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### Pythonã§ã®å®è£
äŸ
```python
def longest_common_substring(s1, s2):
n1, n2 = len(s1), len(s2)
dp = [[0] * (n2 + 1) for _ in range(n1 + 1)]
max_length = 0
end_index = 0
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
if dp[i][j] > max_length:
max_length = dp[i][j]
end_index = i - 1
else:
dp[i][j] = 0
return s1[end_index - max_length + 1:end_index + 1], max_length
# ãã¹ãçšã®æåå
s1 = "ãããã¿ãã"
s2 = "ã¿ãããã¡ã"
result, length = longest_common_substring(s1, s2)
print(f"é£ç¶ããæé·å
±ééšåæåå㯠'{result}' ã§ããã®é·ã㯠{length} ã§ãã")
```
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### 解æ³
1. **åçèšç»æ³ã®ããŒãã«ãæ§ç¯ãã**ïŒ
- 2ã€ã®æåå `s1 = ããããŸã€ã` ãš `s2 = ãŸã€ãããšã` ã®é·ãããããã `n1` ãš `n2` ãšããã
- 2次å
ã®ããŒãã« `dp` ãäœæãã`dp[i][j]` 㯠`s1` ã®æåã® `i` æåãš `s2` ã®æåã® `j` æåã®éã®é£ç¶ããæé·å
±ééšåæååã®é·ããè¡šãã
2. **åæå**ïŒ
- `dp[0][j]` ãš `dp[i][0]` ã 0 ã«åæåããããªããªãã空ã®æååãšä»»æã®æååã®éã«ã¯å
±ééšåã¯ååšããªãããã§ããã
3. **DPããŒãã«ã®æŽæ°ã«ãŒã«**ïŒ
- `s1[i-1] == s2[j-1]` ã®ãšãã`dp[i][j] = dp[i-1][j-1] + 1`ã
- `s1[i-1] != s2[j-1]` ã®ãšãã`dp[i][j] = 0`ã
4. **çµæã®ååŸ**ïŒ
- `dp[n1][n2]` ãçããšãªãã
### å
·äœçãªæé
1. **ããŒãã«ã®åæå**ïŒ
- `n1 = 7`, `n2 = 7`
- `dp` ã®åæå€ã¯å
šãŠ 0ã
2. **ããŒãã«ã®æŽæ°**ïŒ
- `s1 = ããããŸã€ã`, `s2 = ãŸã€ãããšã`
- `dp` ã®åèŠçŽ ãé ã«èšç®ããã
3. **èšç®äŸ**ïŒ
- `dp[1][1]`:
- `s1[0] = ã`, `s2[0] = ãŸ` ãªã®ã§ `dp[1][1] = 0`
- `dp[2][2]`:
- `s1[1] = ã`, `s2[1] = ã€` ãªã®ã§ `dp[2][2] = 0`
- `dp[3][3]`:
- `s1[2] = ãº`, `s2[2] = ã` ãªã®ã§ `dp[3][3] = 0`
- `dp[4][4]`:
- `s1[3] = ã`, `s2[3] = ãŸ` ãªã®ã§ `dp[4][4] = 0`
- `dp[5][5]`:
- `s1[4] = ãŸ`, `s2[4] = ã€` ãªã®ã§ `dp[5][5] = 0`
- `dp[6][6]`:
- `s1[5] = ã€`, `s2[5] = ã` ãªã®ã§ `dp[6][6] = 0`
- `dp[7][7]`:
- `s1[6] = ã`, `s2[6] = ãšã` ãªã®ã§ `dp[7][7] = 0`
- `dp[6][5]`:
- `s1[5] = ã€`, `s2[4] = ã€` ãªã®ã§ `dp[6][5] = dp[5][4] + 1 = 1`
- `dp[5][4]`:
- `s1[4] = ãŸ`, `s2[3] = ãŸ` ãªã®ã§ `dp[5][4] = dp[4][3] + 1 = 1`
- `dp[4][3]`:
- `s1[3] = ã`, `s2[2] = ã` ãªã®ã§ `dp[4][3] = 0`
- `dp[3][2]`:
- `s1[2] = ãº`, `s2[1] = ã€` ãªã®ã§ `dp[3][2] = 0`
- `dp[2][1]`:
- `s1[1] = ã`, `s2[0] = ãŸ` ãªã®ã§ `dp |
以äžã®äŸæã¯ãžã§ãŒã¯ïŒç®èïŒãèšã£ãŠããŸããïŒ
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1. **çŸå®æ§ã®æ¬ åŠ**ïŒåãå¿ãããšããç¶æ³èªäœã¯æ¥åžžçãªåºæ¥äºã§ãç¹ã«é¢šã匷ãæ¥ã«ã¯ããããç¥ãããŠããäºè±¡ã§ãããããããã®æã¯ãã®ç¶æ³ããæšæ¥ã®é¢šã匷ããããããããšããçç±ã§èª¬æããŠããŸããããã¯çŸå®äžçã§ã®é¢šã®åœ±é¿ãšã¯å€§ããç°ãªãçç±ãæ瀺ããŠããŸãã
2. **äžèªç¶ã**ïŒé¢šã匷ãããšãšåãå¿ãããšããé¢é£æ§ã¯ããŸããªãããããã®èª¬æã¯äžèªç¶ã§ãããç®èã®èŠçŽ ãæã£ãŠããŸãã
3. **èšèéã³**ïŒã匷ããããããããšããè¡šçŸã¯ã颚ãåãå¿ããåå ã«ãªã£ããšåŒ·åŒã«è§£éããããšããç®èãªèšèéã³ã§ãã
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解æéçšïŒ
1. ç«ææ¥ããå§ããŠã1æ¥åŸã¯æ°Žææ¥ã§ãã
2. 2æ¥åŸã¯æšææ¥ã§ãã
3. 3æ¥åŸã¯éææ¥ã«ãªããŸãã
ãã£ãŠãç«ææ¥ã®3æ¥åŸã¯éææ¥ãšãªããŸãã |
æ¬åŒ§ãæ£ããéããããããã«ã次ã®é
åãå®æãããŠãã ããã
[ { ( ) ] } | åé¡ã解決ããããã«ãæ¬åŒ§ãæ£ããéããããããã«ã次ã®é
åãå®æãããŸãã
å
ã®é
å: `[ { ( ) ] }`
æ£ããéããããé
å: `[ { ( ) } ]`
ããã§ã®å€æŽç¹ã¯ãå
ã®é
åã®æåŸã® "}" ãäžèŠã§ããããšã確èªã§ããŸããããããã£ãŠãæ£ããéããããããã« "}" ãåé€ã㊠`[ { ( ) } ]` ãšããŸããããã®é
åã§ã¯ããã¹ãŠã®éããæ¬åŒ§ãé©åã«éããããŠããŸãã
å
·äœçã«èª¬æãããšïŒ
- `[` 㯠`]` ã§éããããŸãã
- `{` 㯠`}` ã§éããããŸãã
- `(` 㯠`)` ã§éããããŸãã
ãã®é åºãšãã¢ã§æ¬åŒ§ãéããããããšã確èªããããšã§ãæ£ããé
åãå®æããŸããã |
3ã1ã§å²ã£ãçµæã«25ã足ããŠã7ãæãããæåŸã«5ã§å²ãã | ãŸããåé¡ã段éçã«èšç®ããŠãããŸãããïŒ
1. 3ã1ã§å²ããŸãïŒ
3 ÷ 1 = 3
2. çµæã«25ã足ããŸãïŒ
3 + 25 = 28
3. ãã®çµæã7ã§æããŠãããŸãïŒ
28 Ã 7 = 196
4. æåŸã«5ã§å²ããŸãïŒ
196 ÷ 5 = 39.2
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