Fox Ciel has n boxes in her room. They have the same size and weight, but they might have different strength. The i-th box can hold at most xi boxes on its top (we'll call xi the strength of the box).
Since all the boxes have the same size, Ciel cannot put more than one box directly on the top of some box. For example, imagine Ciel has three boxes: the first has strength 2, the second has strength 1 and the third has strength 1. She cannot put the second and the third box simultaneously directly on the top of the first one. But she can put the second box directly on the top of the first one, and then the third box directly on the top of the second one. We will call such a construction of boxes a pile.
Fox Ciel wants to construct piles from all the boxes. Each pile will contain some boxes from top to bottom, and there cannot be more thanxi boxes on the top of i-th box. What is the minimal number of piles she needs to construct?
The first line contains an integer n (1 ≤ n ≤ 100). The next line contains n integers x1, x2, ..., xn (0 ≤ xi ≤ 100).
Output a single integer — the minimal possible number of piles.
3 0 0 10
2
5 0 1 2 3 4
1
4 0 0 0 0
4
9 0 1 0 2 0 1 1 2 10
3
In example 1, one optimal way is to build 2 piles: the first pile contains boxes 1 and 3 (from top to bottom), the second pile contains only box 2.
In example 2, we can build only 1 pile that contains boxes 1, 2, 3, 4, 5 (from top to bottom).
题意:
给出N(1~100),表示有N个箱子。后给出N个数 Xi (1~100),数字表示这个箱子上面最多只能放 Xi 个箱子。求出最少的叠放堆数。
思路:
模拟。叠放顺序是数字由大到小向上叠放的,但是模拟的时候可以从小到大向下进行。fin 数组维护当前堆数已经有多少个箱子,ans 数组维护同一数的箱子个数,num 数组维护一个有多少种数字的箱子,最后fin 数组的最大值即为所求。
AC:
#include<stdio.h> #include<string.h> #include<algorithm> using namespace std; int num[105],ans[105],fin[105]; int main() { int n,k,maxnum = 1; scanf("%d",&n); memset(ans,0,sizeof(ans)); memset(fin,0,sizeof(fin)); for(int i = 0;i < n;i++) { scanf("%d",&num[i]); ans[num[i]]++; } sort(num,num + n); int i = 0; while(n) { k = 1; while(ans[num[i]]) { if(num[i] < fin[k]) k++; fin[k]++; ans[num[i]]--; n--; } i++; if(k > maxnum) maxnum = k; } printf("%d\n",maxnum); return 0; }
总结:
很容易被题目牵着走,不能跳出固化思维, 看似简单的题可是不能整理出一种思路来,无论多少人觉得容易做得出来都千万不能看题解后再写出来,一定要自己想出来。
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