练习题 POJ1011/The Biggest Rectangle

题目：DFS练习题目

/*POJ 1011
题目：给最多64根棍，每根最长50，拼成等长的几个片段，不能有剩余，问最短的片段长度。
使用DFS+强剪枝
*/
#include <stdio.h>
#define SIZE 65
int num[SIZE], n, max, sum, isFind, key;
void dfs(int cnt, int len, int cur){//已用的条数，凑成key还需的长度，当前位置
    if (isFind > 0)return;
    if (cnt == n - 1 && cur == len){
        isFind = 1;
        return;
    }
    --num[cur];//当前点合法，加入解空间
    int nextcur;
    if (cur == len){//填上这一条就能凑成一个key长度的片段
        for (nextcur = max; nextcur > 0; --nextcur)
            if (num[nextcur] > 0)break;
        dfs(cnt + 1, key, nextcur);
    }else{
        for (nextcur = cur; nextcur > 0; --nextcur){
            if (nextcur > len - cur || num[nextcur] == 0)continue;
            dfs(cnt + 1, len - cur, nextcur);
        }
    }
    ++num[cur];
}
int main(){
    int tdata;
#ifndef ONLINE_JUDGE
    freopen("sample_input.txt", "r", stdin);
#endif
    while (~scanf("%d", &n) && n){
        for (int i = 0; i < SIZE; ++i)num[i] = 0;
        sum = max = isFind = 0;
        for (int i = 0; i < n; ++i){
            scanf("%d", &tdata);
            ++num[tdata];
            sum += tdata;
            if (tdata>max)max = tdata;
        }
        isFind = -1;
        for (key = max; key <= sum / 2; ++key){
            if (sum%key > 0)continue;
            dfs(0, key, max);
            if (isFind > 0){
                printf("%d\n", key);
                break;
            }
        }
        if (isFind < 0)printf("%d\n", sum);;
    }
    return 0;
}

 

附上一道相似的题目，给定一些木棒，求可拼接出的最大矩形面积。 

Execution time : 10 sec(C/C++) / 20 sec(JAVA) for 95  cases combined
Memory : Maximum 256MB  available for heap and stack combined (note: Maximum 1 MB can be used for  stack)

题目描述：

Suppose there are N sticks.
Write a program that figures out out the area of the biggest rectangle among rectangles that could be made with those sticks.
To make a rectangle,you can can connect sticks together but you cannot splict an intact stick.
For example, you can make a stick of length 6 by joining a stick of length 2 with a stick of length 4.

[Input]
The first line contains a single integer Tㅡthe number of total test cases.
The first line of each test case contains one positive integer, N( 4 ≤ N ≤ 16).
The second line contains N space-separated positive integers which represent the lengths of N sticks.
The length of a stick is a positive integer greater than or equal to 1 and less than and equal to 10.

[Output]
Each line begins with ‘#T’(Test case number) followed by a space and then print the area of the biggest possible rectangle for each test case.
If it is not possible to make a rectangle with the given sticks, print -1.

input 下载链接：https://files.cnblogs.com/files/proscientist/biggest_rect_input.zip

题解：DFS题目，配合剪枝

/*The Biggest Rectangle
题意：给定最多16根棍，选取其中一些拼成矩形，问矩形最大面积
*/
#include <stdio.h>
int tc, n, s[17], la, lb, sum, ans, k;
bool visit[17];
void dfs(int loc, int cnt, int cur, int dep){
    if (dep == 4){
        ans = la*lb;
        return;
    }
    if (cnt == 2){
        lb = k;
        while (lb > 0){
            if (la*lb < ans)return;
            dfs(n, 0, lb, dep);
            --lb;
        }
        return;
    }
    int last = -1;
    for (int i = loc - 1; i >= 0; i--){
        if (visit[i] || s[i] == last)continue;
        if (cur == s[i]){
            visit[i] = 1;
            if (dep<2)dfs(n, cnt + 1, la, dep + 1);
            else dfs(n, cnt + 1, lb, dep + 1);
            visit[i] = 0;
            last = s[i];
        }
        if (cur > s[i]){
            visit[i] = 1;
            dfs(i, cnt, cur - s[i], dep);
            visit[i] = 0;
            last = s[i];
        }
    }
}
int main(){
    scanf("%d", &tc);
    for (int t = 1; t <= tc; ++t){
        ans = -1, sum = 0;
        scanf("%d", &n);
        //读入数据以及排序，sum
        for (la = sum / 2 - 1; la > 0; --la){//长边
            k = (sum - 2 * la) / 2;
            if (k > la)k = la;
            if (k*la <= ans)continue;
            dfs(n, 0, la, 0);
        }
        printf("#%d %d\n", t, ans);
    }
    return 0;
}