洛谷P2525 Uim的情人节礼物·其之壱(组合数学/上一个全排列/下一个全排列)

题目

给定长度为n(n<=9)的全排列，

输出比该全排列上一个字典序的全排列，

不存在输出ERROR

思路来源

https://www.luogu.com.cn/problemnew/solution/P2525

题解

组合数学恶补第二弹，orz这个可是洛谷入门题

考虑上一个字典序，一定出现在某一位比当前全排列小了，且是最靠后的一位

对于相邻的正序对，无法交换其顺序，所以一定是从后往前的第一个逆序对

若a[i-1]>a[i]，则可以把a[i-1]调小，变成字典序更小的全排列，

所以找到 $x\epsilon[i,n)$ 范围内满足a[x]<a[i-1]且值最大的那个位置x，将其与a[i-1]交换，

交换之后，起到了降字典序的目的，后面的数应降序排列，使当前的字典序最大

代码1

#include<iostream>
#include<cstdio>
#include<algorithm>
using namespace std;
typedef long long ll;
const int N=10;
int n,a[N],b[N],cnt;
bool ok;
void solve(int x){//[x,n)int mx=-1,pos=-1;for(int i=x+1;i<n;++i){//<a[x]的最大的 从最小的逆序一位开始调小 if(a[i]<a[x]){if(a[i]>mx){mx=a[i];pos=i;}}}swap(a[pos],a[x]);sort(a+x+1,a+n,greater<int>());//后面的降序即可 表示此时的最大
}
int main(){scanf("%d",&n); for(int i=0;i<n;++i){scanf("%d",&a[i]);}for(int i=n-1;i;--i){if(a[i-1]>a[i]){solve(i-1);for(int j=0;j<n;++j){printf("%d%c",a[j]," \n"[j==n-1]);}ok=1;break;}}if(!ok)puts("ERROR");return 0;
}

代码2（prev_permutation）

用STL水，调用该函数，若上一个全排列存在，则会使ai变成上一个全排列，否则返回假

#include<iostream>
#include<cstdio>
#include<algorithm>
using namespace std;
typedef long long ll;
const int N=10;
int n,a[N],b[N],cnt;
int main(){scanf("%d",&n); for(int i=0;i<n;++i){scanf("%d",&a[i]);}if(!prev_permutation(a,a+n))puts("ERROR");else{for(int i=0;i<n;++i){printf("%d%c",a[i]," \n"[i==n-1]);}}return 0;
}

后续（2021.5.7）

下一个全排列类似，可以参考1850. 邻位交换的最小次数

class Solution:def getMinSwaps(self, num: str, k: int) -> int:def getnext(nums):n = len(nums)for i in range(n-2,-1,-1):if nums[i]<nums[i+1]:mn, pos = '9', -1for j in range(i+1,n):if num[j]>nums[i]:if mn > nums[i]:mn, pos = nums[j], j nums[i],nums[pos] = nums[pos],nums[i]nums[i+1:n] = sorted(nums[i+1:n])return numstmp = list(num)num = list(num)n = len(num)ans = 0for i in range(k):num = getnext(num)# print(num)for i in range(n):if tmp[i] == num[i]:continuepos = -1for j in range(i+1,n):if num[j] == tmp[i]:pos = jbreakfor j in range(pos,i,-1):num[j],num[j-1] = num[j-1],num[j]ans += 1return ans

['9', '4', '8', '6', '5', '3']
['9', '5', '3', '4', '6', '8']
['9', '5', '3', '4', '8', '6']
['9', '5', '3', '6', '4', '8']
['9', '5', '3', '6', '8', '4']
['9', '5', '3', '8', '4', '6']
['9', '5', '3', '8', '6', '4']
['9', '5', '4', '3', '6', '8']
['9', '5', '4', '3', '8', '6']
['9', '5', '4', '6', '3', '8']
['9', '5', '4', '6', '8', '3']
['9', '5', '4', '8', '3', '6']
['9', '5', '4', '8', '6', '3']
['9', '5', '6', '3', '4', '8']
['9', '5', '6', '3', '8', '4']
['9', '5', '6', '4', '3', '8']
['9', '5', '6', '4', '8', '3']
['9', '5', '6', '8', '3', '4']
['9', '5', '6', '8', '4', '3']
['9', '5', '8', '3', '4', '6']
['9', '5', '8', '3', '6', '4']
['9', '5', '8', '4', '3', '6']
['9', '5', '8', '4', '6', '3']
['9', '5', '8', '6', '3', '4']
['9', '5', '8', '6', '4', '3']
['9', '6', '3', '4', '5', '8']
['9', '6', '3', '4', '8', '5']
['9', '6', '3', '5', '4', '8']
['9', '6', '3', '5', '8', '4']
['9', '6', '3', '8', '4', '5']
['9', '6', '3', '8', '5', '4']
['9', '6', '4', '3', '5', '8']
['9', '6', '4', '3', '8', '5']
['9', '6', '4', '5', '3', '8']
['9', '6', '4', '5', '8', '3']
['9', '6', '4', '8', '3', '5']
['9', '6', '4', '8', '5', '3']
['9', '6', '5', '3', '4', '8']
['9', '6', '5', '3', '8', '4']
['9', '6', '5', '4', '3', '8']
['9', '6', '5', '4', '8', '3']
['9', '6', '5', '8', '3', '4']
['9', '6', '5', '8', '4', '3']
['9', '6', '8', '3', '4', '5']
['9', '6', '8', '3', '5', '4']
['9', '6', '8', '4', '3', '5']
['9', '6', '8', '4', '5', '3']
['9', '6', '8', '5', '3', '4']
['9', '6', '8', '5', '4', '3']
['9', '8', '3', '4', '5', '6']
['9', '8', '3', '4', '6', '5']
['9', '8', '3', '5', '4', '6']
['9', '8', '3', '5', '6', '4']
['9', '8', '3', '6', '4', '5']
['9', '8', '3', '6', '5', '4']
['9', '8', '4', '3', '5', '6']
['9', '8', '4', '3', '6', '5']
['9', '8', '4', '5', '3', '6']
['9', '8', '4', '5', '6', '3']
['9', '8', '4', '6', '3', '5']
['9', '8', '4', '6', '5', '3']
['9', '8', '5', '3', '4', '6']
['9', '8', '5', '3', '6', '4']
['9', '8', '5', '4', '3', '6']

注意，以下方法是不行的，反例是v=948635，k=64，此时3684找不到下一个后继3846，

所以不能从末尾往前扫交换4，而是应该交换6，即从后往前第一对正序对

class Solution:def getMinSwaps(self, num: str, k: int) -> int:def getnext(nums):n = len(nums)ok = Falsefor i in range(n-1,-1,-1):if ok:breakfor j in range(i-1,-1,-1):if ok:breakif nums[j] < nums[i]:num[j],num[i] = num[i],num[j]ok = Truenums[j+1:n] = sorted(nums[j+1:n])return numstmp = list(num)num = list(num)n = len(num)ans = 0for i in range(k):num = getnext(num)print(num)for i in range(n):if tmp[i] == num[i]:continueprint(i)pos = -1for j in range(i+1,n):if num[j] == tmp[i]:pos = jbreakfor j in range(pos,i,-1):num[j],num[j-1] = num[j-1],num[j]ans += 1return ans

['9', '4', '8', '6', '5', '3']
['9', '5', '3', '4', '6', '8']
['9', '5', '3', '4', '8', '6']
['9', '5', '3', '6', '4', '8']
['9', '5', '3', '6', '8', '4']
['9', '5', '4', '3', '6', '8']
['9', '5', '4', '3', '8', '6']
['9', '5', '4', '6', '3', '8']
['9', '5', '4', '6', '8', '3']
['9', '5', '4', '8', '3', '6']
['9', '5', '4', '8', '6', '3']
['9', '5', '6', '3', '4', '8']
['9', '5', '6', '3', '8', '4']
['9', '5', '6', '4', '3', '8']
['9', '5', '6', '4', '8', '3']
['9', '5', '6', '8', '3', '4']
['9', '5', '6', '8', '4', '3']
['9', '5', '8', '3', '4', '6']
['9', '5', '8', '3', '6', '4']
['9', '5', '8', '4', '3', '6']
['9', '5', '8', '4', '6', '3']
['9', '5', '8', '6', '3', '4']
['9', '5', '8', '6', '4', '3']
['9', '6', '3', '4', '5', '8']
['9', '6', '3', '4', '8', '5']
['9', '6', '3', '5', '4', '8']
['9', '6', '3', '5', '8', '4']
['9', '6', '4', '3', '5', '8']
['9', '6', '4', '3', '8', '5']
['9', '6', '4', '5', '3', '8']
['9', '6', '4', '5', '8', '3']
['9', '6', '4', '8', '3', '5']
['9', '6', '4', '8', '5', '3']
['9', '6', '5', '3', '4', '8']
['9', '6', '5', '3', '8', '4']
['9', '6', '5', '4', '3', '8']
['9', '6', '5', '4', '8', '3']
['9', '6', '5', '8', '3', '4']
['9', '6', '5', '8', '4', '3']
['9', '6', '8', '3', '4', '5']
['9', '6', '8', '3', '5', '4']
['9', '6', '8', '4', '3', '5']
['9', '6', '8', '4', '5', '3']
['9', '6', '8', '5', '3', '4']
['9', '6', '8', '5', '4', '3']
['9', '8', '3', '4', '5', '6']
['9', '8', '3', '4', '6', '5']
['9', '8', '3', '5', '4', '6']
['9', '8', '3', '5', '6', '4']
['9', '8', '4', '3', '5', '6']
['9', '8', '4', '3', '6', '5']
['9', '8', '4', '5', '3', '6']
['9', '8', '4', '5', '6', '3']
['9', '8', '4', '6', '3', '5']
['9', '8', '4', '6', '5', '3']
['9', '8', '5', '3', '4', '6']
['9', '8', '5', '3', '6', '4']
['9', '8', '5', '4', '3', '6']
['9', '8', '5', '4', '6', '3']
['9', '8', '5', '6', '3', '4']
['9', '8', '5', '6', '4', '3']
['9', '8', '6', '3', '4', '5']
['9', '8', '6', '3', '5', '4']
['9', '8', '6', '4', '3', '5']

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洛谷P2525 Uim的情人节礼物·其之壱(组合数学/上一个全排列/下一个全排列)

题目

思路来源

题解

代码1

代码2（prev_permutation）

后续（2021.5.7）

洛谷P2525 Uim的情人节礼物·其之壱(组合数学/上一个全排列/下一个全排列)相关推荐

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