请用C语言实现Once upon a time in the mystical land of Draconis, there existed two powerful arrays: M and N . These arrays were filled with positive integers, each carrying its own magical essence. The inhabitants of the land were intrigued by the concept of similarity between arrays. They discovered that two arrays, M and N , could be considered similar if it was possible to transform a subarray of N into M by adding or subtracting a constant value to each element. You are now summoned to solve a puzzle. Given two arrays, M and N , your task is to determine the number of subarrays of N that are similar to M . Will you be able to unravel this mystical connection? Input The input consists of multiple lines. The first line contains two integers M and N (1≤M≤N≤106) , representing the lengths of arrays M and N respectively. The second line contains M space-separated positive integers m1,m2,…,mM (1≤mi≤109) , representing the magical elements of array M . The third line contains N space-separated positive integers n1,n2,…,nN (1≤ni≤109) , representing the mystical elements of array N . Output Output a single integer, the number of subarrays of N that are similar to M .
时间: 2024-03-21 22:37:46 浏览: 279
为了解决这个问题,我们可以先对两个数组进行排序,然后用双指针法来找到所有相似的子数组。具体实现如下:
```c
#include <stdio.h>
#include <stdlib.h>
#define MAX_N 1000000
int M[MAX_N], N[MAX_N];
int m, n;
int compare(const void *a, const void *b) {
return *(int*)a - *(int*)b;
}
int count_similar() {
int i = 0, j = 0;
int count = 0;
while (i < m && j < n) {
if (M[i] == N[j]) { // 找到相同的元素
int k = j;
while (k < n && N[k] == N[j]) {
k++;
}
count += k - j; // 加上与N[j]相同的元素的个数
i++;
j = k;
} else if (M[i] < N[j]) { // M[i]较小,需要增加N中的元素
i++;
} else { // M[i]较大,需要减少N中的元素
j++;
}
}
return count;
}
int main() {
scanf("%d%d", &m, &n);
for (int i = 0; i < m; i++) {
scanf("%d", &M[i]);
}
for (int i = 0; i < n; i++) {
scanf("%d", &N[i]);
}
qsort(M, m, sizeof(int), compare);
qsort(N, n, sizeof(int), compare);
printf("%d\n", count_similar());
return 0;
}
```
首先读入两个数组的长度和元素,然后对它们进行排序。然后用双指针法找到所有相似的子数组,具体方法如下:
1. 初始化两个指针i和j,分别指向M和N的开头;
2. 如果M[i]等于N[j],说明找到了一个相似的子数组,接着向右移动j,直到N[j]不等于N[j+1];
3. 如果M[i]小于N[j],说明N[j]需要增加,所以向右移动i;
4. 如果M[i]大于N[j],说明N[j]需要减少,所以向右移动j;
5. 重复2~4步,直到i到达M的末尾或j到达N的末尾。
遍历过程中,我们用一个计数器count来累计相似的子数组的个数,每当找到一个相似的子数组时,我们就把与N[j]相同的元素的个数加到count中。最后返回count即可。
时间复杂度为O(MlogM + NlogN),空间复杂度为O(M + N)。
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