A1117. Eddington Number

British astronomer Eddington liked to ride a bike. It is said that in order to show off his skill, he has even defined an "Eddington number", E -- that is, the maximum integer E such that it is for E days that one rides more than E miles. Eddington's own E was 87.

Now given everyday's distances that one rides for N days, you are supposed to find the corresponding E (<=N).

Input Specification:

Each input file contains one test case. For each case, the first line gives a positive integer N(<=10⁵), the days of continuous riding. Then N non-negative integers are given in the next line, being the riding distances of everyday.

Output Specification:

For each case, print in a line the Eddington number for these N days.

Sample Input:

10
6 7 6 9 3 10 8 2 7 8

Sample Output:

6

#include<cstdio>
#include<iostream>
#include<algorithm>
using namespace std;
int N, num[100001];
bool cmp(int a, int b){
    return a > b;
}
int main(){
    int E;
    scanf("%d", &N);
    for(int i = 1; i <= N; i++){
        scanf("%d", &num[i]);
    }
    sort(num + 1, num + N + 1, cmp);
    E = N;
    for(int i = 1; i <= N; i++){
        if(i >= num[i]){
            E = i - 1;
            break;
        }
    }

    printf("%d", E);
    cin >> N;
    return 0;
}

总结：

1、题意：给出N个数，求一个最大的m，使得有m个数大于m。

2、找规律可以发现，先对序列递减排序后，只要 i 大于 num[ i ]，则 i - 1也会大于 num[ i - 1]（i之前的都满足，这里i从1开始）。这样只要找到一个 i 小于等于 num[ i ]，则说i - 1即为所求。

3、要注意遍历完整个序列结果都满足的情况，需要将E 初始化为N。（N = 3， 序列为 4   4   4）