• 基础算法
  • 整数二分
  • 浮点数二分
  • 归并排序
  • 蒙哥马利快速幂取模算法
  • 前缀和

基础算法

整数二分

bool check(int x)  //检查x是否满足某种性质

int l = 1, r = n, ans = 0;
while(l <= r)
{
  int mid = (l+r)>>1;
  if(check(mid)) { ans = mid; r = mid - 1; }
  else l = mid + 1;
}
printf("%d", ans);

浮点数二分

bool check(double x)  //检查x是否满足某种性质

double l = 1, r = n;
while(l + eps < r)
{
  double mid = (l+r)/2;
  if(check(mid)) r = mid; 
  else l = mid;
}
printf("%lf", l);

//或者写成这样
double l = 1, r = n;
for(int i=1; i<=100; i++)
{
  double mid = (l+r)/2;
  if(check(mid)) r = mid; 
  else l = mid;
}
printf("%lf", l);

归并排序

void merge_sort(int q[], int l, int r)
{
    if (l >= r) return;

    int mid = l + r >> 1;
    merge_sort(q, l, mid);
    merge_sort(q, mid + 1, r);

    int k = 0, i = l, j = mid + 1;
    while(i<=mid && j<=r)
    {
        if(q[i] <= q[j]) tmp[k++] = q[i++];
        else tmp[k++] = q[j++];
    }

    while(i <= mid) tmp[k++] = q[i++];
    while(j <= r) tmp[k++] = q[j++];

    for (i=l, j=0; i<=r; i++) q[i] = tmp[j++];
}

蒙哥马利快速幂取模算法

void merge_sort(int q[], int l, int r)
{
  typedef long long ll;
  
  ll montgomery(ll a, ll b, ll c)
  {
  	ll ans = 1;
  	a = a % c;
  	while(b > 0)
  	{
  		if(b & 1) ans = (ans * a) % c;
  		b = b >> 1;
  		a = a * a % c;
  	}
  
	return ans;
}

前缀和

主要用于求数列区间和的问题，是一种重要的预处理方式

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

//a为原数组，s为前缀和
int a[10] = {}, s[10] = {};

int main()
{
	for(int i=1; i<=5; i++)
	{
		scanf("%d", &a[i]);
		s[i] = s[i-1] + a[i];
	}

	int l = 2, r = 4;
	//求a数组区间[l,r]的和
	int ans = s[r] - s[l-1];
	printf("%d", ans);

	return 0;
}