牛客最长递增子序列

妖狐艹你老母 2023-06-04 14:54 17阅读 0赞

题目链接：[https://www.nowcoder.com/practice/30fb9b3cab9742ecae9acda1c75bf927?tpId=101&tqId=33093&tPage=1&rp=1&ru=/ta/programmer-code-interview-guide&qru=/ta/programmer-code-interview-guide/question-ranking][https_www.nowcoder.com_practice_30fb9b3cab9742ecae9acda1c75bf927_tpId_101_tqId_33093_tPage_1_rp_1_ru_ta_programmer-code-interview-guide_qru_ta_programmer-code-interview-guide_question-ranking]

### 题目大意 ###

略。

### 分析 ###

经典 DP，具体怎么 DP 的推荐看左神的书，这里解释一下为什么从后往前不断找第一个 dp\[i\] 减少并且位于 LIS 上的元素就可以找到字典序最小的 LIS。

下面以样例 2,1,5,3,6,4,8,9,7,5,7,2,3 来演示 smallEnds 数组的更新。

![1665214-20190819105328060-284020192.jpg][]

从图中可以直观地看出来，后更新的，并且位于 LIS 路径上的点，一定能取代被它更新的，并且位于 LIS 路径上的点。

### 代码如下 ###

![ContractedBlock.gif][] ![ExpandedBlockStart.gif][]

1 #include <bits/stdc++.h>
      2 using namespace std;
      3  
      4 #define INIT() ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
      5 #define Rep(i,n) for (int i = 0; i < (int)(n); ++i)
      6 #define For(i,s,t) for (int i = (int)(s); i <= (int)(t); ++i)
      7 #define rFor(i,t,s) for (int i = (int)(t); i >= (int)(s); --i)
      8 #define ForLL(i, s, t) for (LL i = LL(s); i <= LL(t); ++i)
      9 #define rForLL(i, t, s) for (LL i = LL(t); i >= LL(s); --i)
     10 #define foreach(i,c) for (__typeof(c.begin()) i = c.begin(); i != c.end(); ++i)
     11 #define rforeach(i,c) for (__typeof(c.rbegin()) i = c.rbegin(); i != c.rend(); ++i)
     12  
     13 #define pr(x) cout << #x << " = " << x << "  "
     14 #define prln(x) cout << #x << " = " << x << endl
     15  
     16 #define LOWBIT(x) ((x)&(-x))
     17  
     18 #define ALL(x) x.begin(),x.end()
     19 #define INS(x) inserter(x,x.begin())
     20 #define UNIQUE(x) x.erase(unique(x.begin(), x.end()), x.end())
     21 #define REMOVE(x, c) x.erase(remove(x.begin(), x.end(), c), x.end()); // 删去 x 中所有 c 
     22 #define TOLOWER(x) transform(x.begin(), x.end(), x.begin(),::tolower);
     23 #define TOUPPER(x) transform(x.begin(), x.end(), x.begin(),::toupper);
     24  
     25 #define ms0(a) memset(a,0,sizeof(a))
     26 #define msI(a) memset(a,0x3f,sizeof(a))
     27 #define msM(a) memset(a,-1,sizeof(a))
     28 
     29 #define MP make_pair
     30 #define PB push_back
     31 #define ft first
     32 #define sd second
     33  
     34 template<typename T1, typename T2>
     35 istream &operator>>(istream &in, pair<T1, T2> &p) {
     36     in >> p.first >> p.second;
     37     return in;
     38 }
     39  
     40 template<typename T>
     41 istream &operator>>(istream &in, vector<T> &v) {
     42     for (auto &x: v)
     43         in >> x;
     44     return in;
     45 }
     46 
     47 template<typename T>
     48 ostream &operator<<(ostream &out, vector<T> &v) {
     49     Rep(i, v.size()) out << v[i] << " \n"[i == v.size() - 1];
     50     return out;
     51 }
     52  
     53 template<typename T1, typename T2>
     54 ostream &operator<<(ostream &out, const std::pair<T1, T2> &p) {
     55     out << "[" << p.first << ", " << p.second << "]" << "\n";
     56     return out;
     57 }
     58 
     59 inline int gc(){
     60     static const int BUF = 1e7;
     61     static char buf[BUF], *bg = buf + BUF, *ed = bg;
     62     
     63     if(bg == ed) fread(bg = buf, 1, BUF, stdin);
     64     return *bg++;
     65 } 
     66 
     67 inline int ri(){
     68     int x = 0, f = 1, c = gc();
     69     for(; c<48||c>57; f = c=='-'?-1:f, c=gc());
     70     for(; c>47&&c<58; x = x*10 + c - 48, c=gc());
     71     return x*f;
     72 }
     73 
     74 template<class T>
     75 inline string toString(T x) {
     76     ostringstream sout;
     77     sout << x;
     78     return sout.str();
     79 }
     80 
     81 inline int toInt(string s) {
     82     int v;
     83     istringstream sin(s);
     84     sin >> v;
     85     return v;
     86 }
     87 
     88 //min <= aim <= max
     89 template<typename T>
     90 inline bool BETWEEN(const T aim, const T min, const T max) {
     91     return min <= aim && aim <= max;
     92 }
     93 
     94 typedef unsigned int uI;
     95 typedef long long LL;
     96 typedef unsigned long long uLL;
     97 typedef vector< int > VI;
     98 typedef vector< bool > VB;
     99 typedef vector< char > VC;
    100 typedef vector< double > VD;
    101 typedef vector< string > VS;
    102 typedef vector< LL > VL;
    103 typedef vector< VI > VVI;
    104 typedef vector< VB > VVB;
    105 typedef vector< VS > VVS;
    106 typedef vector< VL > VVL;
    107 typedef vector< VVI > VVVI;
    108 typedef vector< VVL > VVVL;
    109 typedef pair< int, int > PII;
    110 typedef pair< LL, LL > PLL;
    111 typedef pair< int, string > PIS;
    112 typedef pair< string, int > PSI;
    113 typedef pair< string, string > PSS;
    114 typedef pair< double, double > PDD;
    115 typedef vector< PII > VPII;
    116 typedef vector< PLL > VPLL;
    117 typedef vector< VPII > VVPII;
    118 typedef vector< VPLL > VVPLL;
    119 typedef vector< VS > VVS;
    120 typedef map< int, int > MII;
    121 typedef unordered_map< int, int > uMII;
    122 typedef map< LL, LL > MLL;
    123 typedef map< string, int > MSI;
    124 typedef map< int, string > MIS;
    125 typedef set< int > SI;
    126 typedef stack< int > SKI;
    127 typedef deque< int > DQI;
    128 typedef queue< int > QI;
    129 typedef priority_queue< int > PQIMax;
    130 typedef priority_queue< int, VI, greater< int > > PQIMin;
    131 const double EPS = 1e-8;
    132 const LL inf = 0x7fffffff;
    133 const LL infLL = 0x7fffffffffffffffLL;
    134 const LL mod = 1e9 + 7;
    135 const int maxN = 1e5 + 7;
    136 const LL ONE = 1;
    137 const LL evenBits = 0xaaaaaaaaaaaaaaaa;
    138 const LL oddBits = 0x5555555555555555;
    139 
    140 int N;
    141 int arr[maxN], maxLen; 
    142 int ans[maxN];
    143 // dp[i] 表示以 arr[i] 结尾的最长递增子序列 
    144 int dp[maxN];
    145 // smallEnds[i] 表示LIS长度为 i + 1 的最小结尾 
    146 VI smallEnds;
    147 
    148 int main() {
    149     //freopen("MyOutput.txt","w",stdout);
    150     //freopen("input.txt","r",stdin);
    151     //INIT();
    152     scanf("%d", &N);
    153     For(i, 1, N) scanf("%d", &arr[i]);
    154     
    155     For(i, 1, N) {
    156         auto it = lower_bound(ALL(smallEnds), arr[i]);
    157         dp[i] = it - smallEnds.begin() + 1;
    158         
    159         if(it != smallEnds.end()) *it = arr[i];
    160         else smallEnds.PB(arr[i]);
    161     }
    162     maxLen = smallEnds.size();
    163     
    164     int len = maxLen, nextLen = maxLen + 1;
    165     rFor(i, N, 1) {
    166         if(dp[i] == len && len == nextLen - 1) {
    167             ans[len] = arr[i];
    168             --len;
    169             --nextLen;
    170         }
    171     }
    172     
    173     For(i, 1, maxLen) printf("%d%c", ans[i], " \n"[i == N]);
    174     return 0;
    175 }

转载于:https://www.cnblogs.com/zaq19970105/p/11375849.html

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[1665214-20190819105328060-284020192.jpg]: /images/20230601/89b641522e4f4620ab2fcbdf0083e063.png
[ContractedBlock.gif]: https://images.cnblogs.com/OutliningIndicators/ContractedBlock.gif
[ExpandedBlockStart.gif]: /images/20230601/eda2cdef08c34218805f330f02099b0c.png