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AtCoder Grand Contest 008 D - K-th K

program ios tco lin %d break int ati cst

題目傳送門:https://agc008.contest.atcoder.jp/tasks/agc008_d

題目大意:

給你一個長度為\(N\)的序列\(A\),請你構造一個長度為\(N^2\)的序列\(a\),滿足\(1\sim N\)都出現了\(N\)次,且對於任意\(i\),滿足\(i\)\(a\)中第\(i\)次出現的位置為\(A_i\)

首先我們知道對於一個數\(i\),在\([1,A_i)\)中出現了\(i-1\)次,在\((A_i,N^2]\)中出現了\(N-i\)次(顯然)

然後考慮位置\(i\)應該填什麽數,肯定是給需求最大的對吧?也就是按\(A_i\)排序後最靠前的,且出現次數還沒達到限制的數(限制即為\(i\)

\(A_i\)前只能出現\(i-1\)次)。然後我們正反都做一遍,最後判斷數列是否合法即可

/*program from Wolfycz*/
#include<cmath>
#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
#define inf 0x7f7f7f7f
using namespace std;
typedef long long ll;
typedef unsigned int ui;
typedef unsigned long long ull;
inline char gc(){
    static char buf[1000000],*p1=buf,*p2=buf;
    return p1==p2&&(p2=(p1=buf)+fread(buf,1,1000000,stdin),p1==p2)?EOF:*p1++;
}
inline int frd(){
    int x=0,f=1; char ch=gc();
    for (;ch<'0'||ch>'9';ch=gc())   if (ch=='-')    f=-1;
    for (;ch>='0'&&ch<='9';ch=gc()) x=(x<<3)+(x<<1)+ch-'0';
    return x*f;
}
inline int read(){
    int x=0,f=1; char ch=getchar();
    for (;ch<'0'||ch>'9';ch=getchar())  if (ch=='-')    f=-1;
    for (;ch>='0'&&ch<='9';ch=getchar())    x=(x<<3)+(x<<1)+ch-'0';
    return x*f;
}
inline void print(int x){
    if (x<0)    putchar('-'),x=-x;
    if (x>9)    print(x/10);
    putchar(x%10+'0');
}
const int N=5e2;
int cnt[N+10],A[N*N+10],C[N+10],B[N+10];
int pos[N+10][N+10];
bool cmp(int x,int y){return B[x]<B[y];}
bool check(int n){
    for (int i=1;i<=n*n;i++)    pos[A[i]][++pos[A[i]][0]]=i;
    for (int i=1;i<=n;i++)  if (pos[i][i]!=B[i])    return 0;
    return 1;
}
int main(){
    int n=read();
    for (int i=1;i<=n;i++)  C[i]=A[B[i]=read()]=i;
    sort(C+1,C+1+n,cmp);
    for (int i=1;i<=n;i++)  cnt[i]=i-1;
    for (int i=1;i<=n*n;i++){
        if (A[i])   continue;
        for (int j=1;j<=n;j++){
            if (cnt[C[j]]){
                cnt[A[i]=C[j]]--;
                break;
            }
        }
    }
    for (int i=1;i<=n;i++)  cnt[i]=n-i;
    for (int i=n*n;i>=1;i--){
        if (A[i])   continue;
        for (int j=n;j>=1;j--){
            if (cnt[C[j]]){
                cnt[A[i]=C[j]]--;
                break;
            }
        }
    }
    if (!check(n)){
        printf("No\n");
        return 0;
    }
    printf("Yes\n");
    for (int i=1;i<=n*n;i++)    printf("%d",A[i]),putchar(i==n*n?'\n':' ');
    return 0;
}

AtCoder Grand Contest 008 D - K-th K