【算法笔记自学】入门篇（2）——算法初步

 4.1排序

自己写的题解

#include <stdio.h>
#include <stdlib.h>void selectSort(int A[], int n) {for(int i = 0; i < n - 1; i++) { // 修正索引范围int k = i;for(int j = i + 1; j < n; j++) { // 修正索引范围if(A[j] < A[k]) {k = j;}}if (k != i) { // 仅在需要时进行交换int temp = A[i];A[i] = A[k];A[k] = temp;}}
}int main() {int n = 0;scanf("%d", &n);int A[n];for(int i = 0; i < n; i++) {scanf("%d", &A[i]);}selectSort(A, n); // 直接传递数组名for(int i = 0; i < n; i++) {if(i!=n-1){printf("%d ", A[i]);}else{printf("%d", A[i]);}}system("pause"); // 防止运行后自动退出，需头文件stdlib.hreturn 0;
}

 自己写的题解

#include <stdio.h>
#include <stdlib.h>
void insertSort(int A[], int n) {for(int i=1;i<=n-1;i++){int temp=A[i],j=i;while(j>0&&temp<A[j-1]){A[j]=A[j-1];j--;}A[j]=temp;}
}int main() {int n = 0;scanf("%d", &n);int A[n];for(int i = 0; i < n; i++) {scanf("%d", &A[i]);}insertSort(A, n); // 直接传递数组名for(int i = 0; i < n; i++) {if(i!=n-1){printf("%d ", A[i]);}else{printf("%d", A[i]);}}system("pause"); // 防止运行后自动退出，需头文件stdlib.hreturn 0;
}

4.2散列

#include <stdio.h>
#include <stdlib.h>const int maxn = 100010;
int hashTable[maxn] = {0};int main() {int n, x;scanf("%d", &n);for (int i = 0; i < n; i++) {scanf("%d", &x);if (x >= 0 && x < maxn) { // 确保x在合法范围内hashTable[x]++;}}for (int i = 0; i < maxn; i++) { // 修正遍历范围if (hashTable[i] != 0) {printf("%d %d\n", i, hashTable[i]); // 修正输出格式}}system("pause"); // 防止运行后自动退出，需头文件stdlib.hreturn 0;
}

 标答

#include <cstdio>
#include <cstring>const int MAXN = 26;
const int MAXL = 1001;
char str1[MAXL], str2[MAXL];
bool hashTable[MAXN] = {false};int getHashKey(char c) {return c - 'a';
}int main () {scanf("%s%s", str1, str2);int len1 = strlen(str1);int len2 = strlen(str2);for (int i = 0; i < len1; i++) {hashTable[getHashKey(str1[i])] = true;}for (int i = 0; i < len2; i++) {printf("%d", hashTable[getHashKey(str2[i])]);printf(i < len2 - 1 ? " " : "\n");}return 0;
}

#include <cstdio>const int MAXN = 26 * 26 * 26;
const int MAXL = 1001;
char str[MAXL];
int hashTable[MAXN] = {0};int getHashKey(char s[]) {return (s[0] - 'A') * 26 * 26 + (s[1] - 'A') * 26 + (s[2] - 'A');
}int main () {int n, m;scanf("%d", &n);for (int i = 0; i < n; i++) {scanf("%s", str);hashTable[getHashKey(str)]++;}scanf("%d", &m);for (int i = 0; i < m; i++) {scanf("%s", str);printf("%d", hashTable[getHashKey(str)]);printf(i < m - 1 ? " " : "\n");}return 0;
}

 4.3递归

#include <stdio.h>
#include <stdlib.h>void print(int n) {if (n == 0) {printf("讲你妹的故事啊！快点去睡觉！！！\n");} else {printf("从前有座山，山上有座庙\n庙里有一个老和尚和一个小和尚\n睡前老和尚给小和尚讲故事：\n");print(n - 1);printf("然后老和尚和小和尚就睡觉啦\n");}
}int main() {int n;scanf("%d", &n);print(n);system("pause"); // 防止运行后自动退出，需头文件stdlib.hreturn 0;
}

#include <stdio.h>
#include <stdlib.h>int F(int n) {if(n==1)return 1;if(n==2)return 1;if(n>2)return F(n-1)+F(n-2);
}int main() {int n;scanf("%d", &n);printf("%d",F(n));system("pause"); // 防止运行后自动退出，需头文件stdlib.hreturn 0;
}

#include <stdio.h>
#include <stdlib.h>
const int maxn=11;
int n,P[maxn],hashTable[maxn]={false};
void generateP(int index){if(index==n+1){for(int i=1;i<=n;i++){printf("%d",P[i]);printf(i<n ? " " : "\n");}return;}for(int x=1;x<=n;x++){if(hashTable[x]==false){P[index]=x;hashTable[x]=true;generateP(index+1);hashTable[x]=false;}}
}int main() {n=3;scanf("%d",&n);generateP(1);system("pause"); // 防止运行后自动退出，需头文件stdlib.hreturn 0;
}

4.4贪心

#include <cstdio>
#include <algorithm>
using namespace std;
const int MAXN = 100000;    // 箱子数量上限
int a[MAXN];                // 箱子数组
int main() {int n, maxW;            // 箱子数量、载重scanf("%d%d", &n, &maxW);for (int i = 0; i < n; i++) {    // 输入各箱子重量scanf("%d", &a[i]);}sort(a, a + n);                  // 将箱子按重量从小到大排序int num = 0, sum = 0;            // 最大箱子数量、最大累计重量for (int i = 0; i < n; i++) {    // 从小到大遍历箱子if (sum + a[i] <= maxW) {    // 如果加上当前箱子的重量之后没有超过载重num++;                   // 最大箱子数量加1sum += a[i];             // 最大累计重量加上当前箱子的重量} else {                     // 如果超过载重，那么退出循环break;}}printf("%d %d", num, sum);       // 输出最大箱子数量和最大累计重量return 0;
}

#include <cstdio>
#include <algorithm>
using namespace std;
const int MAXN = 10000;
struct Interval {    // 区间结构体定义int l, r;
} interval[MAXN];    // 区间数组bool cmp(Interval a, Interval b) {    // 区间的比较函数if (a.l != b.l) {                 // 如果左端点不同，那么按左端点从大到小return a.l > b.l;} else {                          // 否则，按右端点从小到大return a.r < b.r;}
}int main() {int n;scanf("%d", &n);for (int i = 0; i < n; i++) {         // 输入n个区间的左右端点scanf("%d%d", &interval[i].l, &interval[i].r);}sort(interval, interval + n, cmp);    // 将区间数组进行排序int num = 1, lastL = interval[0].l;   // 排序后的第一个区间总是被选中for (int i = 1; i < n; i++) {         // 遍历剩余的区间if (interval[i].r <= lastL) {     // 如果和上一个选中的区间不相交lastL = interval[i].l;        // 那么选中当前区间num++;                        // 并令选中的区间数量加1}}printf("%d", num);                    // 输出选中的区间数量return 0;
}

4.5二分法

#include <cstdio>
#include <algorithm>
using namespace std;
const int MAXN = 10000;
int binarySearch(int A[],int left,int right,int x)
{int mid;while(left<=right){mid=(left+right)/2;if(A[mid]==x)return mid;else if(A[mid]>x){right=mid-1;}else{left=mid+1;}}return -1;
}
int main() {int n=0,x=0;scanf("%d %d", &n,&x);int a[n];for (int i = 0; i < n; i++) {         // 输入n个区间的左右端点scanf("%d", &a[i]);}printf("%d", binarySearch(a,0,n-1,x));                    // 输出选中的区间数量return 0;
}

#include <cstdio>
#include <algorithm>
using namespace std;
const int MAXN = 10000;
int lower_bound(int A[],int left,int right,int x)
{int mid;while(left<right){mid=(left+right)/2;if(A[mid]>=x){right=mid;}else{left=mid+1;}}return left;
}
int main() {int n=0,x=0;scanf("%d %d", &n,&x);int a[n];for (int i = 0; i < n; i++) {         // 输入n个区间的左右端点scanf("%d", &a[i]);}printf("%d", lower_bound(a,0,n,x));                    // 输出选中的区间数量return 0;
}

#include <cstdio>
#include <algorithm>
using namespace std;
const int MAXN = 10000;
int upper_bound(int A[],int left,int right,int x)
{int mid;while(left<right){mid=(left+right)/2;if(A[mid]>x){right=mid;}else{left=mid+1;}}return left;
}
int main() {int n=0,x=0;scanf("%d %d", &n,&x);int a[n];for (int i = 0; i < n; i++) {         // 输入n个区间的左右端点scanf("%d", &a[i]);}printf("%d", upper_bound(a,0,n,x));                    // 输出选中的区间数量return 0;
}

#include <cstdio>const int MAXN = 100000;
int n, a[MAXN], target;int binarySearch() {int l = 0, r = n;while (l < r) {int mid = l + (r - l) / 2;if (a[mid] >= target) {r = mid;} else {l = mid + 1;}}if (l < n && a[l] == target) {return l;} else {return -1;}
}int main() {scanf("%d%d", &n, &target);for (int i = 0; i < n; i++) {scanf("%d", &a[i]);}printf("%d", binarySearch());return 0;
}

#include <cstdio>const int MAXN = 100000;
int n, a[MAXN], target;int binarySearch() {int l = 0, r = n;while (l < r) {int mid = l + (r - l) / 2;if (a[mid] > target) {r = mid;} else {l = mid + 1;}}if (l >0 && a[l-1] == target) {return l-1;} else {return -1;}
}int main() {scanf("%d%d", &n, &target);for (int i = 0; i < n; i++) {scanf("%d", &a[i]);}printf("%d", binarySearch());return 0;
}

#include <cstdio>
const int MAXN = 100000;
const double eps=1e-6;
double a;
double f(double x){return x*x*x+x*x+x-a;
}
double calSqrt(){double left=-100,right=100,mid;while(right-left>eps){mid=(left+right)/2;if(f(mid)>0){right=mid;}else{left=mid;}}return mid;
}int main() {scanf("%lf",&a);printf("%.2f",calSqrt());return 0;
}

4.6 two pointers

#include <cstdio>const int MAXN = 100000;
int n, k, a[MAXN];int twoSum() {int counter = 0;int i = 0, j = n - 1;while (i < j) {if (a[i] + a[j] == k) {counter++;i++;j--;} else if (a[i] + a[j] < k) {i++;} else {j--;}}return counter;
}int main() {scanf("%d%d", &n, &k);for (int i = 0; i < n; i++) {scanf("%d", &a[i]);}printf("%d", twoSum());return 0;
}

#include <cstdio>const int MAXN = 100000;
int n, a[MAXN];
int m, b[MAXN];
int merged[MAXN * 2];void merge() {int i = 0, j = 0, cnt = 0;while (i < n && j < m) {if (a[i] < b[j]) {merged[cnt++] = a[i++];} else {merged[cnt++] = b[j++];}}while (i < n) {merged[cnt++] = a[i++];}while (j < m) {merged[cnt++] = b[j++];}
}int main() {scanf("%d%d", &n, &m);for (int i = 0; i < n; i++) {scanf("%d", &a[i]);}for (int i = 0; i < m; i++) {scanf("%d", &b[i]);}merge();for (int i = 0; i < n + m; i++) {printf("%d", merged[i]);if (i < n + m - 1) {printf(" ");}}return 0;
}

#include <cstdio>const int MAXN = 1000;
int n, a[MAXN];
int merged[MAXN];void merge(int l1, int r1, int l2, int r2) {int i = l1, j = l2, cnt = 0;while (i <= r1 && j <= r2) {if (a[i] < a[j]) {merged[cnt++] = a[i++];} else {merged[cnt++] = a[j++];}}while (i <= r1) {merged[cnt++] = a[i++];}while (j <= r2) {merged[cnt++] = a[j++];}for (i = 0; i < cnt; i++) {a[l1 + i] = merged[i];}
}void mergeSort(int l, int r) {if (l < r) {int mid = (l + r) / 2;mergeSort(l, mid);mergeSort(mid + 1, r);merge(l, mid, mid + 1, r);}
}int main() {scanf("%d", &n);for (int i = 0; i < n; i++) {scanf("%d", &a[i]);}mergeSort(0, n - 1);for (int i = 0; i < n; i++) {printf("%d", a[i]);if (i < n - 1) {printf(" ");}}return 0;
}

#include <cstdio>const int MAXN = 1000;
int n, a[MAXN];
int mergedNums[MAXN];int partition(int l, int r) {int temp = a[l];while (l < r) {while (l < r && a[r] > temp) {r--;}a[l] = a[r];while (l < r && a[l] <= temp) {l++;}a[r] = a[l];}a[l] = temp;return l;
}void quickSort(int l, int r) {if (l < r) {int pos = partition(l, r);quickSort(l, pos - 1);quickSort(pos + 1, r);}
}int main() {scanf("%d", &n);for (int i = 0; i < n; i++) {scanf("%d", &a[i]);}quickSort(0, n - 1);for (int i = 0; i < n; i++) {printf("%d", a[i]);if (i < n - 1) {printf(" ");}}return 0;
}

4.7其他高效技巧与算法

#include <cstdio>int main() {int n, x, numZero = 0;scanf("%d", &n);long long result = 0;for (int i = 0; i < n; i++) {scanf("%d", &x);if (x == 1) {result += numZero;} else {numZero++;}}printf("%lld", result);return 0;
}

#include <cstdio>
const int MAXN = 100000;
int n,k,a[MAXN];
int mergedNums[MAXN];int partition(int l, int r) {int temp = a[l];while (l < r) {while (l < r && a[r] > temp) {r--;}a[l] = a[r];while (l < r && a[l] <= temp) {l++;}a[r] = a[l];}a[l] = temp;return l;
}void quickSort(int l, int r) {if (l < r) {int pos = partition(l, r);quickSort(l, pos - 1);quickSort(pos + 1, r);}
}
int main() {scanf("%d %d", &n,&k);for(int i=0;i<n;i++){scanf("%d",&a[i]);}quickSort(0, n - 1);for(int i=0;i<n;i++){if(i==k-1)printf("%d",a[i]);}return 0;
}