G - Reverse Number
Time Limit:1000MS Memory Limit:131072KB 64bit IO Format:%lld & %llu
Description
Given a non-negative integer sequence A with length N, you can exchange two adjacent numbers each time. After K exchanging operations, what’s the minimum reverse number the sequence can achieve? The reverse number of a sequence is the number
of pairs (i, j) such that i < j and Ai > Aj
Input
There are multiple cases. For each case, first line contains two numbers: N, K 2<=N<=100000, 0 <= K < 2^60 Second line contains N non-negative numbers, each of which not greater than 2^30
Output
Minimum reverse number you can get after K exchanging operations.
Sample Input
3 1 3 2 1 5 2 5 1 4 3 2
Sample Output
Case #1: 2 Case #2: 5 先用树状数组求出逆序数。因为每一次交换可以增加或着减少一对逆序数,假设有m对逆序数,我们交换n对,那么这n对我们让他每次都减少一对逆序数,交换n次后 还有m - n对 逆序。注意题目中k的取值,如果求出的逆序数大于k,那么可以直接得出结果 res - k ,如果小于k,此时就要注意数字串中是否有重复的,如果没有那么当交换res - k次后 此时逆序数恰好为0, 剩余交换次数为k - res,如果k - res为偶数,那么我们可以重复交换同一对此时逆序数还为0,如果为奇数,此时只能结果为1。 如果字串中有重复的 那么可以交换那两个重复的数,此时无论是奇数还是偶数,结果并不影响最小逆序对总数。/*============================================================================= # # Author: liangshu - cbam # # QQ : 756029571 # # School : 哈尔滨理工大学 # # Last modified: 2015-08-30 22:32 # # Filename: A.cpp # # Description: # The people who are crazy enough to think they can change the world, are the ones who do ! =============================================================================*/ # #include<iostream> #include<sstream> #include<algorithm> #include<cstdio> #include<string.h> #include<cctype> #include<string> #include<cmath> #include<vector> #include<stack> #include<queue> #include<map> #include<set> using namespace std; #define maxn 100010 struct node { int v,id; } s[maxn]; int c[maxn],n; typedef long long ll; ll res; bool cmp(node x,node y) { return ((x.v>y.v) || ((x.v==y.v)&&(x.id>y.id))); } int Lowbit(int x) { return x&(x^(x-1)); } ll Getsum(int pos) { ll ret = 0LL; while(pos>0) { ret+=c[pos]; pos -= Lowbit(pos); } return ret; } ll update(int pos) { while(pos<=n) { c[pos]++; pos+=Lowbit(pos); } } int main() { int k,x; int cs = 1; while(scanf("%d%d",&n,&k)!=EOF) { set<int>cnt; memset(c,0,sizeof(c)); res = 0; for(int i=1; i<=n; i++) { scanf("%d",&s[i].v); cnt.insert(s[i].v); s[i].id = i; } sort(s+1,s+n+1,cmp); for(int i=1; i<=n; i++) { res += Getsum(s[i].id); update(s[i].id); } if((res-k)>=0) printf("Case #%d: %lld\n",cs ++,res-k); else { if(cnt.size() < n) { printf("Case #%d: 0\n",cs ++); } else { if(abs(res-k)%2) printf("Case #%d: 1\n",cs ++); else printf("Case #%d: 0\n",cs ++); } } } return 0; }
版权声明:本文为博主原创文章,未经博主允许不得转载。
时间: 2024-11-05 12:23:36