基数排序

基数排序的复杂度可以写成：O(k(n+2^logMax/k)，k是维数，n是数据个数，Max是数的最大值。现在需要对10M个32位正整数排序，则可以令k=2，则复杂度为O(2(n+2¹⁶))=O(n)。具体来说，先按低16位进行第一趟排，然后对结果按高16位排，这种排法与32位同时排是等价的。实现时需要链表，因此辅助开销比较大，而时间比std::sort减少了1半多。

 

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#include <bits/stdc++.h> using namespace std; #ifndef ONLINE_JUDGE #include "local.h" #endif #define X first #define Y second #define pb(x) push_back(x) #define mp(x, y) make_pair(x, y) #define all(a) (a).begin(), (a).end() #define mset(a, x) memset(a, x, sizeof(a)) #define mcpy(a, b) memcpy(a, b, sizeof(a)) typedef long long ll; template<typename T>bool umax(T&a, const T&b){return b<=a?false:(a=b,true);} template<typename T>bool umin(T&a, const T&b){return b>=a?false:(a=b,true);} const int maxn = 1e7 + 7; int seq[maxn]; int top; struct HashList { public: HashList() { clr(); } void clr() { sz = 1; memset(head, 0, sizeof(head)); } void ins(int val, int pos) { hlist[sz] = Node(val, head[pos]); head[pos] = sz ++; } void get(int a[]) { for (int i = 0; i < 0x10000; i ++) { int h = head[i]; top = 0; while (h) { seq[top ++] = hlist[h].val; h = hlist[h].next; } while (top) *a ++ = seq[-- top]; } } private: struct Node { int val; int next; Node(int val = 0, int next = 0) { this->val = val; this->next = next; } }; Node hlist[maxn]; int sz; int head[1 << 16]; }; int a[maxn]; HashList hl; void sortint(int *p, int *q) { int n = q - p; for (int i = 0; i < n; i ++) { hl.ins(p[i], p[i] & 0xffff); } hl.get(p); hl.clr(); for (int i = 0; i < n; i ++) { hl.ins(p[i], (p[i] >> 16) & 0xffff); } hl.get(p); } int main() { #ifndef ONLINE_JUDGE freopen("in.txt", "r", stdin); //freopen("out.txt", "w", stdout); #endif // ONLINE_JUDGE int n = 10000000; for (int i = 0; i < n; i ++) { a[i] = rand() * rand(); } Timer ok; sort(a, a + n); ok.get(); ok.start(); sortint(a, a + n); ok.get(); return 0; }