【Algorithm】逆序数的分治求解

逆序数的分治求解，时间复杂度O(nlgn)。基本思想是在归并排序的基础上加逆序计数。

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <ctime>
using namespace std;

#define MAXN 100005

int a[MAXN], b[MAXN];
int c[MAXN];
int ans, n;

void merge(int *a, int l, int r) {
    int mid = (l+r)>>1;
    int i = l, j = mid+1;
    int n = 0;
    
    while (i<=mid && j<=r) {
        if (a[i] <= a[j]) {
            c[n++] = a[i++];
        } else {
            c[n++] = a[j++];
            ans += (mid-i+1);
        }
    }
    while (i <= mid)
        c[n++] = a[i++];
    while (j <= r)
        c[n++] = a[j++];
    for (i=0, j=l; i<n; ++i, ++j)
        a[j] = c[i];
}

void mergeSort(int *a, int l, int r) {
    int mid = (l+r)>>1;
    
    if (l >= r)
        return ;
    mergeSort(a, l, mid);
    mergeSort(a, mid+1, r);
    merge(a, l, r);
}

void bruteSolve(int *b, int l, int r) {
    int i, j;
    
    for (i=l; i<=r; ++i) {
        for (j=l; j<=i; ++j) {
            if (b[j] > b[i])
                ++ans;
        }
    }
}

void init() {
    int i;
    
    n = rand()%(MAXN-1)+1;
    for (i=1; i<=n; ++i) {
        a[i] = rand();
        b[i] = a[i];
    }
}

void solve() {
    clock_t beg, end;
    int tmp;
    
    ans = 0;
    beg = clock();
    mergeSort(a, 1, n);
    end = clock();
    printf("nlgn: ans  = %d
", ans);
    printf("      time = %.2lf
", (double)(end-beg)/CLOCKS_PER_SEC);
    
    tmp = ans;
    ans = 0;
    beg = clock();
    bruteSolve(b, 1, n);
    end = clock();
    printf("n*n : ans  = %d
", ans);
    printf("      time = %.2lf
", (double)(end-beg)/CLOCKS_PER_SEC);
    
    if (tmp != ans)
        printf("**** wrong ****
");
    printf("
");
}

int main() {
    int t = 30;
    
    while (t--) {
        init();
        solve();
    }
    
    return 0;
}