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Commit 61857c7

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feat: add solutions to lc problem: No.1010
No.1010.Pairs of Songs With Total Durations Divisible by 60
1 parent 7129eb8 commit 61857c7

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‎solution/1000-1099/1010.Pairs of Songs With Total Durations Divisible by 60/README.md‎

Lines changed: 123 additions & 40 deletions
Original file line numberDiff line numberDiff line change
@@ -44,13 +44,15 @@
4444

4545
<!-- 这里可写通用的实现逻辑 -->
4646

47-
**方法一:计数 + 枚举**
47+
**方法一:数学 + 计数**
4848

49-
我们可以用一个哈希表或数组 `cnt` 记录当前已经遍历过的歌曲的持续时间 `time[i]` 的数量。
49+
如果一个数对 $(a, b)$ 之和能被 60ドル$ 整除,即 $(a + b) \bmod 60 = 0,ドル那么 $(a \bmod 60 + b \bmod 60) \bmod 60 = 0,ドル不妨记 $x=a \bmod 60,ドル $y = b \bmod 60,ドル那么有 $(x + y) \bmod 60 = 0,ドル即 $y=(60 - x) \bmod 60$。
5050

51-
枚举当前遍历到的歌曲的持续时间 `time[i]`,假设其为 `t`,那么我们只需要枚举 `60` 的倍数 `s`,并统计 `cnt[s - t]` 即可。然后将 `cnt[t]` 的值加 `1`。
51+
因此,我们可以遍历歌曲列表,用一个长度为 60ドル$ 的数组 $cnt$ 记录每个余数 $x$ 出现的次数。对于当前的 $x,ドル如果数组 $cnt$ 中存在余数 $y = (60 - x) \bmod 60,ドル那么将 $cnt[y]$ 累加进答案中。然后,将 $x$ 在数组 $cnt$ 中的出现次数加 1ドル$。继续遍历,直到遍历完整个歌曲列表。
5252

53-
时间复杂度 $O(n \times C),ドル空间复杂度 $O(M)$。其中 $n$ 为数组 `time` 的长度,而 $C$ 和 $M$ 分别为数组 `time` 中的最大值以及 `60` 的倍数的个数。
53+
遍历结束后,即可得到满足条件的歌曲对数目。
54+
55+
时间复杂度 $O(n),ドル空间复杂度 $O(C)$。其中 $n$ 是歌曲列表的长度;而 $C$ 是余数的可能取值,这里 $C=60$。
5456

5557
<!-- tabs:start -->
5658

@@ -61,14 +63,23 @@
6163
```python
6264
class Solution:
6365
def numPairsDivisibleBy60(self, time: List[int]) -> int:
64-
cnt = defaultdict(int)
66+
cnt = Counter(t % 60 for t in time)
67+
ans = sum(cnt[x] * cnt[60 - x] for x in range(1, 30))
68+
ans += cnt[0] * (cnt[0] - 1) // 2
69+
ans += cnt[30] * (cnt[30] - 1) // 2
70+
return ans
71+
```
72+
73+
```python
74+
class Solution:
75+
def numPairsDivisibleBy60(self, time: List[int]) -> int:
76+
cnt = Counter()
6577
ans = 0
66-
for t in time:
67-
s = 60
68-
for _ in range(17):
69-
ans += cnt[s - t]
70-
s += 60
71-
cnt[t] += 1
78+
for x in time:
79+
x %= 60
80+
y = (60 - x) % 60
81+
ans += cnt[y]
82+
cnt[x] += 1
7283
return ans
7384
```
7485

@@ -79,17 +90,31 @@ class Solution:
7990
```java
8091
class Solution {
8192
public int numPairsDivisibleBy60(int[] time) {
82-
int[] cnt = new int[501];
83-
int ans = 0;
93+
int[] cnt = new int[60];
8494
for (int t : time) {
85-
int s = 60;
86-
for (int i = 0; i < 17; ++i) {
87-
if (s - t >= 0 && s - t < cnt.length) {
88-
ans += cnt[s - t];
89-
}
90-
s += 60;
91-
}
92-
cnt[t]++;
95+
++cnt[t % 60];
96+
}
97+
int ans = 0;
98+
for (int x = 1; x < 30; ++x) {
99+
ans += cnt[x] * cnt[60 - x];
100+
}
101+
ans += (long) cnt[0] * (cnt[0] - 1) / 2;
102+
ans += (long) cnt[30] * (cnt[30] - 1) / 2;
103+
return ans;
104+
}
105+
}
106+
```
107+
108+
```java
109+
class Solution {
110+
public int numPairsDivisibleBy60(int[] time) {
111+
int[] cnt = new int[60];
112+
int ans = 0;
113+
for (int x : time) {
114+
x %= 60;
115+
int y = (60 - x) % 60;
116+
ans += cnt[y];
117+
++cnt[x];
93118
}
94119
return ans;
95120
}
@@ -102,17 +127,32 @@ class Solution {
102127
class Solution {
103128
public:
104129
int numPairsDivisibleBy60(vector<int>& time) {
105-
int cnt[501]{};
106-
int ans = 0;
130+
int cnt[60]{};
107131
for (int& t : time) {
108-
int s = 60;
109-
for (int i = 0; i < 17; ++i) {
110-
if (s - t >= 0 && s - t < 501) {
111-
ans += cnt[s - t];
112-
}
113-
s += 60;
114-
}
115-
cnt[t]++;
132+
++cnt[t % 60];
133+
}
134+
int ans = 0;
135+
for (int x = 1; x < 30; ++x) {
136+
ans += cnt[x] * cnt[60 - x];
137+
}
138+
ans += 1LL * cnt[0] * (cnt[0] - 1) / 2;
139+
ans += 1LL * cnt[30] * (cnt[30] - 1) / 2;
140+
return ans;
141+
}
142+
};
143+
```
144+
145+
```cpp
146+
class Solution {
147+
public:
148+
int numPairsDivisibleBy60(vector<int>& time) {
149+
int cnt[60]{};
150+
int ans = 0;
151+
for (int x : time) {
152+
x %= 60;
153+
int y = (60 - x) % 60;
154+
ans += cnt[y];
155+
++cnt[x];
116156
}
117157
return ans;
118158
}
@@ -123,21 +163,64 @@ public:
123163

124164
```go
125165
func numPairsDivisibleBy60(time []int) (ans int) {
126-
cnt := [501]int{}
166+
cnt := [60]int{}
127167
for _, t := range time {
128-
s := 60
129-
for i := 0; i < 17; i++ {
130-
if s-t >= 0 && s-t < 501 {
131-
ans += cnt[s-t]
132-
}
133-
s += 60
134-
}
135-
cnt[t]++
168+
cnt[t%60]++
169+
}
170+
for x := 1; x < 30; x++ {
171+
ans += cnt[x] * cnt[60-x]
172+
}
173+
ans += cnt[0] * (cnt[0] - 1) / 2
174+
ans += cnt[30] * (cnt[30] - 1) / 2
175+
return
176+
}
177+
```
178+
179+
```go
180+
func numPairsDivisibleBy60(time []int) (ans int) {
181+
cnt := [60]int{}
182+
for _, x := range time {
183+
x %= 60
184+
y := (60 - x) % 60
185+
ans += cnt[y]
186+
cnt[x]++
136187
}
137188
return
138189
}
139190
```
140191

192+
### **TypeScript**
193+
194+
```ts
195+
function numPairsDivisibleBy60(time: number[]): number {
196+
const cnt: number[] = new Array(60).fill(0);
197+
for (const t of time) {
198+
++cnt[t % 60];
199+
}
200+
let ans = 0;
201+
for (let x = 1; x < 30; ++x) {
202+
ans += cnt[x] * cnt[60 - x];
203+
}
204+
ans += (cnt[0] * (cnt[0] - 1)) / 2;
205+
ans += (cnt[30] * (cnt[30] - 1)) / 2;
206+
return ans;
207+
}
208+
```
209+
210+
```ts
211+
function numPairsDivisibleBy60(time: number[]): number {
212+
const cnt: number[] = new Array(60).fill(0);
213+
let ans: number = 0;
214+
for (let x of time) {
215+
x %= 60;
216+
const y = (60 - x) % 60;
217+
ans += cnt[y];
218+
++cnt[x];
219+
}
220+
return ans;
221+
}
222+
```
223+
141224
### **...**
142225

143226
```

‎solution/1000-1099/1010.Pairs of Songs With Total Durations Divisible by 60/README_EN.md‎

Lines changed: 117 additions & 36 deletions
Original file line numberDiff line numberDiff line change
@@ -45,14 +45,23 @@
4545
```python
4646
class Solution:
4747
def numPairsDivisibleBy60(self, time: List[int]) -> int:
48-
cnt = defaultdict(int)
48+
cnt = Counter(t % 60 for t in time)
49+
ans = sum(cnt[x] * cnt[60 - x] for x in range(1, 30))
50+
ans += cnt[0] * (cnt[0] - 1) // 2
51+
ans += cnt[30] * (cnt[30] - 1) // 2
52+
return ans
53+
```
54+
55+
```python
56+
class Solution:
57+
def numPairsDivisibleBy60(self, time: List[int]) -> int:
58+
cnt = Counter()
4959
ans = 0
50-
for t in time:
51-
s = 60
52-
for _ in range(17):
53-
ans += cnt[s - t]
54-
s += 60
55-
cnt[t] += 1
60+
for x in time:
61+
x %= 60
62+
y = (60 - x) % 60
63+
ans += cnt[y]
64+
cnt[x] += 1
5665
return ans
5766
```
5867

@@ -61,17 +70,31 @@ class Solution:
6170
```java
6271
class Solution {
6372
public int numPairsDivisibleBy60(int[] time) {
64-
int[] cnt = new int[501];
65-
int ans = 0;
73+
int[] cnt = new int[60];
6674
for (int t : time) {
67-
int s = 60;
68-
for (int i = 0; i < 17; ++i) {
69-
if (s - t >= 0 && s - t < cnt.length) {
70-
ans += cnt[s - t];
71-
}
72-
s += 60;
73-
}
74-
cnt[t]++;
75+
++cnt[t % 60];
76+
}
77+
int ans = 0;
78+
for (int x = 1; x < 30; ++x) {
79+
ans += cnt[x] * cnt[60 - x];
80+
}
81+
ans += (long) cnt[0] * (cnt[0] - 1) / 2;
82+
ans += (long) cnt[30] * (cnt[30] - 1) / 2;
83+
return ans;
84+
}
85+
}
86+
```
87+
88+
```java
89+
class Solution {
90+
public int numPairsDivisibleBy60(int[] time) {
91+
int[] cnt = new int[60];
92+
int ans = 0;
93+
for (int x : time) {
94+
x %= 60;
95+
int y = (60 - x) % 60;
96+
ans += cnt[y];
97+
++cnt[x];
7598
}
7699
return ans;
77100
}
@@ -84,17 +107,32 @@ class Solution {
84107
class Solution {
85108
public:
86109
int numPairsDivisibleBy60(vector<int>& time) {
87-
int cnt[501]{};
88-
int ans = 0;
110+
int cnt[60]{};
89111
for (int& t : time) {
90-
int s = 60;
91-
for (int i = 0; i < 17; ++i) {
92-
if (s - t >= 0 && s - t < 501) {
93-
ans += cnt[s - t];
94-
}
95-
s += 60;
96-
}
97-
cnt[t]++;
112+
++cnt[t % 60];
113+
}
114+
int ans = 0;
115+
for (int x = 1; x < 30; ++x) {
116+
ans += cnt[x] * cnt[60 - x];
117+
}
118+
ans += 1LL * cnt[0] * (cnt[0] - 1) / 2;
119+
ans += 1LL * cnt[30] * (cnt[30] - 1) / 2;
120+
return ans;
121+
}
122+
};
123+
```
124+
125+
```cpp
126+
class Solution {
127+
public:
128+
int numPairsDivisibleBy60(vector<int>& time) {
129+
int cnt[60]{};
130+
int ans = 0;
131+
for (int x : time) {
132+
x %= 60;
133+
int y = (60 - x) % 60;
134+
ans += cnt[y];
135+
++cnt[x];
98136
}
99137
return ans;
100138
}
@@ -105,21 +143,64 @@ public:
105143

106144
```go
107145
func numPairsDivisibleBy60(time []int) (ans int) {
108-
cnt := [501]int{}
146+
cnt := [60]int{}
109147
for _, t := range time {
110-
s := 60
111-
for i := 0; i < 17; i++ {
112-
if s-t >= 0 && s-t < 501 {
113-
ans += cnt[s-t]
114-
}
115-
s += 60
116-
}
117-
cnt[t]++
148+
cnt[t%60]++
118149
}
150+
for x := 1; x < 30; x++ {
151+
ans += cnt[x] * cnt[60-x]
152+
}
153+
ans += cnt[0] * (cnt[0] - 1) / 2
154+
ans += cnt[30] * (cnt[30] - 1) / 2
119155
return
120156
}
121157
```
122158

159+
```go
160+
func numPairsDivisibleBy60(time []int) (ans int) {
161+
cnt := [60]int{}
162+
for _, x := range time {
163+
x %= 60
164+
y := (60 - x) % 60
165+
ans += cnt[y]
166+
cnt[x]++
167+
}
168+
return
169+
}
170+
```
171+
172+
### **TypeScript**
173+
174+
```ts
175+
function numPairsDivisibleBy60(time: number[]): number {
176+
const cnt: number[] = new Array(60).fill(0);
177+
for (const t of time) {
178+
++cnt[t % 60];
179+
}
180+
let ans = 0;
181+
for (let x = 1; x < 30; ++x) {
182+
ans += cnt[x] * cnt[60 - x];
183+
}
184+
ans += (cnt[0] * (cnt[0] - 1)) / 2;
185+
ans += (cnt[30] * (cnt[30] - 1)) / 2;
186+
return ans;
187+
}
188+
```
189+
190+
```ts
191+
function numPairsDivisibleBy60(time: number[]): number {
192+
const cnt: number[] = new Array(60).fill(0);
193+
let ans: number = 0;
194+
for (let x of time) {
195+
x %= 60;
196+
const y = (60 - x) % 60;
197+
ans += cnt[y];
198+
++cnt[x];
199+
}
200+
return ans;
201+
}
202+
```
203+
123204
### **...**
124205

125206
```

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