P1908 逆序对

合集 - 思维题(99)

1.大雪球2024-01-162.E. Final Countdown2024-02-183.D. Divisible Pairs2024-02-194.F. Chat Screenshots2024-02-195.G. One-Dimensional Puzzle2024-02-206.P8775 [蓝桥杯 2022 省 A] 青蛙过河2024-02-217.Watering an Array2024-02-238.Dora and Search2024-02-249.P1137 旅行计划2024-02-2410.P3067 [USACO12OPEN] Balanced Cow Subsets G2024-02-2611.P4799 [CEOI2015 Day2] 世界冰球锦标赛2024-02-2612.A. Brick Wall2024-02-2813.B. Minimize Inversions2024-02-2814.C. XOR-distance2024-02-2815.A. Moving Chips2024-02-2816.B. Monsters Attack!2024-02-2817.C. Find B2024-02-2818.D. Slimes2024-02-2819.C. Turtle Fingers: Count the Values of k2024-02-2820.D. Turtle Tenacity: Continual Mods2024-02-2821.D. Vlad and Division2024-02-2822.C. LR-remainders2024-02-2823.P5322 [BJOI2019] 排兵布阵2024-03-0324.P2946 [USACO09MAR] Cow Frisbee Team S2024-03-0325.P1156 垃圾陷阱2024-03-0326.P1064 [NOIP2006 提高组] 金明的预算方案2024-03-0427.P3047 [USACO12FEB] Nearby Cows G2024-03-0428.P5020 [NOIP2018 提高组] 货币系统2024-03-0429.P3957 [NOIP2017 普及组] 跳房子2024-03-0630.P1550 [USACO08OCT] Watering Hole G2024-03-0631.P1525 [NOIP2010 提高组] 关押罪犯2024-03-0732.P1379 八数码难题2024-03-0733.P6121 [USACO16OPEN] Closing the Farm G2024-03-0834.P2341 [USACO03FALL / HAOI2006] 受欢迎的牛 G2024-03-0835.P9632 [ICPC2020 Nanjing R] K Co-prime Permutation2024-03-0836.P9825 [ICPC2020 Shanghai R] Fibonacci2024-03-0837.P2034 选择数字2024-03-0938.P7072 [CSP-J2020] 直播获奖2024-03-0939.P1714 切蛋糕2024-03-0940.P4147 玉蟾宫2024-03-1041.P2866 [USACO06NOV] Bad Hair Day S2024-03-1042.P2032 扫描2024-03-1043.P1884 [USACO12FEB] Overplanting S2024-03-1044.D. Lonely Mountain Dungeons2024-03-1245.F. Microcycle2024-03-1246.E. Increasing Subsequences__22024-03-1347.D. Valiant's New Map2024-03-1448.Array Repetition2024-03-1449.F. Rudolf and Imbalance2024-03-1450.D. Exam in MAC2024-03-1551.G. Rudolf and Subway2024-03-1552.C. Ehab and Path-etic MEXs2024-03-1753.A. String Transformation 12024-03-1754.D. Solve The Maze2024-03-1855.B. Array Fix2024-03-1856.B. Equal XOR2024-03-1857.F. Maximum White Subtree2024-03-1958.P1652 圆2024-03-2059.P2181 对角线2024-03-2060.P1325 雷达安装2024-03-2061.P3194 [HNOI2008] 水平可见直线2024-03-2062.B - Make Many Triangles2024-03-2363.[ARC172A] Chocolate2024-03-2564.C. Theofanis' Nightmare2024-03-2765.D. Birthday Gift2024-03-2766.C. Arrow Path2024-03-2767.P1265 公路修建2024-03-2868.P1284 三角形牧场2024-03-2869.Kirill and Mushrooms2024-03-2870.C. Sasha and the Casino2024-03-2871.P1470 [USACO2.3] 最长前缀 Longest Prefix2024-04-0172.P5536 【XR-3】核心城市2024-04-0273.P5836 [USACO19DEC] Milk Visits S2024-04-0274.P4391 [BOI2009] Radio Transmission 无线传输2024-04-0475.P3435 [POI2006] OKR-Periods of Words2024-04-0476.P5960 【模板】差分约束2024-04-0477.P3052 [USACO12MAR] Cows in a Skyscraper G2024-04-0578.E. Long Inversions2024-04-0979.C. Deep Down Below2024-04-0980.C. Rings2024-04-0981.F. Unfair Game2024-04-1082.G. GCD on a grid2024-04-1083.C. Inversion Graph2024-04-1084.Increase Subarray Sums2024-04-1085.D. Cross Coloring2024-04-1286.M. Triangle Construction2024-04-1287.D2. Set To Max (Hard Version)2024-04-1288.C. Array Game2024-04-1289.F. Alex's whims2024-04-1290.Queue Sort2024-04-12

91.P1908 逆序对2024-04-13

92.P5094 [USACO04OPEN] MooFest G 加强版2024-04-1593.P5149 会议座位2024-04-1594.P10337 [UESTCPC 2024] 操作序列2024-04-1595.P10330 [UESTCPC 2024] 黑白珠串2024-04-1596.P10252 线性变换2024-04-1697.P3901 数列找不同2024-04-1698.P10288 [GESP样题 八级] 区间2024-04-1699.P5677 [GZOI2017] 配对统计2024-04-17

收起

原题链接

题解1

本质：求一个数前面有几个数大于它，我们把序列分成几段，然后对每段分别进行排序，然后找出这个数在前面已经排好序中的序列里有几个大于它

code

#include<bits/stdc++.h>
using namespace std;

#define ll long long

ll a[500005], b[500005], c[500005]; // a-original, b-replace, c-new
ll ans = 0;

inline void read(ll &x) {
    x = 0;
    ll flag = 1;
    char c = getchar();
    while(c < '0' || c > '9'){
        if(c == '-')flag = -1;
        c = getchar();
    }
    while(c >= '0' && c <= '9') {
        x = (x << 3) + (x << 1) + (c ^ 48);
        c = getchar();
    }
    x *= flag;
}

inline void write(ll x)
{
    if(x < 0){
        putchar('-');
        x = -x;
    }
    if(x > 9)
        write(x / 10);
    putchar(x % 10 + '0');
}

void bg(ll l, ll r)
{

    if (l == r) return;
    ll mid = (l + r) / 2;

    bg(l, mid);
    bg(mid + 1, r);
    ll p1 = l, p2 = mid + 1, p3 = l;
    while (p1 <= mid && p2 <= r)
    {
        if (c[p1] <= c[p2]) b[p3++] = c[p1++];//为什么要等于？因为等于不算逆序对
        else
        {
            b[p3++] = c[p2++];
            ans += mid - p1 + 1;
        }
    }
    while (p1 <= mid) b[p3++] = c[p1++];
    while (p2 <= r) b[p3++] = c[p2++];

    for (ll i = l; i <= r; i++) c[i] = b[i];
    return;
}

int main()
{
    ll n;
    read(n);

    for (ll i = 1; i <= n; i++)
    {
        read(a[i]);
        c[i]=a[i];
    }

    bg(1, n);
    write(ans);
    return 0;
}

题解2：

设遍历到 $i$ 则求已经出现的大于 $a[i]$ 的数的个数 $\to$ 求大于 $a[i]$ 的数出现了几个，这样就变成了区间查询，然后 $a[i]$ 出现代表单点修改，这样我们就就可以用树状数组来解题了，注意由于 $a[i]$ 太大，所以还要离散化

code

#include<bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/hash_policy.hpp>
#define lowbit(x) ((x)&(-x))
using namespace __gnu_pbds;
using namespace std;
int a[500005],c[500005];
int b[500005]={0};
int n;
int len=0;
int query(int x)
{
    int sum=0;
    while(x)
    {
        sum+=b[x];
        x-=lowbit(x);
    }
    return sum;
}

void update(int x)
{
    while(x<=len)
    {
        b[x]++;
        x+=lowbit(x);
    }
}
int main()
{
    cin>>n;

    for(int i=1;i<=n;i++)
    {
        cin>>a[i];
        c[i]=a[i];
    }

    sort(a+1,a+n+1);

    gp_hash_table<int, int> id;
    for(int i=1;i<=n;i++)
    {
        if(!id[a[i]]) id[a[i]]=++len;
    }

    int ans=0;
    for(int i=1;i<=n;i++)
    {
        update(id[c[i]]);
        ans+=i-query(id[c[i]]);//i represent the vals that have appeared,query() function gets the number of vals smaller than a[i] that have appeared
    }
    cout<<ans;
    return 0;
}