基础算法训练题单之排序（从入门到入土）——题解
A. P1177 【模板】排序
三种方法：快速排序，归并排序，STL库的sort函数。
法一、三：https://www.cnblogs.com/expect-999/p/17594345.html
法二：https://www.cnblogs.com/expect-999/p/17599008.html
B. P1923 【深基9.例4】求第 k 小的数
模板题目，直接对数组进行升序排序，如果数组从零开始，则找到下标为k-1的数，从1开始的就找第K个数，具体还是以实际情况为主。
点击查看B题代码
#define _CRT_SECURE_NO_WARNINGS 1
#define all(C) C.begin(),C.end()
#define S second
#define F first
#define PB push_back
#define mod 1000000007
#define import ios_base::sync_with_stdio(false);cin.tie(NULL)
#include <cstring>
#include <iostream>
#include <cstdio>
#include <cmath>
#include <algorithm>
#include <string>
#include <vector>
#include <map>
using namespace std;
typedef long long ll;
const int N = 5e6 + 10;
int q[N];
void quick_sort(int q[], int l, int r)
{
if (l >= r) return;
int i = l - 1, j = r + 1;
int x = q[l + r >> 1];
while (i < j)
{
do ++i; while (q[i] < x);
do --j; while (q[j] > x);
if (i < j) swap(q[i], q[j]);
}
quick_sort(q, l, j);
quick_sort(q, j + 1, r);
}
signed main()
{
import;
int n, k;
cin >> n >> k;
for (int i = 0; i < n; ++i) cin >> q[i];
quick_sort(q,0,n-1);
cout << q[k] << endl;
return 0;
}
C. P1271 【深基9.例1】选举学生会
直接对数组按升序排序输出即可。
点击查看C题代码
#define _CRT_SECURE_NO_WARNINGS 1
#define all(C) C.begin(),C.end()
#define S second
#define F first
#define PB push_back
#define mod 1000000007
#define import ios_base::sync_with_stdio(false);cin.tie(NULL)
#include <cstring>
#include <iostream>
#include <cstdio>
#include <cmath>
#include <algorithm>
#include <string>
#include <vector>
#include <map>
using namespace std;
typedef long long ll;
const int N = 2e6 + 10;
int q[N];
void quick_sort(int q[], int l, int r)
{
if (l >= r) return;
int i = l - 1, j = r + 1;
int x = q[l + r >> 1];
while (i < j)
{
do ++i; while (q[i] < x);
do --j; while (q[j] > x);
if (i < j) swap(q[i], q[j]);
}
quick_sort(q, l, j);
quick_sort(q, j + 1, r);
}
signed main()
{
import;
int n, m;
cin >> n >> m;
for (int i = 0; i < m; ++i) cin >> q[i];
quick_sort(q,0,m-1);
for (int i = 0; i < m; ++i) cout << q[i] << ' ';
return 0;
}
D. [NOIP2006 普及组] 明明的随机数
对数组进行排序，再用unique函数进行去重（这个去重其实就是重复的数字移到后面去了，并不是真正的去重）
点击查看D题代码
#define _CRT_SECURE_NO_WARNINGS 1
#define all(C) C.begin(),C.end()
#define S second
#define F first
#define PB push_back
#define mod 1000000007
#define import ios_base::sync_with_stdio(false);cin.tie(NULL)
#include <cstring>
#include <iostream>
#include <cstdio>
#include <cmath>
#include <algorithm>
#include <string>
#include <vector>
#include <map>
using namespace std;
typedef long long ll;
const int N = 2e6 + 10;
int q[N];
void quick_sort(int q[], int l, int r)
{
if (l >= r) return;
int i = l - 1, j = r + 1;
int x = q[ (l + r) >> 1];
while (i < j)
{
do ++i; while (q[i] < x);
do --j; while (q[j] > x);
if (i < j) swap(q[i], q[j]);
}
quick_sort(q, l, j);
quick_sort(q, j + 1, r);
}
signed main()
{
import;
int n;
cin >> n;
for (int i = 0; i < n; ++i) cin >> q[i];
quick_sort(q,0,n-1);
int k = unique(q,q + n) - q; //unique"去掉"重复的,其实返回去重后最后一个不重复元素地址
//再减去首地址就是下标，
cout << k << endl;
for (int i = 0; i < k; ++i) cout << q[i] << " ";
return 0;
}
E. [NOIP2007 普及组] 奖学金
利用sort和结构体来进行排序————当一个模板题理解记忆就好了。
点击查看E题代码
#define _CRT_SECURE_NO_WARNINGS 1
#define all(C) C.begin(),C.end()
#define S second
#define F first
#define PB push_back
#define mod 1000000007
#define import ios_base::sync_with_stdio(false);cin.tie(NULL)
#include <cstring>
#include <iostream>
#include <cstdio>
#include <cmath>
#include <algorithm>
#include <string>
#include <vector>
#include <map>
using namespace std;
typedef long long ll;
const int N = 2e6 + 10;
struct stu
{
int Id;
int chinese;
int math;
int eglish;
int sum;
}q[N];
bool cmp(stu a, stu b)
{
if (a.sum != b.sum) return a.sum > b.sum;
else if (a.chinese != b.chinese) return a.chinese > b.chinese;
else return a.Id < b.Id;
}
signed main()
{
import;
int n;
cin >> n;
for (int i = 1; i <= n; ++i)
{
cin >> q[i].chinese >> q[i].math >> q[i].eglish;
q[i].Id = i;
q[i].sum = q[i].chinese + q[i].math + q[i].eglish;
}
sort(q + 1, q + n + 1, cmp);
for (int i = 1; i <= 5; ++i) printf("%d %d\n", q[i].Id, q[i].sum);
return 0;
}
F. 宇宙总统
同上一题一样
点击查看F题代码
#define _CRT_SECURE_NO_WARNINGS 1
#define all(C) C.begin(),C.end()
#define S second
#define F first
#define PB push_back
#define mod 1000000007
#define import ios_base::sync_with_stdio(false);cin.tie(NULL)
#include <cstring>
#include <iostream>
#include <cstdio>
#include <cmath>
#include <algorithm>
#include <string>
#include <vector>
#include <map>
using namespace std;
typedef long long ll;
const int N = 2e6 + 10;
int n;
struct stu
{
int id;
int size;
string x;
}q[N];
bool cmp(stu a, stu b)
{
if (a.size != b.size) return a.size > b.size;
else return a.x > b.x;
}
signed main()
{
cin >> n;
for (int i = 1; i <= n; i++)
{
cin >> q[i].x;
q[i].id = i ;
q[i].size = (q[i].x).size();
}
sort(q + 1, q + n + 1, cmp);
cout << q[1].id << endl;
cout << q[1].x << endl;
}
G. [USACO07DEC] Bookshelf B
点击查看G题代码
#define _CRT_SECURE_NO_WARNINGS 1
#define all(C) C.begin(),C.end()
#define S second
#define F first
#define PB push_back
#define mod 1000000007
#define import ios_base::sync_with_stdio(false);cin.tie(NULL)
#include <cstring>
#include <iostream>
#include <cstdio>
#include <cmath>
#include <algorithm>
#include <string>
#include <vector>
#include <map>
using namespace std;
typedef long long ll;
const int N = 2e6 + 10;
int n,cnt;
int q[N];
ll h,sum;
bool cmp(int a, int b)
{
return a > b;
}
signed main()
{
cin >> n >> h;
for (int i = 0; i < n; ++i) cin >> q[i];
sort(q, q + n, cmp);
for (int i = 0; i < n; ++i)
{
if (sum < h)
{
sum += q[i];
cnt++;
}
else break;
}
cout << cnt << endl;
return 0;
}
H. 车厢重组
点击查看H题代码
#define _CRT_SECURE_NO_WARNINGS 1
#define all(C) C.begin(),C.end()
#define S second
#define F first
#define PB push_back
#define mod 1000000007
#define import ios_base::sync_with_stdio(false);cin.tie(NULL)
#include <cstring>
#include <iostream>
#include <cstdio>
#include <cmath>
#include <algorithm>
#include <string>
#include <vector>
#include <map>
using namespace std;
typedef long long ll;
const int N = 2e6 + 10;
int n;
int q[N],p[N];
ll cnt;
void merge_sort(int q[], int l, int r)
{
if (l >= r) return;
int mid = l + r >> 1;
merge_sort(q, l, mid);
merge_sort(q, mid + 1, r);
int i = l, j = mid+1,k=0;
while (i<=mid && j<=r)
{
if(q[i]<=q[j]) p[k++] = q[i++];
else
{
p[k++] = q[j++];
cnt += mid - i + 1;
}
}
while (i <= mid) p[k++] = q[i++];
while (j <= r) p[k++] = q[j++];
for (int i = l, k = 0; i <= r;++i) q[i] = p[k++];
}
signed main()
{
cin >> n;
for (int i = 0; i < n; ++i) cin >> q[i];
merge_sort(q, 0, n-1);
cout << cnt << endl;
return 0;
}
I. 欢乐的跳
点击查看I题代码
#define _CRT_SECURE_NO_WARNINGS 1
#define all(C) C.begin(),C.end()
#define S second
#define F first
#define PB push_back
#define mod 1000000007
#define import ios_base::sync_with_stdio(false);cin.tie(NULL)
#include <cstring>
#include <iostream>
#include <cstdio>
#include <cmath>
#include <algorithm>
#include <string>
#include <vector>
#include <map>
using namespace std;
typedef long long ll;
const int N = 2e6 + 10;
int n, cnt;
int q[N], p[N];
signed main()
{
cin >> n;
for (int i = 0; i < n; ++i) cin >> q[i];
for (int i = 0; i < n - 1; ++i) p[++cnt] = abs(q[i] - q[i + 1]);
sort(p + 1, p + cnt + 1);
int ok = 1;
for (int i = 1; i < n; ++i)
{
if (p[i] != i)
{
ok = 0;
break;
}
}
if (ok) cout << "Jolly" << endl;
else cout << "Not jolly" << endl;
return 0;
}
J. [NOIP2009 普及组] 分数线划定
点击查看J题代码
#define _CRT_SECURE_NO_WARNINGS 1
#define all(C) C.begin(),C.end()
#define S second
#define F first
#define PB push_back
#define mod 1000000007
#define import ios_base::sync_with_stdio(false);cin.tie(NULL)
#include <cstring>
#include <iostream>
#include <cstdio>
#include <cmath>
#include <algorithm>
#include <string>
#include <vector>
#include <map>
using namespace std;
typedef long long ll;
const int N = 2e6 + 10;
int n, m;
struct stu
{
int v;
int p;
}q[N];
bool cmp(stu a, stu b)
{
if (a.p == b.p) return a.v < b.v;
else return a.p > b.p;
}
signed main()
{
cin >> n >> m;
for (int i = 1; i <= n; ++i) cin >> q[i].v >> q[i].p;
int k = m * 1.5;
sort(q+1, q + n + 1, cmp);
for (int i = k; i <= n; ++i)
{
if (q[i].p == q[i + 1].p) k++;
else break;
}
printf("%d %d\n", q[k].p, k);
for (int i = 1; i <= k; ++i) printf("%d %d\n", q[i].v, q[i].p);
return 0;
}
K. 攀爬者
点击查看K题代码
#define _CRT_SECURE_NO_WARNINGS 1
#define all(C) C.begin(),C.end()
#define S second
#define F first
#define PB push_back
#define mod 1000000007
#define import ios_base::sync_with_stdio(false);cin.tie(NULL)
#include <cstring>
#include <iostream>
#include <cstdio>
#include <cmath>
#include <algorithm>
#include <string>
#include <vector>
#include <map>
using namespace std;
typedef long long ll;
const int N = 2e6 + 10;
int n, m;
double sum;
struct stu
{
int x;
int y;
int z;
}q[N];
bool cmp(stu a, stu b)
{
return a.z < b.z;
}
signed main()
{
cin >> n ;
for (int i = 0; i < n; ++i) cin >> q[i].x >> q[i].y >> q[i].z;
sort(q, q + n, cmp);
for (int i = 0; i < n-1; ++i)
{
int x1 = pow(q[i].x - q[i + 1].x, 2);
int y1 = pow(q[i].y - q[i + 1].y, 2);
int z1 = pow(q[i].z - q[i + 1].z, 2);
double p = pow(x1 + y1 + z1, 1.0 / 2);
sum += p;
}
printf("%.3lf", sum);
return 0;
}
L. 生日
点击查看L题代码
#define _CRT_SECURE_NO_WARNINGS 1
#define all(C) C.begin(),C.end()
#define S second
#define F first
#define PB push_back
#define mod 1000000007
#define import ios_base::sync_with_stdio(false);cin.tie(NULL)
#include <cstring>
#include <iostream>
#include <cstdio>
#include <cmath>
#include <algorithm>
#include <string>
#include <vector>
#include <map>
using namespace std;
typedef long long ll;
const int N = 2e6 + 10;
int n, m;
double sum;
struct stu
{
string name;
int year;
int month;
int day;
int id;
}q[N];
bool cmp(stu a, stu b)
{
if (a.year != b.year) return a.year < b.year;
else if (a.month != b.month) return a.month < b.month;
else if (a.day != b.day) return a.day < b.day;
else return a.id > b.id;
}
signed main()
{
cin >> n ;
for (int i = 0; i < n; ++i)
{
cin >> q[i].name >> q[i].year >> q[i].month >> q[i].day;
q[i].id = i;
}
sort(q, q + n, cmp);
for (int i = 0; i < n; ++i) cout << q[i].name << endl;
return 0;
}
M. [NOIP1998 提高组] 拼数
点击查看M题代码
#define _CRT_SECURE_NO_WARNINGS 1
#define all(C) C.begin(),C.end()
#define S second
#define F first
#define PB push_back
#define mod 1000000007
#define import ios_base::sync_with_stdio(false);cin.tie(NULL)
#include <cstring>
#include <iostream>
#include <cstdio>
#include <cmath>
#include <algorithm>
#include <string>
#include <vector>
#include <map>
using namespace std;
typedef long long ll;
const int N = 2e6 + 10;
int n, m;
string q[N];
bool cmp(string a, string b)
{
return a + b > b + a;
}
signed main()
{
import;
cin >> n;
for (int i = 0; i < n; ++i) cin >> q[i];
sort(q, q + n,cmp);
for (int i = 0; i < n; ++i) cout << q[i];
return 0;
}
N. [NOIP2005 提高组] 谁拿了最多奖学金
点击查看N题代码
#define _CRT_SECURE_NO_WARNINGS 1
#define all(C) C.begin(),C.end()
#define S second
#define F first
#define PB push_back
#define mod 1000000007
#define import ios_base::sync_with_stdio(false);cin.tie(NULL)
#include <cstring>
#include <iostream>
#include <cstdio>
#include <cmath>
#include <algorithm>
#include <string>
#include <vector>
#include <map>
using namespace std;
typedef long long ll;
const int N = 1e5 + 10;
int n;
struct stu
{
int id;
string name;
int egrade,pgrade;
char cadre,west;
int papernum;
int sum;
}q[N];
bool cmp(stu a, stu b)
{
if (a.sum != b.sum) return a.sum > b.sum;
else return a.id < b.id;
}
signed main()
{
cin >> n;
for (int i = 0; i < n; ++i)
{
q[i].id = i;
cin >> q[i].name >> q[i].egrade >> q[i].pgrade >> q[i].cadre >> q[i].west >> q[i].papernum;
if (q[i].papernum >= 1 && q[i].egrade > 80) q[i].sum += 8000;
if (q[i].egrade > 85 && q[i].pgrade > 80) q[i].sum += 4000;
if (q[i].egrade > 90) q[i].sum += 2000;
if (q[i].west == 'Y' && q[i].egrade > 85) q[i].sum += 1000;
if (q[i].cadre == 'Y' && q[i].pgrade > 80) q[i].sum += 850;
}
sort(q, q + n,cmp);
cout << q[0].name << endl;
int ans = 0;
for (int i = 0; i < n; ++i)
{
ans += q[i].sum;
}
printf("%d\n%d", q[0].sum,ans);
return 0;
}
O. [NOIP2011 普及组] 瑞士轮
https://www.cnblogs.com/expect-999/p/18162711
P. 逆序对
https://www.cnblogs.com/expect-999/p/18143932
点击查看P题代码
#define _CRT_SECURE_NO_WARNINGS 1
#define all(C) C.begin(),C.end()
#define S second
#define F first
#define PB push_back
#define mod 1000000007
#define import ios_base::sync_with_stdio(false);cin.tie(NULL)
#include <cstring>
#include <iostream>
#include <cstdio>
#include <cmath>
#include <algorithm>
#include <string>
#include <vector>
#include <map>
using namespace std;
typedef long long ll;
const int N = 2e6 + 10;
int n;
int q[N],p[N];
ll cnt;
void merge_sort(int q[], int l, int r)
{
if (l >= r) return;
int mid = l + r >> 1;
merge_sort(q, l, mid);
merge_sort(q, mid + 1, r);
int i = l, j = mid+1,k=0;
while (i<=mid && j<=r)
{
if(q[i]<=q[j]) p[k++] = q[i++];
else
{
p[k++] = q[j++];
cnt += mid - i + 1;
}
}
while (i <= mid) p[k++] = q[i++];
while (j <= r) p[k++] = q[j++];
for (int i = l, k = 0; i <= r;++i) q[i] = p[k++];
}
signed main()
{
cin >> n;
for (int i = 0; i < n; ++i) cin >> q[i];
merge_sort(q, 0, n-1);
cout << cnt << endl;
return 0;
}
以上就是此次排序训练的全部内容了，希望你有所收获。
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