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Add Max Sub Array Test
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2 files changed

+100
-90
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2 files changed

+100
-90
lines changed

‎src/divide-and-conquer/maxSubarr.test.ts

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import findMaxSubarr, { bruteForce, random, transformArr } from "./maxSubarr";
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describe("Max Sub Arr test", () => {
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const SIZE = 1000;
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const MAX = 100;
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const N = 100;
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test("using random arr to check if D&C and BF obtain the same result", () => {
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for (let i = 0; i < N; i++) {
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// create arr with len=SIZE and random values in range [0,MAX)
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const arr = Array.from({ length: SIZE }, () => random(MAX));
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const [buy, sell, sum] = bruteForce(arr);
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const [low, high, val] = findMaxSubarr(transformArr(arr));
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expect(val).toBe(sum);
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}
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});
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});

‎src/divide-and-conquer/maxSubarr.ts

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// Returns the day to buy, to sell and the sum
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const bruteForce = (arr: number[]): [number,number,number] => {
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let sum, buy:number, sell:number;
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let max = Number.NEGATIVE_INFINITY;
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for (let i = 0; i < arr.length; i++) {
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for (let j = i + 1; j < arr.length; j++) {
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// buy in day i and sell in day j
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sum = arr[j] - arr[i];
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if (sum > max) {
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buy = i;
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sell = j;
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max = sum;
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}
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}
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}
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return [buy!, sell!, max];
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};
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// Return an new arr, where arr[i] = arr[i] - arr[i-1]
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const transformArr = (arr :number[]) => {
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const ret = arr.map((e, i) => {
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return e - arr[i - 1];
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});
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return ret.slice(1);
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};
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// Returns the indeces and the sum of vals of one max sub arr
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const findMaxSubarr = (arr :number[], low = 0, high = arr.length - 1):[number,number,number] => {
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// one element
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if (low === high) {
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return [low, high, arr[low]];
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}
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const mid = Math.floor((high + low) / 2);
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const [leftLow, leftHigh, leftSum] = findMaxSubarr(arr, low, mid);
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const [rightLow, rightHigh, rightSum] = findMaxSubarr(arr, mid + 1, high);
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const [crossLow, crossHigh, crossSum] = findMaxCrossSubarr(
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arr,
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low,
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mid,
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high
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);
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if (leftSum >= rightSum && leftSum >= crossSum!) {
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return [leftLow, leftHigh, leftSum];
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} else if (rightSum >= leftSum && rightSum >= crossSum!) {
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return [rightLow, rightHigh, rightSum];
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}
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return [crossLow!, crossHigh!, crossSum!];
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};
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// Returns max sum crossing mid
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// where this subarr starts (buy) and where it ends
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const findMaxCrossSubarr = (arr :number[], low: number, mid: number, high: number):[number,number,number] => {
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let leftSum = Number.NEGATIVE_INFINITY;
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let rightSum = Number.NEGATIVE_INFINITY;
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let sum = 0;
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let buy : number, sell : number
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// we need to start in mid because this subarr MUST contain mid
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for (let i = mid; i > low - 1; i--) {
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sum += arr[i];
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if (sum > leftSum) {
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leftSum = sum;
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export const bruteForce = (arr: number[]): [number, number, number] => {
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let sum, buy: number, sell: number;
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let max = Number.NEGATIVE_INFINITY;
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for (let i = 0; i < arr.length; i++) {
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for (let j = i + 1; j < arr.length; j++) {
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// buy in day i and sell in day j
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sum = arr[j] - arr[i];
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if (sum > max) {
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buy = i;
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}
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}
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sum = 0;
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for (let j = mid + 1; j < high + 1; j++) {
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sum += arr[j];
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if (sum > rightSum) {
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rightSum = sum;
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sell = j;
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max = sum;
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}
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}
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return [buy!, sell!, leftSum + rightSum];
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};
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// Returns a random number between [0,max)
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const random = (max: number) => {
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return Math.floor(Math.random() * max);
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};
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// Prints false if any test fails
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// size: len of arr
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// max: val max allowed
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// n: numer of times to test
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const testMaxSubarr = (size: number, max: number, n: number): void => {
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for (let i = 0; i < n; i++) {
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// create arr with len=size and random values in range [0,max)
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const arr = Array.from({ length: size }, () => random(max));
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const [buy, sell, sum] = bruteForce(arr);
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const [low, high, val] = findMaxSubarr(transformArr(arr));
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console.assert(sum === val);
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}
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return [buy!, sell!, max];
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};
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// Return an new arr, where arr[i] = arr[i] - arr[i-1]
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export const transformArr = (arr: number[]) => {
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const ret = arr.map((e, i) => {
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return e - arr[i - 1];
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});
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return ret.slice(1);
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};
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// Returns the indeces and the sum of vals of one max sub arr
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const findMaxSubarr = (
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arr: number[],
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low = 0,
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high = arr.length - 1
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): [number, number, number] => {
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// one element
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if (low === high) {
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return [low, high, arr[low]];
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}
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const mid = Math.floor((high + low) / 2);
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const [leftLow, leftHigh, leftSum] = findMaxSubarr(arr, low, mid);
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const [rightLow, rightHigh, rightSum] = findMaxSubarr(arr, mid + 1, high);
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const [crossLow, crossHigh, crossSum] = findMaxCrossSubarr(
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arr,
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low,
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mid,
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high
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);
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if (leftSum >= rightSum && leftSum >= crossSum!) {
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return [leftLow, leftHigh, leftSum];
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} else if (rightSum >= leftSum && rightSum >= crossSum!) {
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return [rightLow, rightHigh, rightSum];
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}
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return [crossLow!, crossHigh!, crossSum!];
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};
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// Returns max sum crossing mid
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// where this subarr starts (buy) and where it ends
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const findMaxCrossSubarr = (
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arr: number[],
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low: number,
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mid: number,
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high: number
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): [number, number, number] => {
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let leftSum = Number.NEGATIVE_INFINITY;
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let rightSum = Number.NEGATIVE_INFINITY;
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let sum = 0;
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let buy: number, sell: number;
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// we need to start in mid because this subarr MUST contain mid
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for (let i = mid; i > low - 1; i--) {
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sum += arr[i];
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if (sum > leftSum) {
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leftSum = sum;
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buy = i;
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}
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}
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sum = 0;
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for (let j = mid + 1; j < high + 1; j++) {
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sum += arr[j];
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if (sum > rightSum) {
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rightSum = sum;
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sell = j;
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}
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};
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testMaxSubarr(1000,100,100)
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export {}
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}
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return [buy!, sell!, leftSum + rightSum];
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};
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// Returns a random number between [0,max)
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export const random = (max: number) => {
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return Math.floor(Math.random() * max);
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};
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export default findMaxSubarr;

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