小和问题
在一个数组中,每一个数左边比当前数小的数累加起来,叫做这个数组的小和。求一个数组 的小和。
例子:
[1,3,4,2,5]
1左边比1小的数,没有;
3左边比3小的数,1;
4左边比4小的数,1、3;
2左边比2小的数,1;
5左边比5小的数,1、3、4、2;
所以小和为1+1+3+1+1+3+4+2=16
思路:利用归并排序,在每次合并的过程中,比较左边部分的值比右边部分的值,如果比右边部分的值小,那么结果=左边值*右边值以及之后值得总个数【因为排过序】
package section1;
import java.util.Arrays;
public class SmallSum {
public static int smallSum(int[] arr){
if (arr == null || arr.length < 2) return 0;
return mergeSort(arr, 0, arr.length - 1);
}
public static int mergeSort(int[] arr, int L, int R){
if (L == R) return 0;
int mid = (L + R) / 2;
return mergeSort(arr, L, mid) + mergeSort(arr, mid + 1, R) + merge(arr, L, R, mid);
}
public static int merge(int[] arr, int L, int R, int mid){
int[] flag = new int[R - L + 1];
int p1 = L;
int p2 = mid + 1;
int i = 0;
int sum = 0;
while (p1 <= mid && p2 <= R){
sum += arr[p1] < arr[p2] ? arr[p1] * (R - p2 + 1) : 0;
flag[i++] = arr[p1] < arr[p2] ? arr[p1++] : arr[p2++];
}
while (p1 <= mid){
flag[i++] = arr[p1++];
}
while (p2 <= R){
flag[i++] = arr[p2++];
}
for (int j = 0; j < flag.length; j++){
arr[L + j] = flag[j];
}
return sum;
}
// for test
public static int comparator(int[] arr) {
if (arr == null || arr.length < 2) {
return 0;
}
int res = 0;
for (int i = 1; i < arr.length; i++) {
for (int j = 0; j < i; j++) {
res += arr[j] < arr[i] ? arr[j] : 0;
}
}
return res;
}
// for test
public static int[] generateRandomArray(int maxSize, int maxValue) {
int[] arr = new int[(int) ((maxSize + 1) * Math.random())];
for (int i = 0; i < arr.length; i++) {
arr[i] = (int) ((maxValue + 1) * Math.random()) - (int) (maxValue * Math.random());
}
return arr;
}
// for test
public static int[] copyArray(int[] arr) {
if (arr == null) {
return null;
}
int[] res = new int[arr.length];
for (int i = 0; i < arr.length; i++) {
res[i] = arr[i];
}
return res;
}
// for test
public static boolean isEqual(int[] arr1, int[] arr2) {
if ((arr1 == null && arr2 != null) || (arr1 != null && arr2 == null)) {
return false;
}
if (arr1 == null && arr2 == null) {
return true;
}
if (arr1.length != arr2.length) {
return false;
}
for (int i = 0; i < arr1.length; i++) {
if (arr1[i] != arr2[i]) {
return false;
}
}
return true;
}
// for test
public static void printArray(int[] arr) {
if (arr == null) {
return;
}
for (int i = 0; i < arr.length; i++) {
System.out.print(arr[i] + " ");
}
System.out.println();
}
// for test
public static void main(String[] args) {
int testTime = 500000;
int maxSize = 100;
int maxValue = 100;
boolean succeed = true;
for (int i = 0; i < testTime; i++) {
int[] arr1 = generateRandomArray(maxSize, maxValue);
int[] arr2 = copyArray(arr1);
if (smallSum(arr1) != comparator(arr2)) {
succeed = false;
printArray(arr1);
printArray(arr2);
break;
}
}
System.out.println(succeed ? "Nice!" : "Fucking fucked!");
}
}