä§Ö§Ý§î§ß§à§ã§ä§î {2, 1, 2} §ã§à§à§ä§Ó§Ö§ä§ã§ä§Ó§å§Ö§ä {5, 4, 5}, §ß§à §ß§Ö {4, 5, 4} §Ú§Ý§Ú {5, 4}.
§°§Ò§â§Ñ§ä§Ú§ä§Ö §Ó§ß§Ú§Þ§Ñ§ß§Ú§Ö, §é§ä§à §æ§Ú§Ô§å§â§Ñ §Þ§à§Ø§Ö§ä §Ò§í§ä§î §Ó§ã§ä§Ñ§Ó§Ý§Ö§ß§Ñ §Ó §Ù§Ñ§Õ§Ñ§ß§ß§å§ð §á§à§Ù§Ú§è§Ú§ð §ä§à§Ý§î§Ü§à §Ó §ä§à§Þ §ã§Ý§å§é§Ñ§Ö, §Ö§ã§Ý§Ú §á§à§ã§Ý§Ö§Õ§à§Ó§Ñ§ä§Ö§Ý§î§ß§à§ã§ä§î §Ó§í§ã§à§ä §Ó §ï§ä§à§Û §á§à§Ù§Ú§è§Ú§Ú §ã§à§à§ä§Ó§Ö§ä§ã§ä§Ó§å§Ö§ä §Ü§à§Õ§Ú§â§à§Ó§Ü§Ö §æ§Ú§Ô§å§â§í. §±§à§ï§ä§à§Þ§å, §é§ä§à§Ò§í §á§à§Ý§å§é§Ú§ä§î §â§Ö§ê§Ö§ß§Ú§Ö, §á§â§à§ã§ä§à §ß§å§Ø§ß§à §á§â§à§Ó§Ö§â§Ú§ä§î §Ó§ã§Ö §Ó§à§Ù§Þ§à§Ø§ß§í§Ö §á§à§Ý§à§Ø§Ö§ß§Ú§ñ §Ó§ã§Ö§ç §Ó§â§Ñ§ë§Ö§ß§Ú§Û §Õ§Ý§ñ §Õ§Ñ§ß§ß§à§Û §æ§Ú§Ô§å§â§í §Ú §á§à§Ý§ñ. §°§Ò§â§Ñ§ä§Ú§ä§Ö §Ó§ß§Ú§Þ§Ñ§ß§Ú§Ö, §é§ä§à §ß§Ö §å §Ó§ã§Ö§ç §æ§Ú§Ô§å§â §Ö§ã§ä§î 4 §Ó§à§Ù§Þ§à§Ø§ß§í§ç §á§à§Ó§à§â§à§ä§Ñ. §¶§Ú§Ô§å§â§Ñ 2 §à§ã§ä§Ñ§Ö§ä§ã§ñ §ß§Ö§Ú§Ù§Þ§Ö§ß§ß§à§Û §ß§Ö§Ù§Ñ§Ó§Ú§ã§Ú§Þ§à §à§ä §á§à§Ó§à§â§à§ä§Ñ, §Ñ §æ§Ú§Ô§å§â§í 1, 3 §Ú 4 §Ú§Þ§Ö§ð§ä §ä§à§Ý§î§Ü§à §Õ§Ó§Ñ §Ó§à§Ù§Þ§à§Ø§ß§í§ç §á§à§Ó§à§â§à§ä§Ñ.
?§©§Ñ§Õ§Ñ§é§Ñ E. §±§Ñ§â§Ü§Ú§ß§Ô
?§£ §®§Ú§ß§ã§Ü§Ö §á§à§ñ§Ó§Ú§Ý§Ñ§ã§î §Ú§ß§ä§Ö§â§Ö§ã§ß§Ñ§ñ §á§Ñ§â§Ü§à§Ó§Ü§Ñ. §±§Ý§Ñ§ä§å §Ù§Ñ §á§Ñ§â§Ü§à§Ó§Ü§å §Ò§Ö§â§å§ä §ß§Ö§à§Ò§í§é§ß§í§Þ §ã§á§à§ã§à§Ò§à§Þ ¡ª §à§ß§Ú §Õ§Ñ§ð§ä §ã§Ü§Ú§Õ§Ü§å §Ó §Ù§Ñ§Ó§Ú§ã§Ú§Þ§à§ã§ä§Ú?§à§ä??§Ü§à§Ý§Ú§é§Ö§ã§ä§Ó§Ñ?§Þ§Ñ§ê§Ú§ß.
§¬§à§Ô§Õ§Ñ §á§â§Ú§á§Ñ§â§Ü§à§Ó§Ñ§ß §ä§à§Ý§î§Ü§à §à§Õ§Ú§ß §Ñ§Ó§ä§à§Þ§à§Ò§Ú§Ý§î, §Ó§à§Õ§Ú§ä§Ö§Ý§î §á§Ý§Ñ§ä§Ú§ä?A?§â§å§Ò§Ý§Ö§Û §Ù§Ñ §é§Ñ§ã. §¬§à§Ô§Õ§Ñ §á§â§Ú§á§Ñ§â§Ü§à§Ó§Ñ§ß§à §Õ§Ó§Ö §Þ§Ñ§ê§Ú§ß§í, §Ü§Ñ§Ø§Õ§í§Û §Ó§à§Õ§Ú§ä§Ö§Ý§î §á§Ý§Ñ§ä§Ú§ä §á§à?B?§â§å§Ò§Ý§Ö§Û §Ù§Ñ §é§Ñ§ã. §¬§à§Ô§Õ§Ñ §á§â§Ú§á§Ñ§â§Ü§à§Ó§Ñ§ß§à §ä§â§Ú §Þ§Ñ§ê§Ú§ß§í, §Ü§Ñ§Ø§Õ§í§Û §Ó§à§Õ§Ú§ä§Ö§Ý§î §á§Ý§Ñ§ä§Ú§ä §á§à?C?§â§å§Ò§Ý§Ö§Û §Ù§Ñ §é§Ñ§ã.
§µ§é§Ú§ä§í§Ó§Ñ§ñ?A, B §Ú C, §Ñ §ä§Ñ§Ü§Ø§Ö §Ú§ß§ä§Ö§â§Ó§Ñ§Ý§í, §Ó §Ü§à§ä§à§â§í§ç §á§â§Ú§á§Ñ§â§Ü§à§Ó§Ñ§ß§í §ä§â§Ú §Ñ§Ó§ä§à§Þ§à§Ò§Ú§Ý§ñ, §à§á§â§Ö§Õ§Ö§Ý§Ú§ä§Ö, §ã§Ü§à§Ý§î§Ü§à §ß§å§Ø§ß§à §Ù§Ñ§á§Ý§Ñ§ä§Ú§ä§î §Ó§Ý§Ñ§Õ§Ö§Ý§î§è§å §Ù§Ñ §Ó§ã§Ö §ä§â§Ú §Þ§Ñ§ê§Ú§ß§í.
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§Ó§Ó§à§Õ |
§Ó§í§Ó§à§Õ |
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5 3 1 1 6 3 5 2 8 |
33? |
§²§Ö§ê§Ö§ß§Ú§Ö:
§©§Ñ§Õ§Ñ§é§Ñ §Þ§à§Ø§Ö§ä §Ò§í§ä§î §â§Ö§ê§Ö§ß§Ñ §Þ§à§Õ§Ö§Ý§Ú§â§à§Ó§Ñ§ß§Ú§Ö§Þ. §¯§å§Ø§ß§à §ã§Ý§Ö§Õ§Ú§ä§î §Ù§Ñ §ä§Ö§Þ, §ã§Ü§à§Ý§î§Ü§à §Þ§Ñ§ê§Ú§ß §ß§Ñ§ç§à§Õ§Ú§ä§ã§ñ §ß§Ñ §á§Ñ§â§Ü§à§Ó§Ü§Ö. §¥§Ý§ñ §Ü§Ñ§Ø§Õ§à§Ô§à §é§Ñ§ã§Ñ §à§ä 0 §Õ§à 100 §Þ§í: ?§³§Ü§Ý§Ñ§Õ§í§Ó§Ñ§Ö§Þ §Ü§à§Ý§Ú§é§Ö§ã§ä§Ó§à §Þ§Ñ§ê§Ú§ß, §á§â§Ú§Ò§í§Ó§Ñ§ð§ë§Ú§ç §Ó §ä§Ö§é§Ö§ß§Ú§Ö §ï§ä§à§Ô§à §é§Ñ§ã§Ñ?. §£§í§é§Ú§ä§Ñ§Ö§Þ §Ü§à§Ý§Ú§é§Ö§ã§ä§Ó§à §Þ§Ñ§ê§Ú§ß, §à§ä§á§â§Ñ§Ó§Ý§ñ§ð§ë§Ú§ç§ã§ñ §Ó §ä§Ö§é§Ö§ß§Ú§Ö §ï§ä§à§Ô§à §é§Ñ§ã§Ñ. §±§Ý§Ñ§ä§Ñ §Ù§Ñ §á§Ñ§â§Ü§à§Ó§Ü§å §Ù§Ñ§Ó§Ú§ã§Ú§ä §à§ä §Ü§à§Ý§Ú§é§Ö§ã§ä§Ó§Ñ §á§â§Ú§á§Ñ§â§Ü§à§Ó§Ñ§ß§ß§í§ç §Þ§Ñ§ê§Ú§ß.
?§©§Ñ§Õ§Ñ§é§Ñ H. §¹§Ú§ã§Ý§à §Ó §Ü§Ó§Ñ§Õ§â§Ñ§ä§Ñ§ç
§©§Ñ§Õ§Ñ§ß§à §è§Ö§Ý§à§Ö §é§Ú§ã§Ý§à n, §Ó§Ö§â§ß§Ú§ä§Ö §ß§Ñ§Û§Þ§Ö§ß§î§ê§Ö§Ö §é§Ú§ã§Ý§à §á§à§Ý§ß§í§ç §Ü§Ó§Ñ§Õ§â§Ñ§ä§ß§í§ç §é§Ú§ã§Ö§Ý, §Ü§à§ä§à§â§í§Ö §Ó §ã§å§Þ§Þ§Ö §Õ§Ñ§ð§ä n.
§±§à§Ý§ß§í§Û §Ü§Ó§Ñ§Õ§â§Ñ§ä, §ä§Ñ§Ü§Ø§Ö §ä§à§é§ß§í§Û §Ü§Ó§Ñ§Õ§â§Ñ§ä §Ú§Ý§Ú §Ü§Ó§Ñ§Õ§â§Ñ§ä§ß§à§Ö §é§Ú§ã§Ý§à, ¡ª §é§Ú§ã§Ý§à, §ñ§Ó§Ý§ñ§ð§ë§Ö§Ö§ã§ñ §Ü§Ó§Ñ§Õ§â§Ñ§ä§à§Þ §ß§Ö§Ü§à§ä§à§â§à§Ô§à §è§Ö§Ý§à§Ô§à §é§Ú§ã§Ý§Ñ. §ª§ß§í§Þ§Ú §ã§Ý§à§Ó§Ñ§Þ§Ú, §Ü§Ó§Ñ§Õ§â§Ñ§ä§à§Þ §ñ§Ó§Ý§ñ§Ö§ä§ã§ñ §è§Ö§Ý§à§Ö §é§Ú§ã§Ý§à, §Ü§Ó§Ñ§Õ§â§Ñ§ä§ß§í§Û §Ü§à§â§Ö§ß§î §Ú§Ù §Ü§à§ä§à§â§à§Ô§à §Ú§Ù§Ó§Ý§Ö§Ü§Ñ§Ö§ä§ã§ñ §ß§Ñ§è§Ö§Ý§à.
§¯§Ñ§á§â§Ú§Þ§Ö§â 1, 4, 9 §Ú 16 §ñ§Ó§Ý§ñ§ð§ä§ã§ñ §á§à§Ý§ß§í§Þ§Ú §Ü§Ó§Ñ§Õ§â§Ñ§ä§Ñ§Þ§Ú, §Ñ 5 §Ú 13 §ß§Ö§ä.
Input
§¯§Ñ §Ó§ç§à§Õ §è§Ö§Ý§à§Ö §é§Ú§ã§Ý§à (§ä§Ö§ã§ä§Ú§â§å§Û§ä§Ö §ß§Ñ §é§Ú§ã§Ý§Ñ§ç §à§ä 1 §Õ§à 20)
Output
§¯§Ñ §Ó§í§ç§à§Õ§Ö §è§Ö§Ý§à§Ö §é§Ú§ã§Ý§à?
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§±§à§ñ§ã§ß§Ö§ß§Ú§Ö |
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12 |
3 |
12 = 4 + 4 + 4. |
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13 |
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12 = 9 + 4. |
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8 |
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8 = 4 + 4. |
?§²§Ö§ê§Ö§ß§Ú§Ö:
§³§à§Ù§Õ§Ñ§Ö§Þ §Þ§Ú§ã§ã§Ú§Ó §â§Ñ§Ù§Þ§Ö§â§à§Þ (n+1) let n = 12, dp Array?
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§¯§Ñ 1 §Ú§ä§Ö§â§Ñ§è§Ú§Ú §Ù§Ñ§á§à§Ý§ß§ñ§Ö§Þ §Þ§Ñ§ã§ã§Ú§Ó §ã §á§à§Ý§ß§í§Þ §Ü§Ó§Ñ§â§Õ§Ñ§ä§à§Þ §ä§à§Ý§î§Ü§à 1
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?§¯§Ñ 2 §à§Ò§ß§à§Ó§Ý§ñ§Ö§Þ §ã §ã§Ý§Ö§Õ§å§ð§ë§Ö§Þ §á§à§Ý§ß§í§Þ §Ü§Ó§Ñ§Õ§â§Ñ§ä§à§Þ 4?
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§¯§Ñ 3 §à§Ò§ß§à§Ó§Ý§ñ§Ö§Þ §ã §ã§Ý§Ö§Õ§å§ð§ë§Ö§Þ §á§à§Ý§ß§í§Þ §Ü§Ó§Ñ§Õ§â§Ñ§ä§à§Þ 9?
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§£§â§Ö§Þ§ñ: §Ó§ß§Ö§ê§ß§Ú§Û §è§Ú§Ü§Ý O (n * sqrt (n)) §ã§à§ã§ä§à§Ú§ä §Ú§Ù sqrt (n) §Ú§ä§Ö§â§Ñ§è§Ú§Û, §Ñ §Ó§à §Ó§ß§å§ä§â§Ö§ß§ß§Ö§Þ §è§Ú§Ü§Ý§Ö §á§â§Ú§Þ§Ö§â§ß§à < n §Ú§ä§Ö§â§Ñ§è§Ú§Û.
§±§Ñ§Þ§ñ§ä§î: O(n).
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§©§Ñ§Õ§Ñ§é§Ñ G. §±§à§Ú§ã§Ü§Þ§Ý§Ñ§Õ§ê§Ú§ç§ã§à§ã§Ö§Õ§Ö§Û
§µ §Ó§Ñ§ã §Ú§Þ§Ö§Ö§ä§ã§ñ §Þ§Ñ§ã§ã§Ú§Ó §è§Ö§Ý§í§ç §é§Ú§ã§Ö§Ý, §Ó§Ñ§Þ §ß§Ö§à§Ò§ç§à§Õ§Ú§Þ§à §Ó§Ö§â§ß§å§ä§î §Þ§Ñ§ã§ã§Ú§Ó §é§Ú§ã§Ö§Ý, §Ó §Ü§à§ä§à§â§à§Þ §Ù§Ñ§á§Ú§ã§Ñ§ß§í §Ü§à§Ý§Ú§é§Ö§ã§ä§Ó§à §ï§Ý§Ö§Þ§Ö§ß§ä§à§Ó §Þ§Ö§ß§î§ê§Ö §Ü§Ñ§Ø§Õ§à§Ô§à §ï§Ý§Ö§Þ§Ö§ß§ä§Ñ §Þ§Ñ§ã§Ú§Ó§Ñ §ã§á§â§Ñ§Ó§Ñ.
§³§á§â§Ñ§Ó§Ñ §à§ä 7 §Ö§ã§ä§î 2 §Þ§Ö§ß§î§ê§Ú§ç §ï§Ý§Ö§Þ§Ö§ß§ä§Ñ (3 §Ú 1).
§³§á§â§Ñ§Ó§Ñ §à§ä 3 §Ö§ã§ä§î §ä§à§Ý§î§Ü§à 1 §Þ§Ö§ß§î§ê§Ú§Û §ï§Ý§Ö§Þ§Ö§ß§ä (1).
§³§á§â§Ñ§Ó§Ñ §à§ä 9 §ß§Ñ§ç§à§Õ§Ú§ä§ã§ñ 1 §ï§Ý§Ö§Þ§Ö§ß§ä §Þ§Ö§ß§î§ê§Ö§Ô§à §â§Ñ§Ù§Þ§Ö§â§Ñ (1).
§³§á§â§Ñ§Ó§Ñ §à§ä 1 §ß§Ñ§ç§à§Õ§Ú§ä§ã§ñ 0 §Þ§Ö§ß§î§ê§Ú§ç §ï§Ý§Ö§Þ§Ö§ß§ä§à§Ó.
§ª§ã§á§à§Ý§î§Ù§å§Û§ä§Ö §Þ§Ñ§ã§ã§Ú§Ó [7,3,9,1] §Ü§Ñ§Ü §ß§Ñ§é§Ñ§Ý§î§ß§à§Ö §å§ã§Ý§à§Ó§Ú§Ö. §±§â§Ú§Þ§Ö§â §ß§Ñ Python print(counterSmall([7,3,9,1]))
Input
§¯§Ñ §Ó§ç§à§Õ §Þ§Ñ§ã§Ú§Ó §é§Ú§ã§Ö§Ý [7, 3, 9, 1]
Output
§¯§Ñ §Ó§í§ç§à§Õ§Ö §Þ§Ñ§ã§Ú§Ó §ß§Ñ§Û§Õ§Ö§ß§í§ç §é§Ú§ã§Ö§Ý [2, 1, 1, 0]
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[7, 3, 9, 1] |
[2, 1, 1, 0] |
§²§Ö§ê§Ö§ß§Ú§Ö:
§±§â§Ú§Þ§Ö§â, §á§â§Ú§Ó§Ö§Õ§Ö§ß§ß§í§Û §Ó §à§á§Ú§ã§Ñ§ß§Ú§Ú §Ù§Ñ§Õ§Ñ§é§Ú: [7, 3, 9, 1]
§£§í§á§à§Ý§ß§Ú§Þ §à§Ò§í§é§ß§å§ð §ã§à§â§ä§Ú§â§à§Ó§Ü§å §ã§Ý§Ú§ñ§ß§Ú§Ö§Þ §Õ§Ý§ñ §Õ§Ñ§ß§ß§à§Ô§à §Þ§Ñ§ã§ã§Ú§Ó§Ñ.
§±§â§Ú §à§Ò§í§é§ß§à§Û §ã§à§â§ä§Ú§â§à§Ó§Ü§Ö §ã§Ý§Ú§ñ§ß§Ú§Ö§Þ, §Þ§í §â§Ö§Ü§å§â§ã§Ú§Ó§ß§à §â§Ñ§Ù§Õ§Ö§Ý§ñ§Ö§Þ §Þ§Ñ§ã§ã§Ú§Ó §ã§Ó§Ö§â§ç§å §Ó§ß§Ú§Ù, §á§à§Ü§Ñ §Ü§Ñ§Ø§Õ§í§Û? §Ú§Ù §á§à§Õ§Þ§Ñ§ã§ã§Ú§Ó§à§Ó §ß§Ö §Ò§å§Õ§Ö§ä §Ú§Þ§Ö§ä§î §â§Ñ§Ù§Þ§Ö§â 1
[7, 3, 9, 1]
[7, 3] [9, 1]
[7] [3] [9] [1]
§´§Ö§á§Ö§â§î §Ó§Ö§â§ß§Ö§Þ§ã§ñ §ã§ß§Ú§Ù§å §Ó§Ó§Ö§â§ç.
§®§í §à§Ò§ì§Ö§Õ§Ú§ß§ñ§Ö§Þ [7] §Ú [3] §Ó §â§Ö§Ù§å§Ý§î§ä§Ú§â§å§ð§ë§Ú§Û §Þ§Ñ§ã§ã§Ú§Ó.
§°§Ò§í§é§ß§à §Þ§í §á§â§à§ã§ä§à §Õ§à§Ý§Ø§ß§í §ã§â§Ñ§Ó§ß§Ú§ä§î §á§Ö§â§Ó§í§Û §ï§Ý§Ö§Þ§Ö§ß§ä §à§Ò§à§Ú§ç §á§à§Õ§Þ§Ñ§ã§ã§Ú§Ó§à§Ó (7 §Ú 3) §Ú §Ó§Ù§ñ§ä§î §Þ§Ö§ß§î§ê§Ú§Û §ï§Ý§Ö§Þ§Ö§ß§ä (3) §á§à§Þ§Ö§ã§ä§Ú§ä§Ö §Þ§Ö§ß§î§ê§Ú§Û §ï§Ý§Ö§Þ§Ö§ß§ä §Ó ?§à§Ò§ì§Ö§Õ§Ú§ß§Ö§ß§ß§å§ð? §à§Ò§Ý§Ñ§ã§ä§î
§£§¯§ª§®§¡§¯§ª§¦: §Ó §ï§ä§à§Þ §ã§Ý§å§é§Ñ§Ö §Þ§í §Ù§ß§Ñ§Ö§Þ, §é§ä§à: §á§Ö§â§Ö§Õ §ã§à§â§ä§Ú§â§à§Ó§Ü§à§Û §Ó§ã§Ö §ï§Ý§Ö§Þ§Ö§ß§ä§í §Ó §Ý§Ö§Ó§à§Þ §á§à§Õ§Þ§Ñ§ã§ã§Ú§Ó§Ö [7] §Ú§Ù§ß§Ñ§é§Ñ§Ý§î§ß§à §â§Ñ§ã§á§à§Ý§Ñ§Ô§Ñ§ð§ä§ã§ñ §³§§¦§£§¡ §à§ä §Ó§ã§Ö§ç §ï§Ý§Ö§Þ§Ö§ß§ä§à§Ó §Ó §á§â§Ñ§Ó§à§Þ §á§à§Õ§Þ§Ñ§ã§ã§Ú§Ó§Ö [3] 7 > 3
§´§Ö§á§Ö§â§î §Þ§í §ß§Ñ§ê§Ý§Ú 1 §ï§Ü§Ù§Ö§Þ§á§Ý§ñ§â §ï§Ý§Ö§Þ§Ö§ß§ä§Ñ (3), §Ü§à§ä§à§â§í§Û §â§Ñ§ã§á§à§Ý§à§Ø§Ö§ß §ã§á§â§Ñ§Ó§Ñ §à§ä 7 §Ú §Þ§Ö§ß§î§ê§Ö 7.
§®§í §Þ§à§Ø§Ö§Þ §å§Ó§Ö§Ý§Ú§é§Ú§ä§î §ß§Ñ 1, §â§Ö§Ù§å§Ý§î§ä§Ñ§ä §à§ä§Ó§Ö§ä§Ñ §Õ§Ý§ñ 7.
§¦§ã§Ý§Ú §Þ§í §á§à§Ó§ä§à§â§Ú§Þ §ï§ä§à§ä §á§â§à§è§Ö§ã§ã §ß§Ö§ã§Ü§à§Ý§î§Ü§à §â§Ñ§Ù §á§à§Ý§å§é§Ú§Þ §ß§å§Ø§ß§í§Û §à§ä§Ó§Ö§ä.
§±§â§à§Õ§à§Ý§Ø§Ú§Þ §ß§Ñ§ê §á§Ö§â§Ó§à§ß§Ñ§é§Ñ§Ý§î§ß§í§Û §á§â§Ú§Þ§Ö§â:
[7, 3, 9, 1]
[7, 3] [9, 1]
[7] [3] [9] [1]
§¯§Ñ§é§Ñ§Ý§î§ß§í§Û §â§Ö§Ù§å§Ý§î§ä§Ñ§ä: 7(0) 3(0) 9(0) 1(0) §Ö§ã§Ý§Ú §Þ§í §á§à§Õ§ß§Ú§Þ§Ú§Þ§ã§ñ §ß§Ñ §à§Õ§Ú§ß §å§â§à§Ó§Ö§ß§î §ã§ß§Ú§Ù§å
3 §Þ§Ö§ß§î§ê§Ö §Ú §á§â§Ñ§Ó§Ö§Ö 7 ==> §å§Ó§Ö§Ý§Ú§é§Ö§ß§Ú§Ö §ã§é§Ö§ä§é§Ú§Ü§Ñ §Õ§Ý§ñ 7
1 §Þ§Ö§ß§î§ê§Ö §Ú §á§â§Ñ§Ó§Ö§Ö 9 ==> §å§Ó§Ö§Ý§Ú§é§Ö§ß§Ú§Ö §ã§é§Ö§ä§é§Ú§Ü§Ñ §Õ§Ý§ñ 9
[7, 3, 9, 1]
[7, 3] [9, 1]
§´§Ö§Ü§å§ë§Ú§Û §â§Ö§Ù§å§Ý§î§ä§Ñ§ä: 7(1) 3(0) 9(1) 1(0)
§´§Ö§á§Ö§â§î §ß§Ñ§Þ §ß§å§Ø§ß§à §à§Ò§ì§Ö§Õ§Ú§ß§Ú§ä§î:
§Ý§Ö§Ó§í§Û §á§à§Õ§Þ§Ñ§ã§ã§Ú§Ó, [3, 7] §Ú §á§â§Ñ§Ó§í§Û §á§à§Õ§Þ§Ñ§ã§ã§Ú§Ó [1, 9]
§£§ã§Ö §ï§Ý§Ö§Þ§Ö§ß§ä§í §Ó §á§â§Ñ§Ó§à§Þ §á§à§Õ§Þ§Ñ§ã§ã§Ú§Ó§Ö §Ú§Ù§ß§Ñ§é§Ñ§Ý§î§ß§à §â§Ñ§ã§á§à§Ý§à§Ø§Ö§ß§í §ã§á§â§Ñ§Ó§Ñ §à§ä §Ó§ã§Ö§ç §ï§Ý§Ö§Þ§Ö§ß§ä§à§Ó §Ó §Ý§Ö§Ó§à§Þ §á§à§Õ§Þ§Ñ§ã§ã§Ú§Ó§Ö
§°§Ò§â§Ñ§ä§Ú§ä§Ö §Ó§ß§Ú§Þ§Ñ§ß§Ú§Ö, §é§ä§à 1 §Ú§Ù §á§â§Ñ§Ó§à§Ô§à §á§à§Õ§Þ§Ñ§ã§ã§Ú§Ó§Ñ §Þ§Ö§ß§î§ê§Ö 3 §Ú§Ù §Ý§Ö§Ó§à§Ô§à §á§à§Õ§Þ§Ñ§ã§ã§Ú§Ó§Ñ.
§¿§ä§à §à§Ù§ß§Ñ§é§Ñ§Ö§ä, §é§ä§à 1 §â§Ñ§ã§á§à§Ý§à§Ø§Ö§ß §ã§á§â§Ñ§Ó§Ñ §à§ä 3 §Ú §Þ§Ö§ß§î§ê§Ö 3.
§±§à§ï§ä§à§Þ§å §Þ§í §Õ§à§Ý§Ø§ß§í §å§Ó§Ö§Ý§Ú§é§Ú§ä§î §Ü§à§Ý§Ú§é§Ö§ã§ä§Ó§à §Þ§Ö§ß§î§ê§Ú§ç §ï§Ý§Ö§Þ§Ö§ß§ä§à§Ó §Õ§Ý§ñ 3.
§°§Ò§â§Ñ§ä§Ú§ä§Ö §Ó§ß§Ú§Þ§Ñ§ß§Ú§Ö, §é§ä§à 1 §ä§Ñ§Ü§Ø§Ö §Þ§Ö§ß§î§ê§Ö 7 §Ú §â§Ñ§ã§á§à§Ý§à§Ø§Ö§ß§à §ã§á§â§Ñ§Ó§Ñ §à§ä 7.
1 §Þ§Ö§ß§î§ê§Ö §Ú §â§Ñ§ã§á§à§Ý§à§Ø§Ö§ß §á§â§Ñ§Ó§Ö§Ö §Ó§ã§Ö§ç §ï§Ý§Ö§Þ§Ö§ß§ä§à§Ó §Ó §Ý§Ö§Ó§à§Þ §á§à§Õ§Þ§Ñ§ã§ã§Ú§Ó§Ö, §ï§ä§à §ã§Ó§ñ§Ù§Ñ§ß§à §ã §ä§Ö§Þ, §é§ä§à §Ý§Ö§Ó§í§Û §á§à§Õ§Þ§Ñ§ã§ã§Ú§Ó §å§Ø§Ö §Ò§í§Ý §à§ä§ã§à§â§ä§Ú§â§à§Ó§Ñ§ß §Ú§Ù §á§â§Ö§Õ§í§Õ§å§ë§Ú§ç §Ó§í§Ù§à§Ó§à§Ó §â§Ö§Ü§å§â§ã§Ú§Ó§ß§à§Û §ã§à§â§ä§Ú§â§à§Ó§Ü§Ú §ã§Ý§Ú§ñ§ß§Ú§Ö§Þ.
§ª§Ù §ï§ä§à§Ô§à §ã§Ý§Ö§Õ§å§Ö§ä §é§ä§à: 1 < 3 < 7
§±§à§ï§ä§à§Þ§å §ß§Ñ§Þ §ä§Ñ§Ü§Ø§Ö §ß§å§Ø§ß§à §Ò§å§Õ§Ö§ä §å§Ó§Ö§Ý§Ú§é§Ú§ä§î §Ü§à§Ý§Ú§é§Ö§ã§ä§Ó§à §Þ§Ö§ß§î§ê§Ú§ç §ï§Ý§Ö§Þ§Ö§ß§ä§à§Ó §Õ§Ý§ñ 7
§¿§ä§à §à§Ò§ß§à§Ó§Ý§Ö§ß§ß§à§Ö §ã§à§ã§ä§à§ñ§ß§Ú§Ö:
7(1) 3(0) 9(1) 1(0) -------> 7(2) 3(1) 9(1) 1(0)
§´§Ö§á§Ö§â§î §Ö§Õ§Ú§ß§ã§ä§Ó§Ö§ß§ß§í§Þ §ï§Ý§Ö§Þ§Ö§ß§ä§à§Þ §Ó §á§â§Ñ§Ó§à§Þ §á§à§Õ§Þ§Ñ§ã§ã§Ú§Ó§Ö §ñ§Ó§Ý§ñ§Ö§ä§ã§ñ 9. §£§ã§Ö §ï§Ý§Ö§Þ§Ö§ß§ä§í §Ó §Ý§Ö§Ó§à§Þ §á§à§Õ§Þ§Ñ§ã§ã§Ú§Ó§Ö [3,7] §Þ§Ö§ß§î§ê§Ö 9, §á§à§ï§ä§à§Þ§å §á§â§à§ã§ä§à §á§Ö§â§Ö§Þ§Ö§ã§ä§Ú§ä§Ö §Ú§ç §Ó ?§à§Ò§ì§Ö§Õ§Ú§ß§Ö§ß§ß§å§ð? §à§Ò§Ý§Ñ§ã§ä§î, §ä§Ñ§Ü§Ñ§ñ §Ø§Ö, §Ü§Ñ§Ü §Ú §á§â§Ú §à§Ò§í§é§ß§à§Û §ã§à§â§ä§Ú§â§à§Ó§Ü§à§Û §ã§Ý§Ú§ñ§ß§Ú§Ö§Þ.
[3, 7] [1, 9] ----------> [1,3,7,9]
§¶§Ú§ß§Ñ§Ý§î§ß§í§Û §â§Ö§Ù§å§Ý§î§ä§Ñ§ä§à§Ó: 7(1) 3(0) 9(1) 1(0) -------> 7(2) 3(1) 9(1) 1(0)
§³§à§â§ä§Ú§â§à§Ó§Ü§Ñ §ã§Ý§Ú§ñ§ß§Ú§Ö§Þ §Ù§Ñ§Ó§Ö§â§ê§Ö§ß§Ñ.
§°§Ü§à§ß§é§Ñ§ä§Ö§Ý§î§ß§í§Û §â§Ö§Ù§å§Ý§î§ä§Ñ§ä [2,1,1,0], §Ü§Ñ§Ü §Ú §Ó §à§á§Ú§ã§Ñ§ß§Ú§Ú §Ù§Ñ§Õ§Ñ§é§Ú.
§±§à§ã§Ü§à§Ý§î§Ü§å §Þ§í §ä§à§Ý§î§Ü§à §é§ä§à §Ó§í§á§à§Ý§ß§Ú§Ý§Ú §à§Ò§í§é§ß§å§ð §ã§à§â§ä§Ú§â§à§Ó§Ü§å §ã§Ý§Ú§ñ§ß§Ú§Ö§Þ §Ú §á§à §ç§à§Õ§å §Õ§à§Ò§Ñ§Ó§Ú§Ý§Ú §ß§Ö§Ü§à§ä§à§â§å§ð §á§â§à§Ó§Ö§â§à§é§ß§å§ð §Ý§à§Ô§Ú§Ü§å, §Ó§â§Ö§Þ§ñ §Ó§í§á§à§Ý§ß§Ö§ß§Ú§ñ §ä§Ñ§Ü§à§Ö §Ø§Ö, §Ü§Ñ§Ü §Ú §á§â§Ú §à§Ò§í§é§ß§à§Û §ã§à§â§ä§Ú§â§à§Ó§Ü§Ö §ã§Ý§Ú§ñ§ß§Ú§Ö§Þ, O(n log n)
?
13.10.2021 §á§â§à§ê§Ý§Ñ §Ú§ß§Õ§Ú§Ó§Ú§Õ§å§Ñ§Ý§î§ß§Ñ§ñ §à§Ý§Ú§Þ§á§Ú§Ñ§Õ§Ñ §¢§¤§´§µ
§±§à§Ù§Õ§â§Ñ§Ó§Ý§ñ§Ö§Þ §á§à§Ò§Ö§Õ§Ú§ä§Ö§Ý§Ö§Û:
1 §Þ§Ö§ã§ä§à - §³§Ü§à§â§à§Õ§å§Þ§à§Ó §ª§Ó§Ñ§ß, §±§°§ª§´ 3-5
2 §Þ§Ö§ã§ä§à - §´§Ú§ç§à§ß§à§Ó§Ú§é §¯§Ú§Ü§Ú§ä§Ñ, §±§°§ª§´ 2-4
3 §Þ§Ö§ã§ä§à - §©§Ý§à§Ò§Ú§ß §²§à§Þ§Ñ§ß, §ª§³§Ú§´ 4-2
?
27.04.2021 §á§â§à§ê§Ý§Ñ §Ü§à§Þ§Ñ§ß§Õ§ß§Ñ§ñ §à§Ý§Ú§Þ§á§Ú§Ñ§Õ§Ñ §¢§¤§´§µ
§±§à§Ù§Õ§â§Ñ§Ó§Ý§ñ§Ö§Þ §Ü§à§Þ§Ñ§ß§Õ§í:
1 §Þ§Ö§ã§ä§à: §¬§à§Þ§Ñ§ß§Õ§Ñ ?HouseOfFire?,
§´§Ñ§Ò§à§Ý§Ú§é §¡§â§ä§×§Þ §³§Ö§â§Ô§Ö§Ö§Ó§Ú§é, 2 §Ü§å§â§ã, §ã§á§Ö§è. §±§°§ª§´ §Ô§â. 5,
§®§à§ä§à§Ý§ñ§ß§Ö§è §¦§Ü§Ñ§ä§Ö§â§Ú§ß§Ñ §³§Ö§â§Ô§Ö§Ö§Ó§ß§Ñ, 2 §Ü§å§â§ã, §ª§³§ª§´ §ã§á§Ö§è. §Ô§â. 1,
§¶§Ú§Ý§Ú§á§á§à§Ó §³§Ö§â§Ñ§æ§Ú§Þ §ª§Ô§à§â§Ö§Ó§Ú§é, 2 §Ü§å§â§ã, §±§°§ª§´ §ã§á§Ö§è. §Ô§â. 5
2 §Þ§Ö§ã§ä§à: §¬§à§Þ§Ñ§ß§Õ§Ñ ?BigO?,
§¬§Ñ§Ý§à§ê§Ñ §ª§Ý§î§ñ §£§Ñ§Ý§Ö§â§î§Ö§Ó§Ú§é, 3 §Ü§å§â§ã, §ã§á§Ö§è. §ª§³§ª§´ §Ô§â. 2,
§©§Ý§à§Ò§Ú§ß §²§à§Þ§Ñ§ß §À§â§î§Ö§Ó§Ú§é, 3 §Ü§å§â§ã, §ã§á§Ö§è. §ª§³§ª§´ §Ô§â. 2,
§®§Ñ§Ü§Ö§Ö§Ó §¥§Þ§Ú§ä§â§Ú§Û §£§Ñ§ã§Ú§Ý§î§Ö§Ó§Ú§é, 3 §Ü§å§â§ã, §ª§³§ª§´ §ã§á§Ö§è. §Ô§â. 1
3 §Þ§Ö§ã§ä§à: §¬§à§Þ§Ñ§ß§Õ§Ñ ?IPatel?,
§¬§Ú§ê§Ü§à §ª§Ó§Ñ§ß §±§Ö§ä§â§à§Ó§Ú§é, 2 §Ü§å§â§ã, §ã§á§Ö§è. §±§°§ª§´ §Ô§â. 5,
§³§Ü§à§â§à§Õ§å§Þ§à§Ó §ª§Ó§Ñ§ß §ª§Ó§Ñ§ß§à§Ó§Ú§é, 2 §Ü§å§â§ã, §ã§á§Ö§è. §±§°§ª§´ §Ô§â. 5,
§º§å§ã§ä §À§â§Ú§Û §°§Ý§Ö§Ô§à§Ó§Ú§é, 2 §Ü§å§â§ã, §ã§á§Ö§è. §±§°§ª§´ §Ô§â. 4