UVALive - 6257 K - Chemist's vows 【DFS】【BFS】【DP】

题目链接

https://icpcarchive.ecs.baylor.edu/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&problem=4268

题意

给出化学元素周期表，然后给出一个字符串，判断字符串里面的字符，能不能够完全由元素周期表里面的元素构成

或者换一种说法，将字符串切割成若干个子串，能不能有一种切割的方式，使得切割下来的每一个子串都是元素周期表里面的元素

思路

其实可以发现 元素周期表里面的元素 不是一个字母的，就是两个字母的

其实 不管是搜索还是DP 思路都是差不多的

搜索：

void dfs(int index)

表示 从 0 - index - 1 这个字段 是可以满足要求的

那么我们去判断 s[index] 是不是元素周期表的元素 如果是 那么0 - index 也是满足要求的 那么我们继续dfs(index + 1)

如果 s[index] + s[index + 1] 是元素周期表的元素 就dfs(index + 2)

Tips:

很重要的一点 ，一定要记得访问标记啊，不然会T到不知道什么样子。。。

如果这个当前下标的状态是访问过的，就不用再继续搜下去了

DP:

dp[i] 表示 从 0 - 第i 个字符构成的子段是否是满足要求的

那么有两种情况可以转移过来

如果 dp[i - 1] 是满足要求 并且 s[i] 是元素周期表里面的元素 那么 dp[i] 也是满足要求的

如果 dp[i - 2] 满足要求 并且 s[i - 1] 和 s[i] 构成的子段 是元素周期表里面的元素 那么 dp[i] 也是满足要求的

上面两个条件满足其中一个就可以了

AC代码

DP

#include <cstdio>
#include <cstring>
#include <ctype.h>
#include <cstdlib>
#include <cmath>
#include <climits>
#include <ctime>
#include <iostream>
#include <algorithm>
#include <deque>
#include <vector>
#include <queue>
#include <string>
#include <map>
#include <stack>
#include <set>
#include <list>
#include <numeric>
#include <sstream>
#include <iomanip>
#include <limits>

#define CLR(a, b) memset(a, (b), sizeof(a))
#define pb push_back
#define bug puts("***bug***");
#define fi first
#define se second
#define stack_expand #pragma comment(linker, "/STACK:102400000,102400000")
//#define bug
//#define gets gets_s

using namespace std;
typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;
typedef pair <int, int> pii;
typedef pair <ll, ll> pll;
typedef pair <string, int> psi;
typedef pair <string, string> pss;
typedef pair <double, int> pdi;

const double PI = acos(-1.0);
const double E = exp(1.0);
const double eps = 1e-8;

const int INF = 0x3f3f3f3f;
const int maxn = 5e4 + 10;
const int MOD = 1e9 + 7;

char single[25][2] = { "h","b","c","n","o","f","k","p","s","y","i","w","u","v" };
char ss[130][3] = { "he","li","be","ne","na","mg",
"al","si","cl","ar","ca","sc","ti","cr","mn",
"fe","co","ni","cu","zn","ga","ge","as","se",
"br","kr","rb","sr","zr","nb","mo","tc","ru",
"rh","pd","ag","cd","in","sn","sb","te","xe",
"cs","ba","hf","ta","re","os","ir","pt","au",
"hg","tl","pb","bi","po","at","rn","fr","ra",
"rf","db","sg","bh","hs","mt","ds","rg","cn",
"fl","lv","la","ce","pr","nd","pm","sm","eu",
"gd","tb","dy","ho","er","tm","yb","lu","ac",
"th","pa","np","pu","am","cm","bk","cf","es",
"fm","md","no","lr" };

int len;

char s[maxn];
int dp[maxn];

bool judge_single(int index)
{
    for (int i = 0; i < 14; i++)
    {
        if (single[i][0] == s[index])
            return true;
    }
    return false;
}

bool judge_tw(int index)
{
    for (int i = 0; i < 100; i++)
    {
        if (ss[i][0] == s[index] && ss[i][1] == s[index + 1])
            return true;
    }
    return false;
}

int main()
{
    int t;
    cin >> t;
    while (t--)
    {
        scanf("%s", s);
        len = strlen(s);
        for (int i = 0; i < len; i++)
            dp[i] = 0;
        if (judge_single(0))
            dp[0] = 1;
        if ((judge_single(1) && dp[0]) || judge_tw(0))
            dp[1] = 1;
        for (int i = 2; i < len; i++)
            dp[i] = ((judge_single(i) && dp[i - 1]) || (judge_tw(i - 1) && dp[i - 2]));
        puts(dp[len - 1] ? "YES" : "NO");
    }
}

DFS

#include <cstdio>
#include <cstring>
#include <ctype.h>
#include <cstdlib>
#include <cmath>
#include <climits>
#include <ctime>
#include <iostream>
#include <algorithm>
#include <deque>
#include <vector>
#include <queue>
#include <string>
#include <map>
#include <stack>
#include <set>
#include <list>
#include <numeric>
#include <sstream>
#include <iomanip>
#include <limits>

#define CLR(a, b) memset(a, (b), sizeof(a))
#define pb push_back
#define bug puts("***bug***");
#define fi first
#define se second
#define stack_expand #pragma comment(linker, "/STACK:102400000,102400000")
//#define bug
//#define gets gets_s

using namespace std;
typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;
typedef pair <int, int> pii;
typedef pair <ll, ll> pll;
typedef pair <string, int> psi;
typedef pair <string, string> pss;
typedef pair <double, int> pdi;

const double PI = acos(-1.0);
const double E = exp(1.0);
const double eps = 1e-8;

const int INF = 0x3f3f3f3f;
const int maxn = 5e4 + 10;
const int MOD = 1e9 + 7;

char single[20] =   //14
{
    'h', 'b', 'c', 'n', 'o', 'p', 's', 'v', 'k', 'y', 'i', 'u', 'f', 'w',
};

char ss[105][3]
{
    "he", "li", "be", "ne", "na", "mg", "al", "si", "cl", "ar", "ca", "sc", "ti", "cr", "mn", "fe", "co", "ni", "cu", "zn", "ga", "ge", "as", "se", "br", "kr", "rb", "sr", "zr", "nb", "mo", "tc", "ru", "rh", "pd", "ag", "cd", "in", "sn", "sb", "te", "xe", "cs", "ba", "hf", "ta", "re", "os", "ir", "pt", "au", "hg", "tl", "pb", "bi", "po", "at", "rn", "fr", "ra", "rf", "db", "sg", "bh", "hs", "mt", "ds", "rg", "cn", "fl", "lv", "la", "ce", "pr", "nd", "pm", "sm", "eu", "gd", "tb", "dy", "ho", "er", "tm", "yb", "lu", "ac", "th", "pa", "np", "pu", "am", "cm", "bk", "cf", "es", "fm", "md", "no", "lr",
};

int len;

char s[maxn];

bool judge_single(int index)
{
    for (int i = 0; i < 14; i++)
    {
        if (single[i] == s[index])
            return true;
    }
    return false;
}

bool judge_tw(int index)
{
    for (int i = 0; i < 100; i++)
    {
        if (ss[i][0] == s[index] && ss[i][1] == s[index + 1])
            return true;
    }
    return false;
}

int tag;

int used[maxn];

void dfs(int index)
{
    used[index] = 1;
    if (index == len)
    {
        tag = 1;
        return;
    }
    if (judge_single(index) && !used[index + 1])
        dfs(index + 1);
    if (index + 1 < len && judge_tw(index) && !used[index + 2])
        dfs(index + 2);
}

int main()
{
    int t;
    cin >> t;
    while (t--)
    {
        scanf("%s", s);
        len = strlen(s);
        for (int i = 0; i <= len; i++)
            used[i] = 0;
        tag = 0;
        dfs(0);
        puts(tag ? "YES" : "NO");
    }
}

BFS

#include <cstdio>
#include <cstring>
#include <ctype.h>
#include <cstdlib>
#include <cmath>
#include <climits>
#include <ctime>
#include <iostream>
#include <algorithm>
#include <deque>
#include <vector>
#include <queue>
#include <string>
#include <map>
#include <stack>
#include <set>
#include <list>
#include <numeric>
#include <sstream>
#include <iomanip>
#include <limits>

#define CLR(a, b) memset(a, (b), sizeof(a))
#define pb push_back
#define bug puts("***bug***");
#define fi first
#define se second
#define stack_expand #pragma comment(linker, "/STACK:102400000,102400000")
//#define bug
//#define gets gets_s

using namespace std;
typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;
typedef pair <int, int> pii;
typedef pair <ll, ll> pll;
typedef pair <string, int> psi;
typedef pair <string, string> pss;
typedef pair <double, int> pdi;

const double PI = acos(-1.0);
const double E = exp(1.0);
const double eps = 1e-8;

const int INF = 0x3f3f3f3f;
const int maxn = 5e4 + 10;
const int MOD = 1e9 + 7;

char single[20] =   //14
{
    'h', 'b', 'c', 'n', 'o', 'p', 's', 'v', 'k', 'y', 'i', 'u', 'f', 'w',
};

char ss[105][3]
{
    "he", "li", "be", "ne", "na", "mg", "al", "si", "cl", "ar", "ca", "sc", "ti", "cr", "mn", "fe", "co", "ni", "cu", "zn", "ga", "ge", "as", "se", "br", "kr", "rb", "sr", "zr", "nb", "mo", "tc", "ru", "rh", "pd", "ag", "cd", "in", "sn", "sb", "te", "xe", "cs", "ba", "hf", "ta", "re", "os", "ir", "pt", "au", "hg", "tl", "pb", "bi", "po", "at", "rn", "fr", "ra", "rf", "db", "sg", "bh", "hs", "mt", "ds", "rg", "cn", "fl", "lv", "la", "ce", "pr", "nd", "pm", "sm", "eu", "gd", "tb", "dy", "ho", "er", "tm", "yb", "lu", "ac", "th", "pa", "np", "pu", "am", "cm", "bk", "cf", "es", "fm", "md", "no", "lr",
};

int len;

char s[maxn];

int used[maxn];

bool judge_single(int index)
{
    for (int i = 0; i < 14; i++)
    {
        if (single[i] == s[index])
            return true;
    }
    return false;
}

bool judge_tw(int index)
{
    for (int i = 0; i < 100; i++)
    {
        if (ss[i][0] == s[index] && ss[i][1] == s[index + 1])
            return true;
    }
    return false;
}

bool bfs()
{
    queue <int> q;
    if (judge_single(0))
        q.push(1), used[1] = 1;
    if (1 < len && judge_tw(0))
        q.push(2), used[2] = 1;
    while (!q.empty())
    {
        int u = q.front();
        q.pop();
        if (u == len)
            return true;
        if (judge_single(u) && !used[u + 1])
            q.push(u + 1), used[u + 1] = 1;
        if (u + 1 < len && judge_tw(u) && !used[u + 2])
            q.push(u + 2), used[u + 2] = 1;
    }
    return false;
}

int tag;

int main()
{
    int t;
    cin >> t;
    while (t--)
    {
        scanf("%s", s);
        len = strlen(s);
        for (int i = 0; i <= len; i++)
            used[i] = 0;
        puts(bfs() ? "YES" : "NO");
    }
}