题意:求一个数列中所有的绝对值差大于2的数,并用后面的数字减前面的数字的加和。
分析:可以用树状数组每次找前面的差值大于2的数,也可以直接每次加前面所有的数字,再减去差值为1的数字。题目最坑爹的是答案也许会爆long long,可以用long double或者使用unsigned long long手动模拟符号位,或者用python
C++代码:
1 #define _CRT_SECURE_NO_DEPRECATE 2 #pragma comment(linker, "/STACK:102400000,102400000") 3 #include<iostream> 4 #include<cstdio> 5 #include<fstream> 6 #include<iomanip> 7 #include<algorithm> 8 #include<cmath> 9 #include<deque> 10 #include<vector> 11 #include<bitset> 12 #include<queue> 13 #include<string> 14 #include<cstring> 15 #include<map> 16 #include<stack> 17 #include<set> 18 #include<functional> 19 #define pii pair<int, ll> 20 #define mod 1000000007 21 #define mp make_pair 22 #define pi acos(-1) 23 #define eps 0.00000001 24 #define mst(a,i) memset(a,i,sizeof(a)) 25 #define all(n) n.begin(),n.end() 26 #define lson(x) ((x<<1)) 27 #define rson(x) ((x<<1)|1) 28 #define inf 0x3f3f3f3f 29 typedef long long ll; 30 typedef unsigned long long ull; 31 using namespace std; 32 const int maxn = 2e5 + 50; 33 map<ll, ll>a; 34 int main() 35 { 36 ios::sync_with_stdio(false); 37 cin.tie(0); cout.tie(0); 38 ll i, j, k, m, n; 39 cin >> n; 40 long double ans = 0; 41 ll sum = 0; 42 for (int i = 1; i <= n; ++i) 43 { 44 cin >> m; 45 sum += m; 46 ans += i*m - sum; 47 ans -= a[m - 1]; 48 ans += a[m + 1]; 49 a[m]++; 50 } 51 cout << setiosflags(ios::fixed) << setprecision(0) << ans << endl; 52 return 0; 53 }
python:
1 n=input() 2 mp = list(map(int,input().split())) 3 sum = 0 4 ans = 0 5 cnt = 0 6 tt = dict() 7 for i in mp: 8 sum+=i 9 cnt=cnt+1 10 ans+=cnt*i-sum 11 if i-1 in tt: 12 ans-=tt[i-1] 13 if i+1 in tt: 14 ans+=tt[i+1] 15 if i not in tt: 16 tt[i]=0 17 tt[i]=tt[i]+1 18 print(ans)
树状数组错误代码(答案爆long long)
1 #define _CRT_SECURE_NO_DEPRECATE 2 #pragma comment(linker, "/STACK:102400000,102400000") 3 #include<iostream> 4 #include<cstdio> 5 #include<fstream> 6 #include<iomanip> 7 #include<algorithm> 8 #include<cmath> 9 #include<deque> 10 #include<vector> 11 #include<bitset> 12 #include<queue> 13 #include<string> 14 #include<cstring> 15 #include<map> 16 #include<stack> 17 #include<set> 18 #include<functional> 19 #define pii pair<int, ll> 20 #define mod 1000000007 21 #define mp make_pair 22 #define pi acos(-1) 23 #define eps 0.00000001 24 #define mst(a,i) memset(a,i,sizeof(a)) 25 #define all(n) n.begin(),n.end() 26 #define lson(x) ((x<<1)) 27 #define rson(x) ((x<<1)|1) 28 #define inf 0x3f3f3f3f 29 typedef long long ll; 30 typedef unsigned long long ull; 31 using namespace std; 32 const int maxn = 2e5 + 50; 33 ll ori[maxn]; 34 int n; 35 ll t[maxn]; 36 37 int Lowbit(int x) 38 { 39 return x&(-x); 40 } 41 void update(ll i, ll x) 42 { 43 while (i <= n) 44 { 45 t[i] += x; 46 i += Lowbit(i); 47 } 48 } 49 ll sum(int x) 50 { 51 ll sum = 0; 52 while (x>0) 53 { 54 sum += t[x]; 55 x -= Lowbit(x); 56 } 57 return sum; 58 } 59 60 map<ll, ll>id; 61 ll orin[maxn]; 62 set<ll>kp; 63 int main() 64 { 65 ios::sync_with_stdio(false); 66 cin.tie(0); cout.tie(0); 67 int i, j, k, m; 68 cin >> n; 69 int cnt = 1; 70 for (int i = 1; i <= n; ++i) 71 { 72 cin >> ori[i]; 73 kp.insert(ori[i]); 74 } 75 for (auto it : kp) 76 { 77 orin[cnt] = it; 78 id[it] = cnt++; 79 } 80 for (int i = 1; i <= n; ++i) 81 { 82 int iid = id[ori[i]]; 83 update(id[ori[i]], 1); 84 } 85 ll fans = 0; 86 for (int i = 1; i <= n; ++i) 87 { 88 auto it = id.lower_bound(ori[i] + 2); 89 if (it != id.end()) 90 { 91 auto ta = sum(n); 92 auto tb = sum(it->second - 1); 93 ll cnt = ta - tb; 94 fans -= cnt*ori[i]; 95 } 96 it = id.lower_bound(ori[i] - 1); 97 if (it != id.begin()) 98 { 99 it--; 100 ll ta = sum(it->second); 101 fans -= ta*ori[i]; 102 } 103 update(id[ori[i]], -1); 104 } 105 mst(t, 0); 106 for (int i = 1; i <= n; ++i) 107 { 108 int iid = id[ori[i]]; 109 update(id[ori[i]], 1); 110 } 111 112 for (int i = n; i>= 1; --i) 113 { 114 auto it = id.lower_bound(ori[i] + 2); 115 if (it != id.end()) 116 { 117 auto ta = sum(n); 118 auto tb = sum(it->second - 1); 119 ll cnt = ta - tb; 120 fans += cnt*ori[i]; 121 } 122 it = id.lower_bound(ori[i] - 1); 123 if (it != id.begin()) 124 { 125 it--; 126 ll ta = sum(it->second); 127 fans += ta*ori[i]; 128 } 129 update(id[ori[i]], -1); 130 } 131 cout << fans << endl; 132 return 0; 133 }