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- ããã§ãå³æžé€šã¯å¹³æ¥ã®ååäžã¯Cããã ããååŸã¯Dããã ããããœã³ã³ã䜿ãããšãèš±å¯ããŸããã
- ç¿é±ãCãããšDããã¯ã©ã¡ãã14æããããœã³ã³ã§ä»äºãå§ããŸããã
- ãã®æ¥ããœã³ã³ã¯ã¯ã©ãã·ã¥ããŠããŸããŸããã
2. **æšç**:
- éåžžãå³æžé€šã¯å¹³æ¥ã®ååŸã¯Dããã ããããœã³ã³ã䜿ãããšãèš±å¯ããŠããŸãã
- ãããããã®æ¥CãããšDãããã©ã¡ãã14æããããœã³ã³ã§ä»äºãå§ããŸããã
- ããã¯éåžžã®ã«ãŒã«ãç Žã£ãè¡åã§ãããäž¡è
ãåæã«ããœã³ã³ã䜿ãããšã«ãªãåŸãŸãã
3. **çµè«**:
- äž¡è
ãåæã«ããœã³ã³ã䜿ãããšãåå ã§ã¯ã©ãã·ã¥ããå¯èœæ§ãé«ãã§ãã
- å³æžé€šã®ã«ãŒã«ãç Žã£ãŠäž¡è
ãåæã«ããœã³ã³ã䜿çšããçµæãã¯ã©ãã·ã¥ãèµ·ãã£ããšèããããŸãã
ãããã£ãŠããã®åé¡ã«å¯ŸããŠã®åçã¯ãCãããšDãããäž¡æ¹åæã«ããœã³ã³ã䜿çšããããšãåå ã§ããœã³ã³ãã¯ã©ãã·ã¥ããå¯èœæ§ãé«ãããšãªããŸãã |
次ã®æã®ãã¡ãã©ã¡ããããæå³ãéããã§ããããã
éžæè¢1: 圌ã¯äŒç€ŸãèŸããã®ã¯ãèµ·æ¥ããããã ã
éžæè¢2: 圌ã¯èµ·æ¥ããã®ã¯ãäŒç€ŸãèŸããããã ã | ãã®åé¡ã§ã¯ãäž¡æ¹ã®æãææ³çã«ã¯æ£ããã§ãããæå³åããç°ãªãããšã«æ³šæãå¿
èŠã§ãã
éžæè¢1: ã圌ã¯äŒç€ŸãèŸããã®ã¯ãèµ·æ¥ããããã ãã
ããã¯ã圌ãäŒç€ŸãèŸããçç±ã¯ãèµ·æ¥ããããã ããšããæå³ã«ãªããŸããã€ãŸãã圌ã¯èµ·æ¥ããããã«äŒç€ŸãèŸããããšã瀺ããŠããŸãã
éžæè¢2: ã圌ã¯èµ·æ¥ããã®ã¯ãäŒç€ŸãèŸããããã ãã
ããã¯ã圌ãèµ·æ¥ããçç±ã¯ãäŒç€ŸãèŸããããã ããšããæå³ã«ãªããŸããã€ãŸãã圌ã¯äŒç€ŸãèŸããåŸã§èµ·æ¥ããããšã瀺ããŠããŸãã
ã©ã¡ãã®éžæè¢ãããæå³ãéãããã¯ãæèã«ãã£ãŠå€ãããŸãããã圌ãäŒç€ŸãèŸããŠããèµ·æ¥ããã®ã§ããã°ãéžæè¢2ãããæ£ç¢ºã§ãããããããã圌ãèµ·æ¥ããããã«äŒç€ŸãèŸããã®ã§ããã°ãéžæè¢1ãããé©åã§ãã
éåžžããã®ãããªæã¯ååŸã®æèã«ãã£ãŠè§£éãå€ãããããå®å
šãªæèãäžããããŠããã°ããæ£ç¢ºãªå€æãã§ããã§ãããã |
2ã€ã®æååã§é£ç¶ããæé·å
±ééšåæååã®é·ããæ±ããã | ãã®åé¡ã¯å
žåçãªDPïŒåçèšç»æ³ïŒåé¡ã«è©²åœããŸããé£ç¶ããæé·å
±ééšåæååïŒLCS: Longest Common SubsequenceïŒãæ±ããŸãã以äžã«ããã®åé¡ã解ãããã®ã¹ããããšã³ãŒãã瀺ããŸãã
### 解æ³ã®æé
1. **DPããŒãã«ã®åæå**:
- DPããŒãã«ã¯ã2ã€ã®æååã®é·ãã«åãããŠ2次å
ã®é
åãäœããŸãã
- åèŠçŽ `dp[i][j]` ã¯ãæåå1ã®åiæåãšæåå2ã®åjæåã®æé·å
±ééšåæååã®é·ããè¡šããŸãã
2. **DPããŒãã«ã®æŽæ°ã«ãŒã«**:
- æåãäžèŽããå Žå (`æåå1[i-1] == æåå2[j-1]`): `dp[i][j] = dp[i-1][j-1] + 1`
- æåãäžèŽããªãå Žå: `dp[i][j] = max(dp[i-1][j], dp[i][j-1])`
3. **çµæã®ååŸ**:
- æçµçãªçµæ㯠`dp[n1][n2]` ã«æ ŒçŽãããŸãã
### å®è£
äŸ
以äžã«Pythonã«ããå®è£
äŸã瀺ããŸãã
```python
def longest_common_subsequence(s1, s2):
n1, n2 = len(s1), len(s2)
# DPããŒãã«ã®åæå
dp = [[0] * (n2 + 1) for _ in range(n1 + 1)]
# DPããŒãã«ã®æŽæ°
for i in range(1, n1 + 1):
for j in range(1, n2 + 1):
if s1[i - 1] == s2[j - 1]:
dp[i][j] = dp[i - 1][j - 1] + 1
else:
dp[i][j] = max(dp[i - 1][j], dp[i][j - 1])
# æçµçãªçµæã®ååŸ
return dp[n1][n2]
# å
¥åæåå
s1 = "ããããããã"
s2 = "ããããããã«ãã"
# 解ç
result = longest_common_subsequence(s1, s2)
print("é£ç¶ããæé·å
±ééšåæååã®é·ã:", result)
```
### å®è¡çµæ
äžèšã®ã³ãŒããå®è¡ãããšã`é£ç¶ããæé·å
±ééšåæååã®é·ã: 5` ãåºåãããŸããããã¯ãæåå1ãšæåå2ã®æé·å
±ééšåæååã "ãããã" ã§ããããšãæå³ããŸãã
### 説æ
- `s1` ãš `s2` ã®å
±ééšåæåå㯠"ãããã" ã§ãããé£ç¶ããéšåãšã¯éããªãã
- ãã®åé¡ã§ã¯ãé£ç¶ããæ¡ä»¶ã§ãªãããããã®è§£ãæ£ããã§ãã
ãã®æ¹æ³ã§ãä»»æã®2ã€ã®æååã«å¯Ÿããé£ç¶ããæé·å
±ééšåæååã®é·ããæ±ããããšãã§ããŸãã |
以äžã®äŸæã¯ãžã§ãŒã¯ïŒç®èïŒãèšã£ãŠããŸããïŒ
ä»æ¥ã®å€©æ°ã¯æé«ã ããåè²·ã£ãŠããã®å¿ããŠãããã | ãã®äŸæã¯ãžã§ãŒã¯ïŒç®èïŒãšããŠè§£éããããšãã§ããŸããæèããã倩æ°ãè¯ãæ¥ã«ã¯åãè²·ãå¿
èŠããªãããšãåæã«ãæ
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解æéçšïŒ
1. ç«ææ¥ããæ°ããŠ1æ¥ç®ã¯æ°Žææ¥ã§ãã
2. 2æ¥ç®ã¯æšææ¥ã§ãã
3. 3æ¥ç®ã¯éææ¥ã§ãã
4. 4æ¥ç®ã¯åææ¥ã§ãã
5. 5æ¥ç®ã¯æ¥ææ¥ã§ãã
6. 6æ¥ç®ã¯æææ¥ã§ãã
7. 7æ¥ç®ã¯ç«ææ¥ã§ãã
8. 8æ¥ç®ã¯æ°Žææ¥ã§ãã
9. 9æ¥ç®ã¯æšææ¥ã§ãã
10. 10æ¥ç®ã¯éææ¥ã§ãã
ãããã£ãŠãç«ææ¥ã®10æ¥åŸã¯éææ¥ã«ãªããŸãã |
æ¬åŒ§ãæ£ããéããããããã«ã次ã®é
åãå®æãããŠãã ããã
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åæ¯ `[ { ( ) ] }`ïŒæ们æ¥æ£æ¥äžäžïŒ
1. `[` éèŠ `]` æ¥éåã
2. `{` éèŠ `}` æ¥éåã
3. `(` éèŠ `)` æ¥éåã
åœåçé
å `[ { ( ) ] }` äžïŒ`[` å `{` éœè¢«æ£ç¡®éåäºïŒäœæ¯é¡ºåºäžå¯¹ãæ£ç¡®ç顺åºåºè¯¥æ¯å
éåæè¿çïŒå³æå
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ååºè¯¥æ¯ïŒ
`[ { ( ) } ]`
è¿æ ·ïŒææçæ¬å·éœæ£ç¡®éåäºã |
以äžã®æã¯ããæ°åŒãèªç¶èšèªã§è¡šãããã®ã§ããå
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\[
\left( \left( \frac{5}{8} \right) + 23 \right) \times 15 \div 5
\]
ãã®åŒã®èšç®æé ã¯ä»¥äžã®éãã§ãïŒ
1. ãŸãã5ã8ã§å²ããŸãïŒ \(\frac{5}{8}\)
2. 次ã«ããã®çµæã«23ã足ããŸãïŒ \(\frac{5}{8} + 23\)
3. ãã®çµæã15åããŸãïŒ \(\left( \frac{5}{8} + 23 \right) \times 15\)
4. æåŸã«ããã®çµæã5ã§å²ããŸãïŒ \(\left( \frac{5}{8} + 23 \right) \times 15 \div 5\)
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2. 3æ©åŸããžè¡ã£ãŠãïŒåãåãããŸãŸåŸãã«3æ©é²ã¿ãŸããïŒ
3. 4æ©å³ãžè¡ã£ãŠãïŒå³ã«4æ©é²ã¿ãŸããïŒ
4. 1æ©åŸããžè¡ã£ãŠãïŒå³ãåãããŸãŸåŸãã«1æ©é²ã¿ãŸããïŒ
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6. 2æ©å·Šã«é²ãã§ãïŒå³ããå·Šãžåãããå·Šã«2æ©é²ã¿ãŸããïŒ
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4. **ç¹å®ã®æ¥çãè·æ¥çšèª**ïŒäŸãã°ãç¹å®ã®ããžãã¹ãç£æ¥åéã§ããã©ãŒã«ããç¹å¥ãªæå³ãæã€å ŽåããããŸãã
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å ±ãæäŸããŠããã ããã°ãããæ£ç¢ºãªåçãæäŸã§ãããããããŸããã |
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èŠããããŸãã |
ã¢ããã«ãšãªã¬ã³ãžã¯ã©ã®ããã«äŒŒãŠããŸããïŒ | ã¢ããã«ãšãªã¬ã³ãžã¯ãããã€ãã®é¢ã§äŒŒãŠããŸããäž»ãªé¡äŒŒç¹ã¯ä»¥äžã®éãã§ãïŒ
1. äž¡è
ãšãæç©ã§ãïŒã¢ããã«ãšãªã¬ã³ãžã¯ãšãã«æç©ã®äžçš®ã§ãäž¡æ¹ãšãé£çšã§ãã
2. ã©ã¡ããæ é€äŸ¡ãé«ããå¥åº·ã«è¯ãïŒã¢ããã«ãšãªã¬ã³ãžã¯ãã¿ãã³Cãç¹ç¶è³ªãªã©ã®æ é€çŽ ãå€ãå«ãã§ãããå¥åº·ç¶æãå
ç«ã®åŒ·åã«åœ¹ç«ã¡ãŸãã
3. äž¡è
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Once upon a time, in a lush forest filled with the rustling of leaves and the chirping of birds, lived a young and curious rabbit named Usagi. Usagi was unlike other rabbits, as he was always eager to explore the vast and mysterious world beyond the safety of his burrow. One sunny morning, as Usagi was nibbling on the tender grass near the edge of the forest, he spotted a peculiar sight - a group of colorful toads, led by an unusually wise and kind-hearted toad named Uribou, who was known as the "toad philosopher" among the forest creatures.
Curious about these unusual visitors, Usagi approached the group and introduced himself. Uribou, recognizing the kindness in Usagi's eyes, welcomed him warmly and invited the young rabbit to join their gathering. Over time, Usagi found himself drawn to Uribou's stories and teachings, which emphasized the importance of friendship, understanding, and the beauty of the natural world.
As days turned into weeks, Usagi and Uribou became inseparable friends. Uribou shared with Usagi the secrets of the forest, the importance of living in harmony with nature, and the value of empathy and kindness. In return, Usagi introduced Uribou to the wonders of the world beyond the forest, sharing tales of cities, people, and the diverse experiences that life had to offer.
One day, as Usagi and Uribou were sitting by a tranquil pond, Uribou looked at Usagi with a gentle expression. "Usagi," he began, "you have grown so much in wisdom and compassion. The world is vast, and there are many paths you can choose to follow. But remember, no matter where your journey takes you, the lessons and friendships you've gained here will stay with you always."
Usagi felt a mix of emotions as he listened to Uribou's words. He realized that it was time for him to embark on his own journey, to see the world and discover what lay beyond the forest. With a heavy heart, Usagi bid farewell to his friend, promising to return and share his adventures.
As Usagi left the forest, he felt a sense of belonging to both the forest and the wider world. He knew that the friendships he had formed and the lessons he had learned would guide him on his journey. And though he had to leave, he carried the memory of his time with Uribou and the other forest creatures in his heart.
Years passed, and Usagi's travels took him to many places, where he met new friends and experienced different cultures. But whenever he missed the peace and beauty of the forest, he would recall the wise and kind toad, Uribou, and the lessons he had imparted. And though he never forgot the forest, Usagi eventually found a new home in a nearby village, where he shared his stories and wisdom with the people, just as Uribou had shared his teachings with him.
And so, Usagi's journey continued, a testament to the power of friendship, the importance of learning, and the enduring bond between different worlds and creatures. |
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5. **å¶ç¶ã®åå **ïŒããŸããŸãã®æ¥ã«ç¹å¥ãªè² è·ããããå¯èœæ§ããããŸããäŸãã°ãå³æžé€šã§å€§éã®ããŒã¿ãããŠã³ããŒããããã倧éã®ãã¡ã€ã«ãä¿åãããããå Žåãªã©ã
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±ééšåãæ±ããåé¡ã§ãããã®åé¡ã解決ããããã«ãåçèšç»æ³ïŒDynamic ProgrammingïŒãçšããæ¹æ³ããããŸãã以äžã«ããã®æ¹æ³ãšãã®é©çšäŸã瀺ããŸãã
### 1. ã¡ã¢åååž°ãçšããåçèšç»æ³ã«ãã解æ³
#### 1.1. é¢æ°ã®å®çŸ©
ãŸãã`dp[i][j]` ãæåå1ã®åiæåãšæåå2ã®åjæåã®æé·å
±ééšåæååã®é·ããšå®çŸ©ããŸãã
#### 1.2. ããŒã¹ã±ãŒã¹
- `dp[0][j] = 0` ãš `dp[i][0] = 0` ã§åæåããŸããããã¯ãã©ã¡ãã®æååãé·ã0ã®å Žåã¯å
±ééšåãååšããªãããã§ãã
#### 1.3. ãªã«ã¬ã³ãé¢ä¿
- `dp[i][j] = dp[i-1][j-1] + 1` ã `æåå1[i-1] == æåå2[j-1]` ã®å Žå
- `dp[i][j] = max(dp[i-1][j], dp[i][j-1])` ã `æåå1[i-1] != æåå2[j-1]` ã®å Žå
#### 1.4. ã³ãŒãå®è£
```python
def longest_common_substring(s1, s2):
m, n = len(s1), len(s2)
dp = [[0] * (n + 1) for _ in range(m + 1)]
for i in range(1, m + 1):
for j in range(1, n + 1):
if s1[i - 1] == s2[j - 1]:
dp[i][j] = dp[i - 1][j - 1] + 1
else:
dp[i][j] = max(dp[i - 1][j], dp[i][j - 1])
return dp[m][n]
# ãã¹ãçšã®æåå
s1 = "ãã¿ãŸããã"
s2 = "ãããŸããã§ãã"
# åŠçå®è¡
result = longest_common_substring(s1, s2)
print("æé·å
±ééšåæååã®é·ã:", result)
```
### 2. 解ç
å®è¡çµæ㯠`æé·å
±ééšåæååã®é·ã: 3` ãšãªããŸããããã¯ããããããããããããé£ç¶ããŠå
±ééšåãšããŠååšããããã§ãã
### 3. 説æ
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å
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åã¯:
```
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```
ãã®é
åãä¿®æ£ããåæ¬åŒ§ãæ£ããéããããããã«ãããšã次ã®ããã«ãªããŸã:
```
[ { ( ) } ]
```
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3. éãè±ãååšããã
4. 2人ã¯éãè±ã®è¿ãã«ããã
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1. çŸåšãç¹å¥ãªæçãç¹å¥äŸ¡æ Œã®ã¡ãã¥ãŒãæäŸãããŠããªãããšã瀺ããŠããŸãã
2. ä»æ¥ã®æçã®ã©ã€ã³ãããã¯éåžžéãã§ãããç¹å¥ãªãã®ãçšæãããŠããªããšããããšãäŒããŠããŸãã
3. å Žé¢ãç¶æ³ã«ãã£ãŠã¯ãåºãç¹å¥ãªã¡ãã¥ãŒãæºåããããšãªãå¶æ¥ããŠããããšãæå³ãããããããŸãããäŸãã°ãã¹ã¿ãããäžåšã ã£ãããç¹å¥ãªææã足ããªãã£ããããå Žåãªã©ã
4. ææ¶åïŒè¿æ ·çåçå¯èœæå«çæå¡å对顟客çæç§äžæ»¡æ
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5. å¯èœæ瀺ä»å€©çéå®æ
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èŠãªã ã䜿ã£ãŠãææ¥ã®æãã¯ããæºåããŠãã ããã | NIGHTINGALE (It seems there was a misunderstanding; "Nightingale" is not the name of the character I should be. Let me correct that and provide a response as Qwen.)
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1. **ææã®ç¢ºèªãšèª¿é**:
- å·èµåº«ã«ãªã³ãŽãbananaãçä¹³ããã³ããããŸãã
- éèãè²·ããåºã®ãã©ã·ã䜿ã£ãŠãéèã調éããŸãããã©ã·ãèŠããšãå¿
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3. **é£æã®æºå**:
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- ããããçãããã«ããããæŽã£ãŠãé©åãªå€§ããã«åããŸãã
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4. **æçã®äœæ**:
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- ãªã³ãŽãšbananaãæ··ããé»åã¬ã³ãžã§å ç±ããŠæãããããŸãã
- ããããçãããã«ãããããªã³ãŽãbananaã®ãµã©ããäœããŸãã
- ãã³ãããŒã¹ã¿ãŒã§çŒããŸãã
- çä¹³ãçä¹³ã«ããã«å
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5. **æãã¯ãã®æäŸ**:
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1. ãããã§ãšãããããŸãïŒããªããåãçµãã§ããåªåãå®ãçµã³ãŸããããã
2. ãçŽ æŽãããã§ããïŒåæ Œã®åã³ãå
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3. ãæ¬åœã«ããã§ãšãããããŸãïŒè©Šéšã®æºåã¯å€§å€ã ã£ãã§ããããããã®çµæãããã ãšã¯ãã
4. ãããªãã®åæ Œã¯å€§ãã«èªãã«æããŸãããããããçŽ æŽãããæ瞟ãåããããšã§ããããã
5. ãããã§ãšãïŒè©Šéšå匷ã®æ¥ã
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1. **è·çš®å¥ã®è©³çŽ°èª¬æ**: åºæ¬çãªæ¥åãããŒã ãã§ãªããåè·çš®ã®å
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5. **ãã£ãŒãããã¯ã®æ©äŒ**: å®æçãªãã£ãŒãããã¯ã»ãã·ã§ã³ãèšããããšã§ãæ°å
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